Randomizing in Software...
Dave Hart
Although not the mathematicians that some are on here, I would like some
to ponder the actual source code and/or logic that goes into the server
and/or client side systems on FIBS. Hence...
1. When using a Random() function, normally, a seed is also used to
help produce a "more random" number. As seen with Intel chips, even
this does not produce randomness, just a larger pattern over time.
2. The smaller/faster the looping construct you use, or the faster the
instructions are given, the more likely a pattern is to develop.
3. My "grudge" if you will, is not that the dice are "random" but that
the dice tend to have a pattern at certain intervals of the game. My
own experience of late has been literally no doubles during the start or
mid game, then a wallop of doubles during the end game and especially
the bear-off. For example: I just finished playing three 5 pointers
over the last two nights. IN ALL 3 MATCHES, my opponent out-doubled me
3:1 on doubles IN THE BEAROFF. In two of the matches, my opponent
received 3 doubles in a row during the bearoff, on 3 of the games in
each match. Alas... why I rant about the code as opposed to the number
generator itself.
4. Although I cannot conceive that there is less code executing with
less checkers in play, I can perceive that due to the moves being
executed faster (especially with auto bear-off) requests to the number
generator are sent at less time intervals than in the beginning of the
game, thus possibly leading to seeing repeat #'s and/or doubles more
often, as the generator is being hit faster. With only 36 possible
rolls, the faster I can bang at the # generator with source code, the
more likely I am to get a repeat #.
Adding to this, if the # generator itself is not that great, then the
chance increases.
5. Maybe it's just me, but I have yet to see the same # of doubles
occur in the bearoffs when I play in person than when I play on FIBS.
And with those who know how to
use their lipless cups with a "soft" or "hard" roll from the cup, ya'd
think I'd see more doubles, etc. from the in-person folks than on a
machine! <g>
6. Maybe an explanation on how the number generator works would help?
Is it a constantly running generator, that is "peeked" at while it's
"spinning" or does it generate the number on request? There is a big
difference between those two...
Anyways, food for thought...
--
Dave Hart
dh...@niteshift.com
Team Night Shift: http://www.niteshift.com
Stephen Turner
Dave Hart wrote:
>
> 2. The smaller/faster the looping construct you use, or the faster the
> instructions are given, the more likely a pattern is to develop.
>
I'm afraid you don't know much about random number generation. I don't know
what FIBS uses (marvin very sensibly hasn't published it) but the normal
procedure is to start the generator off at a random point (often seeded from
the clock) and then generate other numbers as required. So it doesn't matter
how fast you ask for them.
--
Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
Stochastic Networks Group, Statistical Laboratory,
16 Mill Lane, Cambridge, CB2 1SB, England Tel.: +44 1223 337955
"Collection of rent is subject to Compulsive Competitive Tendering" Cam. City
Sake Blok
Stephen Turner (sr...@cam.ac.uk) wrote:
: Dave Hart wrote:
: >
: > 2. The smaller/faster the looping construct you use, or the faster the
: > instructions are given, the more likely a pattern is to develop.
: >
: I'm afraid you don't know much about random number generation. I don't know
: what FIBS uses (marvin very sensibly hasn't published it) but the normal
: procedure is to start the generator off at a random point (often seeded from
: the clock) and then generate other numbers as required. So it doesn't matter
: how fast you ask for them.
For the volume of random-numbers needed on Fibs, even a straight loop through
the 36 possible rolls would be like random for an individual player (taken
that every roll in every game is generated by the same loop) ;-)
Sake
--
+------------------- There is a purpose to time: --------------------+
| Sake Blok (sa...@euronet.nl) EuroNet Internet BV |
| http://www.euronet.nl/~sake Herengracht 208-214 |
| phone: +31 (0)20 625 6161 1016 BS Amsterdam |
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+---------- It prevents everything from happening at once.-----------+
Stephen Turner
Sake Blok wrote:
>
> For the volume of random-numbers needed on Fibs, even a straight loop through
> the 36 possible rolls would be like random for an individual player (taken
> that every roll in every game is generated by the same loop) ;-)
>
Possibly, except when greedy or automove is on. Or in the first game after a
crash, I suppose.
Richard McIntosh
I must have had too much coffee this morning. I usually just
delete threads related to random dice. Herewith a modest proposal.
Stephen Turner wrote:
[... elision ...]
> I don't know
> what FIBS uses (marvin very sensibly hasn't published it) but the normal
> procedure is to start the generator off at a random point (often seeded from
> the clock) and then generate other numbers as required.
I wonder how sensible it is, given the number of times we've all
been through these lines of discussion. If Andreas published the
random number generator algorithm, there would be two reasonable
outcomes:
1. People who know something about random number generation would
confirm that he is doing (a version of) the right thing, and
hope to cut down on the traffic in these sorts of threads (there
is, unfortunately, no guarantee, but keep reading).
2. People who know something about random number generation would
suggest improvements, which Andreas would be under no obligation
to incorporate into his code, but at least the discussion would
be informed by the facts.
A general statement of the algorithm could then be published in the
FAQ, to which we could gently guide newbies who wanted to know how
it works.
Either of those alternatives seems better to me than this constant
traffic in statistical (and lesser) musings and guesses. I'm not
suggesting that Andreas publish any code -- it's his baby -- but is
the algorithm for the generator too much to ask to put a damper on
these discussions?
I for one am very tired of them. Yes, I know, I can (and usually
do) delete these threads whenever they appear, but wouldn't real
information be a better solution? I don't see any benefit to
keeping the algorithm secret, and a lot of benefit to educating
everyone on how good random number generation works by providing
a solid example of good practice.
I personally believe that Andreas know what he's doing. I wish
everyone else did.
My $.02, obviously; your mileage will certainly vary.
Regards,
Richard (moderately competent in statistics) McIntosh
Robert-Jan Veldhuizen
On 20-maa-97 11:55:48, Stephen Turner wrote:
[stuff about random number generators snipped]
ST> I don't
ST> know what FIBS uses (marvin very sensibly hasn't published it)
If FIBS's random number generator can't be manipulated, then I see no sensible
reason why marvin shouldn't publish this information. It could prevent lots of
articles in this newsgroup about FIBS's /supposed/ method for this from being
written and posted.
Like this one ;)
--
<tsb>Zorba
Patti Beadles
In article <466.7019...@xs4all.nl>,
Robert-Jan Veldhuizen <veld...@xs4all.nl> wrote:
>If FIBS's random number generator can't be manipulated, then I see no sensible
>reason why marvin shouldn't publish this information. It could prevent lots of
>articles in this newsgroup about FIBS's /supposed/ method for this from being
>written and posted.
No it wouldn't. 99% of the population wouldn't understand it anyway,
and they'd still be skeptical. Worse, they'd believe that the 1% who
do understand the algorithm have some method of controlling it.
At pseudo-random intervals, some nutcase would come out of the
woodwork pointing out some allegedly well-known flaw in the algorithm,
like it repeats every 13 billion rolls, and we'd have another round of
skepticism.
We'll always have dice-skepticism, it's just a matter of choosing your
flavor.
-Patti
--
Patti Beadles | Knowing how to play well doesn't
pat...@netcom.com/pat...@gammon.com | win-- you must actually do it.
http://www.gammon.com/ |
or just yell, "Hey, Patti!" | No longer pa...@velo.com
Stephen Turner
Richard McIntosh wrote:
>
> Stephen Turner wrote:
>
> > I don't know
> > what FIBS uses (marvin very sensibly hasn't published it)
>
> been through these lines of discussion. If Andreas published the
> random number generator algorithm, there would be two reasonable
> outcomes:
>
> 1. People who know something about random number generation would
> confirm that he is doing (a version of) the right thing, and
> hope to cut down on the traffic in these sorts of threads (there
> is, unfortunately, no guarantee, but keep reading).
>
> 2. People who know something about random number generation would
> suggest improvements, which Andreas would be under no obligation
> to incorporate into his code, but at least the discussion would
> be informed by the facts.
>
> A general statement of the algorithm could then be published in the
> FAQ, to which we could gently guide newbies who wanted to know how
> it works.
>
I'm more pessimistic than you. Two reasonable outcomes, but four very
likely unreasonable ones too:
3) The people who post "unfair dice" theories without reading past stuff
still would.
4) People who didn't understand the program or formula wouldn't try to, but
would continue with their conspiracy theories.
5) Other people would spot (false) loopholes in the algorithm, and post
"evidence" that it is non-random in some way.
6) Lots of people would badger marvin with suggestions for supposed
improvement.
When was the last time you heard a competent mathematician or a good player
who thought that FIBS dice were non-random? And how many of the doubters
do you think would be persuaded even if the formula were published?
--
Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, England
"This store will remain open during modernisation. We apologise
for any inconvenience this may cause" Topshop, Cambridge
MJR
I think marvin is in a no-win situation here....if people dont
trust his word when he says the dice aren't fixed, why then, if he
were to post the random number generator source, would people
trust that the source he posted was REALLY what FIBS uses. since
there's nothing he can do erase skepticism, why should marvin get
involved at all?
Robert-Jan Veldhuizen
On 21-maa-97 03:38:38, Patti Beadles wrote:
PB> Robert-Jan Veldhuizen <veld...@xs4all.nl> wrote:
>>If FIBS's random number generator can't be manipulated, then I see no
>>sensible reason why marvin shouldn't publish this information. It could
>>prevent lots of articles in this newsgroup about FIBS's /supposed/ method
>>for this from being written and posted.
PB> No it wouldn't. 99% of the population wouldn't understand it anyway,
I think you greatly underestimate FIBS's users.
I don't really understand Backgammon, for instance, but I'm still interested in
what, let's say, Kit Woolsey has to say about it. I would believe most of it,
even if I don't (yet) underastand it fully.
PB> and they'd still be skeptical. Worse, they'd believe that the 1% who
PB> do understand the algorithm have some method of controlling it.
Why think so negative about 99% of FIBS's users ?
PB> At pseudo-random intervals, some nutcase would come out of the
PB> woodwork pointing out some allegedly well-known flaw in the algorithm,
PB> like it repeats every 13 billion rolls, and we'd have another round of
PB> skepticism.
Maybe. But at least we would then have some facts to argue with, instead of all
the vague idea's we have to come up with now.
PB> We'll always have dice-skepticism, it's just a matter of choosing your
PB> flavor.
Bringing it out in the open and clear could at least clarify lots of things.
Without any information on FIBS's dice, it's almost *obligatory* to be
skeptical.
--
<tsb>Zorba
Robert-Jan Veldhuizen
On 21-maa-97 13:35:02, Stephen Turner wrote:
[why doesn't marvin tell us something about FIBS RNG]
ST> I'm more pessimistic than you. Two reasonable outcomes, but four very
ST> likely unreasonable ones too:
ST> 3) The people who post "unfair dice" theories without reading past stuff
ST> still would.
That's no argument *against* publishing it.
ST> 4) People who didn't understand the program or formula wouldn't try to,
ST> but
ST> would continue with their conspiracy theories.
Do you mean that keeping something "secret" is the way to fight "conspiracy
theories" ?
ST> 5) Other people would spot (false) loopholes in the algorithm, and post
ST> "evidence" that it is non-random in some way.
If it was true, that would only be good. If it was false, we would now have
arguments with which to convince those persons, instead of (as happens so often
now) saying "You're paranoid" or something.
ST> 6) Lots of people would badger marvin with suggestions for supposed
ST> improvement.
Still better than badging him with questioning the RNG FIBS uses.
ST> When was the last time you heard a competent mathematician or a good
ST> player who thought that FIBS dice were non-random?
Another argument, it seems, to *inform* people instead of keeping things secret.
ST> And how many of the
ST> doubters do you think would be persuaded even if the formula were
ST> published?
We can only know if marvin does exactly that.
--
<tsb>Zorba
Patti Beadles
In article <1522.7020...@xs4all.nl>,
> PB> No it wouldn't. 99% of the population wouldn't understand it anyway,
>I think you greatly underestimate FIBS's users.
I think you greatly underestimate the subtleties of random number
generation.
> PB> woodwork pointing out some allegedly well-known flaw in the algorithm,
> PB> like it repeats every 13 billion rolls, and we'd have another round of
> PB> skepticism.
>Maybe. But at least we would then have some facts to argue with, instead of all
>the vague idea's we have to come up with now.
Hey, the tools exist to analyze the dice right now. Check out the
commands "dicetest" and "matrix" for good information about the dice.
There's plenty of information there for analysis, but nobody who
complains ever bothers to look at it... it's far too easy to come up
with vague and unsubstantiated generalizations, and far too much work
to look at the data and find out that you're wrong.
Robert P. Smith
In article <333280...@cam.ac.uk>, Stephen Turner <sr...@cam.ac.uk> wrote:
>
> When was the last time you heard a competent mathematician or a good player
> who thought that FIBS dice were non-random?
>
Let me offer my opinion. I am not here to trumpet academic credentials,
but I believe that I do understand probability and statistics enough to
make reasonable statements. I also am a competent (but not expert)
backgammon player (FIBS rating of ~1670).
For the past week or so I have been collecting data to see if FIBS produces
outcomes that are consistent with expected random behavior. Specifically,
I have been observing whether getting men off the bar is more difficult
than one would expect. Every time there were men on the bar I observed how
many possible landing spaces there were (open, blots or held by friendly
troops) and whether or not the roll succeeded in landing at least one man
off the bar. (I did not concern myself with the issue of more than one man
on the bar.)
Probability theory suggests that if there is one landing pace, there will
be a successful roll 11/36 of the time; 2 spaces 20/36; 3 spaces 27/36; 4
spaces 32/36; 5 spaces 35/36. I observed the following data:
landing Total Expected
spaces rolls Successes Failures successes Variance
1 104 21 85 32.39 22.49
2 97 46 51 53.89 23.95
3 108 83 25 81 20.25
4 63 53 10 56 6.22
5 57 56 1 55.42 1.54
As you can see from the data there were fewer successes than expected for
the instances when there were 1, 2 and 4 landing spaces, and basically
matching the expectation if there were 3 or 5 landing spaces. The question
then is whether the difference between the observation and the expectation
is statistically significant.
I will aggregate the data together: total number of successes was 259, the
expected value was 278.69. The variance of this number (the sum of the
variances of each case) is 74.45. By probability theory and by the central
limit theorem, we would expect the statistic
(T-E[T])
-------------
(Var(T))^0.5
to have an approximately normal distribution of mean 0 and variance 1. The
value of this statistic is -2.28. Looking up in a standard normal
probability table there is a probability of 1.1% that this statistic will
have a value of -2.28 or smaller if the probability distribution is
correct. The difference between observation and theory is therefore
statistically significant at the 0.011 level.
There are (at least) three possible hypotheses that can explain this result:
A) FIBS dice are non-random.
B) I happened to observe a non-typical series of rolls, and additional
data will cause the observed data to lose their statistical significance.
C) I was not diligent in my observations, and I incorrectly recorded
actual behavior.
I do not entirely discount hypothesis (C), but I was trying to be fair and
complete in my collection of data. (I was also trying to win the games, so
I may have gotten caught up in the heat of battle.) I did my best.
Hypothesis (B) is also plausible, and additional data will clarify.
But the hypothesis that I believe is (A). I think that FIBS dice are
non-random in the instance of bringing men off the bar.
I would be happy to see someone write an observation bot that observes
games and records similar data. I know programmers are not uncommon in the
usenet community, I offer this as a challenge. A bot would be able to
record a greater number of data and not be as subject to the criticism that
data were recorded incorrectly. This would go futther to discount
hypotheses (B) and (C) than I can do by hand.
In any event, it seems to me not impossible that FIBS, for whatever reason,
may have dice that are non-random for some situations. I would be happy if
someone could correct me, but that is what my data say to me.
Respectfully submitted,
Rob Smith
Robert P. Smith
In article <smith-ya02408000...@news.u.washington.edu>,
sm...@ieng.washington.edu (Robert P. Smith) wrote:
>
> I think that FIBS dice are
> non-random in the instance of bringing men off the bar.
>
> Respectfully submitted,
>
> Rob Smith
If anyone is having trouble replying to my posted e-mail address please
reply to me at robs...@u.washington.edu. The address in the header is
supposed to work, but seems not to be working correctly today.
Rob
Greycat Sharpclaw
There is an allegation that sm...@ieng.washington.edu (Robert P.
Smith) wrote:
snip...
>In article <333280...@cam.ac.uk>, Stephen Turner <sr...@cam.ac.uk> wrote:
>For the past week or so I have been collecting data to see if FIBS produces
>outcomes that are consistent with expected random behavior. Specifically,
>I have been observing whether getting men off the bar is more difficult
>than one would expect. Every time there were men on the bar I observed how
>many possible landing spaces there were (open, blots or held by friendly
>troops) and whether or not the roll succeeded in landing at least one man
>off the bar. (I did not concern myself with the issue of more than one man
>on the bar.)
snip...
>I observed the following data:
>landing Total Expected
>spaces rolls Successes Failures successes Variance
> 1 104 21 85 32.39 22.49
> 2 97 46 51 53.89 23.95
> 3 108 83 25 81 20.25
> 4 63 53 10 56 6.22
> 5 57 56 1 55.42 1.54
NOTE: case 1 has an addition error (104 does not equal 21+85). Assume
21, 85 correct, and roll count is 106. This fits the "expected
successes"
I will requote the raw data with altered statistical analysis:
landing Total Expected std. dev in
spaces rolls Successes successes expectation "zeta"
1 106 21 32.39 4.123 -2.76
2 97 46 53.89 4.943 -1.60
3 108 83 81 4.404 +0.45
4 63 53 56 2.900 -1.03
5 57 56 55.42 1.000 +0.58
This is an interesting result, with a zeta of -2.76 in one case. But
as an isolated experiment, it is inconclusive.
>As you can see from the data there were fewer successes than expected for
>the instances when there were 1, 2 and 4 landing spaces, and basically
>matching the expectation if there were 3 or 5 landing spaces. The question
>then is whether the difference between the observation and the expectation
>is statistically significant.
>I will aggregate the data together: total number of successes was 259, the
>expected value was 278.69. The variance of this number (the sum of the
>variances of each case) is 74.45. By probability theory and by the central
>limit theorem, we would expect the statistic
> (T-E[T])
>-------------
>(Var(T))^0.5
>to have an approximately normal distribution of mean 0 and variance 1. The
>value of this statistic is -2.28. Looking up in a standard normal
>probability table there is a probability of 1.1% that this statistic will
>have a value of -2.28 or smaller if the probability distribution is
>correct. The difference between observation and theory is therefore
>statistically significant at the 0.011 level.
Again suggestive, but not conclusive in isolation.
>There are (at least) three possible hypotheses that can explain this result:
>A) FIBS dice are non-random.
>B) I happened to observe a non-typical series of rolls, and additional
>data will cause the observed data to lose their statistical significance.
>C) I was not diligent in my observations, and I incorrectly recorded
>actual behavior.
>I do not entirely discount hypothesis (C), but I was trying to be fair and
>complete in my collection of data. (I was also trying to win the games, so
>I may have gotten caught up in the heat of battle.) I did my best.
>Hypothesis (B) is also plausible, and additional data will clarify.
>But the hypothesis that I believe is (A). I think that FIBS dice are
>non-random in the instance of bringing men off the bar.
Without offense to you, I will not trust manual counting except when
the counter is not distracted. I think (C) has a high likelyhood, due
to human nature... it is difficult to _reliably_ gather data when even
mildly distracted.
>I would be happy to see someone write an observation bot that observes
>games and records similar data.
This is an excellent proposal.
Greycat
Gre...@tribeca.ios.com
Does anyone have any spare tunafish??
Steve Mellen
It is so implausible to me that someone would program the random number
generator on a backgammon server to scan the board before each roll to see
if a player has men on the bar, determine which points are open, and
reduce the chance of rolling those numbers by some small percentage, that
it really blows my mind that people waste time on exercises like this.
In article <smith-ya02408000...@news.u.washington.edu>,
sm...@ieng.washington.edu (Robert P. Smith) wrote:
> In article <333280...@cam.ac.uk>, Stephen Turner <sr...@cam.ac.uk> wrote:
>
> >
> > When was the last time you heard a competent mathematician or a good player
> > who thought that FIBS dice were non-random?
> >
>
> Let me offer my opinion. I am not here to trumpet academic credentials,
> but I believe that I do understand probability and statistics enough to
> make reasonable statements. I also am a competent (but not expert)
> backgammon player (FIBS rating of ~1670).
>
> For the past week or so I have been collecting data to see if FIBS produces
> outcomes that are consistent with expected random behavior. Specifically,
> I have been observing whether getting men off the bar is more difficult
> than one would expect. Every time there were men on the bar I observed how
> many possible landing spaces there were (open, blots or held by friendly
> troops) and whether or not the roll succeeded in landing at least one man
> off the bar. (I did not concern myself with the issue of more than one man
> on the bar.)
>
> Probability theory suggests that if there is one landing pace, there will
> be a successful roll 11/36 of the time; 2 spaces 20/36; 3 spaces 27/36; 4
> spaces 32/36; 5 spaces 35/36. I observed the following data:
>
> landing Total Expected
> spaces rolls Successes Failures successes Variance
> 1 104 21 85 32.39 22.49
> 2 97 46 51 53.89 23.95
> 3 108 83 25 81 20.25
> 4 63 53 10 56 6.22
> 5 57 56 1 55.42 1.54
>
> As you can see from the data there were fewer successes than expected for
> the instances when there were 1, 2 and 4 landing spaces, and basically
> matching the expectation if there were 3 or 5 landing spaces. The question
> then is whether the difference between the observation and the expectation
> is statistically significant.
>
> I will aggregate the data together: total number of successes was 259, the
> expected value was 278.69. The variance of this number (the sum of the
> variances of each case) is 74.45. By probability theory and by the central
> limit theorem, we would expect the statistic
>
> (T-E[T])
> -------------
> (Var(T))^0.5
>
> to have an approximately normal distribution of mean 0 and variance 1. The
> value of this statistic is -2.28. Looking up in a standard normal
> probability table there is a probability of 1.1% that this statistic will
> have a value of -2.28 or smaller if the probability distribution is
> correct. The difference between observation and theory is therefore
> statistically significant at the 0.011 level.
>
> There are (at least) three possible hypotheses that can explain this result:
>
> A) FIBS dice are non-random.
> B) I happened to observe a non-typical series of rolls, and additional
> data will cause the observed data to lose their statistical significance.
> C) I was not diligent in my observations, and I incorrectly recorded
> actual behavior.
>
> I do not entirely discount hypothesis (C), but I was trying to be fair and
> complete in my collection of data. (I was also trying to win the games, so
> I may have gotten caught up in the heat of battle.) I did my best.
>
> Hypothesis (B) is also plausible, and additional data will clarify.
>
> But the hypothesis that I believe is (A). I think that FIBS dice are
> non-random in the instance of bringing men off the bar.
>
> I would be happy to see someone write an observation bot that observes
Kit Woolsey
Robert P. Smith (sm...@ieng.washington.edu) wrote:
: In article <333280...@cam.ac.uk>, Stephen Turner <sr...@cam.ac.uk> wrote:
<A lot of math which demonstrates that, given the assumption that the
dice are random, the probability of being as far from the norm as the
collected data is is about 1.1%. I don't claim to follow the math, but I
will assume for the sake of argument that it is correct.>
: There are (at least) three possible hypotheses that can explain this result:
: A) FIBS dice are non-random.
: B) I happened to observe a non-typical series of rolls, and additional
: data will cause the observed data to lose their statistical significance.
: C) I was not diligent in my observations, and I incorrectly recorded
: actual behavior.
: I do not entirely discount hypothesis (C), but I was trying to be fair and
: complete in my collection of data. (I was also trying to win the games, so
: I may have gotten caught up in the heat of battle.) I did my best.
: Hypothesis (B) is also plausible, and additional data will clarify.
: But the hypothesis that I believe is (A). I think that FIBS dice are
: non-random in the instance of bringing men off the bar.
Hmmm. So it appears we have to choose between the following hypotheses:
1) The data collection wasn't accurate, which certainly seems possible
given the way the data was collected.
2) Old lady luck, which will cause this offbeat result a little over 1%
of the time.
3) Marvin, that evil man, intentionally subverts his own product, for no
apparent reason whatsoever. Considering that Marvin wrote FIBS not for
profit but for his own ego satisfaction and to supply a working
backgammon server for the internet, I guess we can estimate this
probability at .0001%.
4) The random number generator has suddenly taken a life of its own,
learned to examine backgammon positions, and spit out extra flunking
numbers when a player is on the bar. Tough to judge -- I'd put that
probability at, say, .000001%.
So, now we have to make a value judgment on what the real cause is. My
money is on 1) or 2). Anybody else?
: I would be happy to see someone write an observation bot that observes
: games and records similar data. I know programmers are not uncommon in the
: usenet community, I offer this as a challenge. A bot would be able to
: record a greater number of data and not be as subject to the criticism that
: data were recorded incorrectly. This would go futther to discount
: hypotheses (B) and (C) than I can do by hand.
Guess what -- it's already been done. A couple of years ago Mark Damish
wrote his Big_Brother program which does exactly that -- automatically
observes and records backgammon matches played on FIBS. These matches
are stored on Patti's ftp site, I believe. So, all you have to do is dig
them up, play through a bunch of them, and record the results when a
player is on the bar. Not a difficult project. And since most of the
matches are between high-rated players it could be instructive as well.
Btw, my money says that when you have done this for, say, 5000 samples,
the results will be within two standard deviations of the norm. Anybody
willing to bet otherwise?
Kit
Chris Wilson
In article <raccoon.859459803@shellx>, rac...@best.com (Daniel Murphy) wrote:
>You can't possibly expect anyone to take seriously any conclusions you
>choose to draw from your tiny sample of 429 rolls ... but your idea for
>program to observe and record such off-the-bar rolls seems like a good
>way to collect a meaningfully larger sample.
I'm far from a stastician, but I seem to remember that a sample size of
greater than 400 is plenty big to draw conclusions from. National poll
sample sizes range from 400-3000 I believe. Course I could be wrong.
Chris
--
------------------------------------------------------------------------
| Chris Wilson "Give me old Buffett music or give me the BeeGees" |
|------------------------------------------------------------------------|
| http://www.iei.net/~wilson/work/biz.html for web design |
| http://www.iei.net/~wilson/boots.html for trading |
|------------------------------------------------------------------------|
| If you're bored enough to read this, you're bored enough to visit my |
| home page at <http://www.iei.net/~wilson> |
------------------------------------------------------------------------
Daniel Murphy
You can't possibly expect anyone to take seriously any conclusions you
choose to draw from your tiny sample of 429 rolls ... but your idea for
program to observe and record such off-the-bar rolls seems like a good
way to collect a meaningfully larger sample.
[nothing but smith follows ...]
>There are (at least) three possible hypotheses that can explain this result:
>A) FIBS dice are non-random.
>B) I happened to observe a non-typical series of rolls, and additional
>data will cause the observed data to lose their statistical significance.
>C) I was not diligent in my observations, and I incorrectly recorded
>actual behavior.
>I do not entirely discount hypothesis (C), but I was trying to be fair and
>complete in my collection of data. (I was also trying to win the games, so
>I may have gotten caught up in the heat of battle.) I did my best.
>Hypothesis (B) is also plausible, and additional data will clarify.
>But the hypothesis that I believe is (A). I think that FIBS dice are
>non-random in the instance of bringing men off the bar.
>I would be happy to see someone write an observation bot that observes
>games and records similar data. I know programmers are not uncommon in the
>usenet community, I offer this as a challenge. A bot would be able to
>record a greater number of data and not be as subject to the criticism that
>data were recorded incorrectly. This would go futther to discount
>hypotheses (B) and (C) than I can do by hand.
>In any event, it seems to me not impossible that FIBS, for whatever reason,
>may have dice that are non-random for some situations. I would be happy if
>someone could correct me, but that is what my data say to me.
>Respectfully submitted,
>Rob Smith
--
_______________________________________________________
Daniel Murphy | San Francisco | rac...@cityraccoon.com
Monthly tourneys in San Mateo: See www.gammon.com/bgbb/ for details
and some excellently annotated matches. On-line: telnet fibs.com 4321.
Patti Beadles
In article <smith-ya02408000...@news.u.washington.edu>,
Robert P. Smith <sm...@ieng.washington.edu> wrote:
>A) FIBS dice are non-random.
>B) I happened to observe a non-typical series of rolls, and additional
>data will cause the observed data to lose their statistical significance.
>C) I was not diligent in my observations, and I incorrectly recorded
>actual behavior.
First, let me commend you on actually producing actual numbers rather
than just random unsubstantiated rantings. This is a far cry better
than the usual FIBS dice debates.
There is a large database of saved matches on http://www.gammon.com/
... look for the Big Brother matches. It should be a relatively
simple programming exercise to walk through all of the games, find
positions where someone is entering from the bar, count the valid
rolls, and keep track of whether or not he entered.
I suspect that B and C are about equally correct.
-Patti
--
Patti Beadles |
pat...@netcom.com/pat...@gammon.com |
http://www.gammon.com/ | "I trust you. It's just
or just yell, "Hey, Patti!" | that I'm scared of you."
Daniel Murphy
wil...@iei.net (Chris Wilson) writes:
>In article <raccoon.859459803@shellx>, rac...@best.com (Daniel Murphy) wrote:
>>You can't possibly expect anyone to take seriously any conclusions you
>>choose to draw from your tiny sample of 429 rolls ... but your idea for
>>program to observe and record such off-the-bar rolls seems like a good
>>way to collect a meaningfully larger sample.
>I'm far from a stastician, but I seem to remember that a sample size of
>greater than 400 is plenty big to draw conclusions from. National poll
>sample sizes range from 400-3000 I believe. Course I could be wrong.
Chris, we're not talking here about opinion polls or the accuracy of
surveys using representative sampling. We're talking about a random
number generator which simulates rolling two dice and the 36 possible ways
they can be thrown. The statistics provided were further subdivided into
6 different categories, depending on how many home board points were open
when the dice were rolled -- so the samples provided were actually much
smaller than 429 -- approximately 50 to 100 instances of each case.
Rolling dice 50 times and noting how often a 1 in 36 possibility occurs,
or rolling dice 100 times and seeing how often a 1 in 3 or 20 in 36
possibility occurs proves nothing -- unless the results are so far off as
to make it impossible for the dice to be fair, which wasn't the case with
the statistics provided.
So yes, the sampling provided was so small that it would be absurd to
think it proves anything at all about the random number generator.
Robert-Jan Veldhuizen
Maybe I've missed something, but I've never seen any "claim" from anyone from
FIBS stating that the dice are random. Nothing on FIBS, nothing in the FAQ or
elsewhere on the WWW, nor anything in this newsgroup.
I would trust any statement, I even asked for it once, but didn't get any
reply...
I wonder what most BGplayers would prefer when playing in a club against someone
they don't know: 1. The opponent just calls his rolls, saying for example "five
six", without any way to check if he really rolls (fairly) random dice, or 2.
The opponent shows you his dice and how he rolls them.
Well good luck to all anyway :)
Cheers,
--
<tsb>Zorba
Robert-Jan Veldhuizen
On 24-maa-97 11:06:30, Patti Beadles wrote:
PB> In article <1522.7020...@xs4all.nl>,
>> PB> No it wouldn't. 99% of the population wouldn't understand it anyway,
>>I think you greatly underestimate FIBS's users.
PB> I think you greatly underestimate the subtleties of random number
PB> generation.
Thank you for proving my point and putting me in that 99% of yours...
>> PB> woodwork pointing out some allegedly well-known flaw in the algorithm,
>> PB> like it repeats every 13 billion rolls, and we'd have another round of
>> PB> skepticism.
>>Maybe. But at least we would then have some facts to argue with, instead of
>>all the vague idea's we have to come up with now.
PB> Hey, the tools exist to analyze the dice right now. Check out the
PB> commands "dicetest" and "matrix" for good information about the dice.
Done that, nothing about the RNG FIBS uses.
PB> There's plenty of information there for analysis, but nobody who
PB> complains ever bothers to look at it... it's far too easy to come up
PB> with vague and unsubstantiated generalizations, and far too much work
PB> to look at the data and find out that you're wrong.
*sigh* Let me refresh your memory: I analyzed 5 million rolls and the amount of
doubles FIBS throwed was far too high; chances of that many doubles or more
occuring are less than 0.1%. Posted not too long ago in rgb. Confirmed by
Stephen Turner and mailed to you and marvin.
I never got any reply on that...so, I don't know what you mean with your remarks
above.
Cheers,
--
<tsb>Zorba
Chuck Bower
This (LONG) post has three parts: A) soapbox (mild scolding of some
r.g.b. posters), B) rework of Rob Smith's original analysis, and
C) analogy to modern scientific practice and proposal for further study.
A) SOAPBOX stuff (IHMO, as always):
I find Rob's post sincere, diligent, and interesting. Here is an
attempt to question the randomness of FIBS dice, and it's done with
intelligence, rigor, and (apparently) without emotional involvement.
This is what randomness "believers" have been crying for forever.
I think it should be addressed with AT LEAST as much sincerity,
diligence, and emotionlessness. Anything less places posters back
in the stone age (REGARDLESS of which side of the debate you are on).
I have a lot of respect for the posters whose replies I have read.
However, there are three arguments in particular that I've seen, and don't
like. Paraphrased: 1) "this proposal is so preposterous and FIBS so
beyond reproach that it isn't worth considering". With this general
attitude, we'd ALL still be in the above mentioned stoneage. 2) "You
can't believe any result which is based on small number of trials."
I believe this statement shows a lack of understanding of statistics.
More will be said about this in part C below, but consider the following:
Suppose Rob's study showed 5 entries total (say, one for each of the five
inner board conditions) out of the same 431 trials. Would you still say
that 431 wasn't a large enough sample? I would certainly ask for further
study (as I am doing here) but not because the sample size was too small!
3) "This study is meaningless." Maybe just a poor choice of words, but not
at all an objective, scientific statement!
I am NOT an expert on statistics. You don't need to be to apply
them (intelligently) to backgammon. I've only taken one elementary prob.
and stat. class in my life. I have learned some by reading, thinking, and
discussing with those more versed in the subject than I. Thus I certainly
could be way off in what I have to say. Frankly, I'd like to see posts
from experts in the field. I believe that Fredrik Dahl, Bob Koca, and
Steven Turner may be experts. (How could anyone with "University of
Cambridge Statistics Laboratory" in his mail headers/trailers NOT be able
to do this stuff with his left hand tied behind his back!)
B) REWORK of Rob Smith's original analysis:
In article <smith-ya02408000...@news.u.washington.edu>,
Robert P. Smith <sm...@ieng.washington.edu> wrote:
(snip)
>For the past week or so I have been collecting data to see if FIBS produces
>outcomes that are consistent with expected random behavior. Specifically,
>I have been observing whether getting men off the bar is more difficult
>than one would expect. Every time there were men on the bar I observed how
>many possible landing spaces there were (open, blots or held by friendly
>troops) and whether or not the roll succeeded in landing at least one man
>off the bar. (I did not concern myself with the issue of more than one man
>on the bar.)
I'm a bit confused here. Did you or did you not include the "more
than one checker on the bar" case in your study??
CRB
>
>Probability theory suggests that if there is one landing pace, there will
>be a successful roll 11/36 of the time; 2 spaces 20/36; 3 spaces 27/36; 4
>spaces 32/36; 5 spaces 35/36. I observed the following data:
>
>landing Total Expected
>spaces rolls Successes Failures successes Variance
> 1 106* 21 85 32.39 22.49
> 2 97 46 51 53.89 23.95
> 3 108 83 25 81 20.25
> 4 63 53 10 56 6.22
> 5 57 56 1 55.42 1.54
>
totals 431 259 172 278.69 74.45 (line by CRB)
* corrected from "104" of original post.
>
>As you can see from the data there were fewer successes than expected for
>the instances when there were 1, 2 and 4 landing spaces, and basically
>matching the expectation if there were 3 or 5 landing spaces. The question
>then is whether the difference between the observation and the expectation
>is statistically significant.
>
>I will aggregate the data together: total number of successes was 259, the
>expected value was 278.69. The variance of this number (the sum of the
>variances of each case) is 74.45. By probability theory and by the central
>limit theorem, we would expect the statistic
>
> (T-E[T])
>-------------
>(Var(T))^0.5
>
>to have an approximately normal distribution of mean 0 and variance 1. The
>value of this statistic is -2.28. Looking up in a standard normal
>probability table there is a probability of 1.1% that this statistic will
>have a value of -2.28 or smaller if the probability distribution is
>correct. The difference between observation and theory is therefore
>statistically significant at the 0.011 level.
>
>There are (at least) three possible hypotheses that can explain this result:
>
>A) FIBS dice are non-random.
>B) I happened to observe a non-typical series of rolls, and additional
> data will cause the observed data to lose their statistical significance.
>C) I was not diligent in my observations, and I incorrectly recorded
> actual behavior.
I have two technical concerns about this analysis. Again--disclaimer
--I could be wrong on both (and thus Rob right on both). Let's hear from
you other pencil pushers!
1) If Rob would have also made a similar post if the number of entries
had been TOO LARGE by 2.28 standard deviations, then you must multiply
the 1.1% by 2. The jargon used here is "two-tailed" versus "one-tailed"
analysis. The Gaussian (normal, bell-shaped, etc.) distribution mentioned
by Rob above is symmetric. He took only the area under to LOW SIDE tail
to come up with his number. (That is, there is a 1.1% chance of getting
too few entries by this amount.) BUT, the HIGH SIDE tail represents the
chance of getting too many entries. Thus if this would garner equal
eyebrow raising, it is only fair to say "the chances of the number of
entries being off by 2.28 standard deviations or more is 2.2%").
2) I see another way to analyze the data. (NOTE: SINCE MY ANSWER
DISAGREES WITH ROB, AT MOST ONE OF US IS DOING IT CORRECTLY! I challenge
all of you to find out which one (IF EITHER) is doing the analysis right.)
The sum of the expected outcomes is 278.69 Entries (and 152.31 Wiffs).
So the standard deviation (for a binomial distribution) for 431 trials is:
srqt( e*w/n ) = sqrt( 278.69 * 152.31 / 431) = 9.92
(NOTE that Rob's method gets sqrt(74.45) = 8.63 for the standard dev.)
Now, dividing this into the difference (278.69 - 259)/9.92 = 1.98
standard deviation result (instead of the 2.28 s.d. result Rob indicates).
Although this doesn't seem like much of a difference, in fact it results
in another factor of two (because the Gaussian distribution is non-linear).
In summary of part 2, my conclusion is that Rob's data indicates
a 4.7% chance that the hypothesis "FIBS gives randomly distributed dice
rolls when entering a single checker from the bar" is correct. (BTW, my
indiscriminate rework of the data in part A to 5 entries in 431 trials
would be a whopping 27.6 std.dev. result. This is 1 chance in 10^166 !!
That's a pretty small likelihood...)
C) analogy to modern scientific practice and proposal for further study.
I am now going to relate how this kind of issue is handled in
the scientific literature (specifically in physics and astronomy,
and I assume also in geology, chemistry, biology, and mathematics).
Qualitatively, the following quote from Carl Sagan (from the
book "UFO's: A Scientific Debate" Sagan and Page (eds.) W.W. Norton
1972, p. 265) describes the general approach taken in real science:
There is a wide range of concepts which would be fascinating
if only they were true. But precisely because these ideas
have charm, exactly because they are of deep emotional
significance to us, they are the ideas we must examine most
critically. We must consider them with the greatest
skepticism, and exmaine in the greatest detail the evidence
relevant to them. Where we have an emotional stake in an
idea, we are most likely to deceive ourselves.
Although he was referring to issues of far greater importance than
what has been presented on this newsgroup, these principles apply.
The procedure in science would be for the author(s), in this
case Rob, to submit a manuscript to the editor of a journal. If
a refereed journal, the editor would pass a few copies on to persons
who are widely recognized to be knowledgeable on the particular
subject (random numbers and generators). These referees would read
the paper and submit questions and suggestions to the author through
the editor. They would also make a judgement as to whether the
information reported is appropriate for publication in this journal.
The referee's reports would then be given back to the author for
rebuttal. If the objections weren't severe, usually the author will
either modify the paper to address the questions/suggestions of the
referees, or write replies addressing those concerns and explain why
the paper was not modified. The editor will then decide whether to
pass this new work on to the referees for further recommendations or
just go ahead with publication. Some papers will be rejected without
further review (with a suggestion for major rewrite and resubmission)
but typically papers are accepted for publication (in experience and
fields, anyway). NOTE: The referees are NOT being asked to agree or
disagree with the result, but only to judge the legitimacy of the
techniques (data taking and analysis). To do more would be a
disservice to the progress of knowledge.
Publication in no way guarantees acceptance of the ideas!
The (critical) scientific readership is basically the jury. If they
disagree, typically some will propose new experiments (and acquire
funding and perform those experiments). These new studies will either
confirm or refute the original ideas (or possibly be inconclusive).
Subsequent papers will be submitted and published and the cycle
continues. It may take many years for ideas to be accepted, particularly
new, revolutionary concepts. There is never 100% guaranteed "fact".
Classical mechanics ideas (of Galileo, Decartes, Newton, etc.) stood
as the "last word" for 200 years until modified in the early part of
this century by many including Bohr, Born, Einstein, Shroedinger, etc.
Someday their ideas are likely to be overthrown (or at least updated).
Often in parallel to the experimental reporting of observations,
theorists will try to explain how these results come about. There is
a back and forth exchange of ideas MOST OF WHICH TURN OUT TO BE WRONG!
These are the inevitable growing pains of scientific ideas. Much of
what you read in newspapers about "black and white" or "right and wrong"
or "fact and fantasy", when given in absolute terms, is not real
science, no matter how convincing the arguments seem to be. It sells
papers, but it's not proper science. The apostle, Thomas, was surely
a scientist! And it's no surprise that very few politicians
have a clue of how science is done. Authoritarianism and deal making
are unfortunately present in science as well, but to the detriment of
true knowledge. Skepticism is healthy, and a fundamental requirement
for progress in science.
Now, back to this standard deviation, confidence level stuff.
There is no clear cut criterion (that I know of, anyway) for converting
statistical confidence to acceptance of an idea. For example, if a school
student comes to you and says that s/he has done a statistical survey
and concluded wtih 95% confidence (2-tailed 2 standard deviation result)
that there are fewer left handed people than right handed, you'd probably
yawn and go back to reading your paper. Since this is status quo
(the "accepted" truth) there is no reason to get excited. If the next
day that same student reports to you that another study produced a 95%
statistical confidence result that left handers are smarter than right
handers, you might raise your eyebrows and start asking some questions
(unless you happened to be one of these intellectually superior south-
paws)! And if later s/he announces that there is 95% confidence result
that left handers were deposited here on the earth by UFO's, even the
most laid-back sinesterian would likely snap to attention! "...(for)
concepts which would be fascinating, ...we must consider them with the
greatest skepticism, and examine in the greatest detail the evidence
relevant to them."
So this 2.28 (1.98) single-tailed (two-tailed) result reported
by Rob should pique our interests. Either it will be refuted by further
testing (supporting the status quo), in which case FIBS will be safe for
all of humanity, or it will be confirmed (at a much higher confidence
level!) and we will re-evaluate the worth of time spent playing on the
server. It is this higher confidence level search which necessitates
more data taking NOT the mere requirement of larger sample size. If
431,000 trials results in a two standard deviation discrepancy, we won't
be any farther along than we are now. So do your stuff, computer jockeys.
I'm waiting impatiently (but emotionlessly).
Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS
Greycat Sharpclaw
Meow, all...
Much snippage follows, I do not attempt to mark it all.
There is an allegation that bo...@bigbang.astro.indiana.edu (Chuck
Bower) wrote:
> This (LONG) post has three parts: A) soapbox (mild scolding of some
>r.g.b. posters), B) rework of Rob Smith's original analysis, and
>C) analogy to modern scientific practice and proposal for further study.
>A) SOAPBOX stuff (IHMO, as always):
> I find Rob's post sincere, diligent, and interesting. Here is an
>attempt to question the randomness of FIBS dice, and it's done with
>intelligence, rigor, and (apparently) without emotional involvement.
>This is what randomness "believers" have been crying for forever.
> I think it should be addressed with AT LEAST as much sincerity,
>diligence, and emotionlessness. Anything less places posters back
>in the stone age (REGARDLESS of which side of the debate you are on).
I agree. His method is unreliable, but at least he _attempts_ to get
real results. For that, I give him much credit for.
>3) "This study is meaningless." Maybe just a poor choice of words, but not
>at all an objective, scientific statement!
Except when a reason is given (and preferably a politely worded way of
saying "meaningless").
>B) REWORK of Rob Smith's original analysis:
> I have two technical concerns about this analysis. Again--disclaimer
>--I could be wrong on both (and thus Rob right on both). Let's hear from
>you other pencil pushers!
>1) If Rob would have also made a similar post if the number of entries
>had been TOO LARGE by 2.28 standard deviations, then you must multiply
>the 1.1% by 2.
Well, this is true, but his error only magnifies the "unusual" result.
My main issues are
Would a "average" result be as likely to be reported? The _media_
is suspect, even if the individual data set is not.
He admits to counting on the fly, while (quickly) playing games.
This creates a very high probability of a counting error, and it
is reasonable to wonder if that error might not be systematic.
(For the non-statistically trained, a systematic error is one that
tends to go in the same direction, rather than to average out).
>C) analogy to modern scientific practice and proposal for further study.
> The procedure in science would be for the author(s), in this
>case Rob, to submit a manuscript to the editor of a journal.
In a sense, he did... this is as much of a journal that exists on the
topic of FIBS. Of course, we don't have an editor (much less a
referee).
Good point. His thesis is hard to believe ... that the rolls are
affected by the precence of men on the bar and of possible entry
rolls. Thus, a very high confidence is needed to accept the theory.
The statistically unusual result reported _does_ justify further
research. But I _strongly_ recommend that the testing be automated,
for reliability. If I didn't have too many programming jobs
backlogged already, I'd take a crack at it. Any one else interested?
Robert P. Smith
I very much appreciate this and other thoughful replies to my original post.
In article <5hjjd8$2...@dismay.ucs.indiana.edu>,
bo...@bigbang.astro.indiana.edu (Chuck Bower) wrote:
> This (LONG) post has three parts: A) soapbox (mild scolding of some
> r.g.b. posters), B) rework of Rob Smith's original analysis, and
> C) analogy to modern scientific practice and proposal for further study.
>
(snip)
>
> B) REWORK of Rob Smith's original analysis:
>
> In article <smith-ya02408000...@news.u.washington.edu>,
> Robert P. Smith <sm...@ieng.washington.edu> wrote:
>
> (snip)
>
> >For the past week or so I have been collecting data to see if FIBS produces
> >outcomes that are consistent with expected random behavior. Specifically,
> >I have been observing whether getting men off the bar is more difficult
> >than one would expect. Every time there were men on the bar I observed how
> >many possible landing spaces there were (open, blots or held by friendly
> >troops) and whether or not the roll succeeded in landing at least one man
> >off the bar. (I did not concern myself with the issue of more than one man
> >on the bar.)
>
> I'm a bit confused here. Did you or did you not include the "more
> than one checker on the bar" case in your study??
> CRB
I treated cases where there were one or more than one man on the bar
equivalently. Did each roll succeed in getting (at least) one man off the
bar?
Two mechanical points:
1) Deciding to use a one-tailed test or a two-tailed test is a
philoposphical difference to which there is not a clean answer. The
outcome of this argument will chance the specific level of significance
produced, but will not materially change the nature of the argument.
2) Treating the total number of successes and failures as a Binomial random
variable in order to calcualte the variance is not correct. Doing so means
that each roll has a chance of success of 0.645. In fact some rolls have a
chance of success of 11/36, some rolls have a chance of success of 5/9,
some rolls have a chance of success of 3/4, and so on. Each line of the
table should have a Binomial distribution, and this is how I calculated the
variance of each line. The variance of the total is the sum of the
variance of each line, which leads to the 8.63 standard deviaion, rather
than the 9.92.
I agree that manual collection of data is inherently suspect. I would
greatly appreciate if someone could write a data collection program either
for the Big Brother games or for ongoing games. Don't worry if you do not
feel prepared to do the statistical analysis required, I and others are
more than willing to use the data once they are gathered.
Respectfully,
Rob Smith
Steve Mellen
In article <5hjjd8$2...@dismay.ucs.indiana.edu>,
bo...@bigbang.astro.indiana.edu (Chuck Bower) wrote:
> I find Rob's post sincere, diligent, and interesting. Here is an
> attempt to question the randomness of FIBS dice, and it's done with
> intelligence, rigor, and (apparently) without emotional involvement.
> This is what randomness "believers" have been crying for forever.
>
> I think it should be addressed with AT LEAST as much sincerity,
> diligence, and emotionlessness. Anything less places posters back
> in the stone age (REGARDLESS of which side of the debate you are on).
>
> I have a lot of respect for the posters whose replies I have read.
> However, there are three arguments in particular that I've seen, and don't
> like. Paraphrased: 1) "this proposal is so preposterous and FIBS so
> beyond reproach that it isn't worth considering". With this general
> attitude, we'd ALL still be in the above mentioned stoneage. 2) "You
> can't believe any result which is based on small number of trials."
> I believe this statement shows a lack of understanding of statistics.
> More will be said about this in part C below, but consider the following:
> Suppose Rob's study showed 5 entries total (say, one for each of the five
> inner board conditions) out of the same 431 trials. Would you still say
> that 431 wasn't a large enough sample? I would certainly ask for further
> study (as I am doing here) but not because the sample size was too small!
> 3) "This study is meaningless." Maybe just a poor choice of words, but not
> at all an objective, scientific statement!
>
As one of the Stone Age posters, I would like to offer a brief response.
The problem I have with the original post is not so much that it questions
the randomness of the FIBS dice (after all, if someone can show an
unintentional bias in the dice, I am sure marvin would want to know about
it and correct it). On the contrary, the original post, while thoughtful
and detailed, proffers a hypothesis that, if valid, can only be explained
by an intentional (and utterly inexplicable) act by marvin in constructing
the random number generator.
I do not believe that marvin's integrity and honesty should be the subject
of debate in the same way as, for example, we might discuss the value of
making the 2-point with an opening 6-4. The man has provided thousands of
backgammon players with a 24-hour worldwide backgammon club and received
practically nothing in return aside from personal satisfaction. I do not
agree that assaults on his character, if dressed up with statistics, can
only be properly answered with more statistical analysis. I think it's
entirely proper to suggest that we find something more worthwhile to talk
about than whether marvin is a cheating scoundrel.
Steve Mellen (fnurt)
Alexander Nitschke
Rob's post dealt with the probability of entering from the bar and he
collected manually some sample data which suggested at a high confidence
level that one is more likely to stay on the bar than one would expect.
My critic is:
Manual counting of such data is and will always be with a big risk of
making errors. It is easy to forget a count when one is entering on a
one point board. So I will only accept machine acquired data, which is
easy to get.
List your moves after every game with the command 'oldmoves' or record
your games from the beginning which is easy with a frontend like FIBS/W.
Then write a small program which plays back the game and counts the
whiffs vs. enters. This would be a count which a would accept to the
fullest extent.
Now the surprise: Peter Fankhauser (funk) already did exactly this for
the huge number of matches recorded by BigBrother. I haven't his numbers
at hand but he posted them to rgb. He even listed the entering
probabilities sorted after players and there was nothing unusual. There
were some players who danced often and some players who danced few but
overall the distribution was fairly normal.
I think this test was a much better test than the one of Rob. Of course
he could do something similar and provide us with new data, but until
this I believe in the results of the large machine computed test and
believe that the FIBS random number generator is fair.
Best greetings and (nevertheless) good luck wishes
Alexander (acey_deucey@FIBS)
Robert-Jan Veldhuizen
On 30-maa-97 22:41:32, Steve Mellen wrote:
SM> As one of the Stone Age posters, I would like to offer a brief response.
SM> The problem I have with the original post is not so much that it
SM> questions the randomness of the FIBS dice (after all, if someone can show
SM> an unintentional bias in the dice, I am sure marvin would want to know
SM> about it and correct it).
Well I did that once but didn't get any reply from anyone of FIBS. Patti's own
sampled data of 5 million randomly chosen FIBS rolls show an amount of doubles
that has an unlikeliness of 0.1%.
It's kind of strange that as soon as you come up with some data to back up your
initial opinions, all the (mostly rude) responders suddenly seem to have
disappeared...
SM> On the contrary, the original post, while
SM> thoughtful and detailed, proffers a hypothesis that, if valid, can only
SM> be explained by an intentional (and utterly inexplicable) act by marvin
SM> in constructing the random number generator.
Well that's not entirely true, I think. Just a systematic, unintentional error
could produce the same results.
SM> I do not believe that marvin's integrity and honesty should be the
SM> subject of debate in the same way as, for example, we might discuss the
SM> value of making the 2-point with an opening 6-4. The man has provided
SM> thousands of backgammon players with a 24-hour worldwide backgammon club
SM> and received practically nothing in return aside from personal
SM> satisfaction. I do not agree that assaults on his character, if dressed
SM> up with statistics, can only be properly answered with more statistical
SM> analysis. I think it's entirely proper to suggest that we find something
SM> more worthwhile to talk about than whether marvin is a cheating
SM> scoundrel.
I fully agree. But sometimes this opinion about marvin is put into people's
mouth when they're just talking about dice, not about marvin.
--
<tsb>Zorba
bob koca
Rob wrote:
>>landing Total Expected
>>spaces rolls Successes Failures successes Variance
>> 1 106* 21 85 32.39 22.49
>> 2 97 46 51 53.89 23.95
>> 3 108 83 25 81 20.25
>> 4 63 53 10 56 6.22
>> 5 57 56 1 55.42 1.54
>>
> totals 431 259 172 278.69 74.45 (line by CRB)
> * corrected from "104" of original post.
>>
>>
>>I will aggregate the data together: total number of successes was 259, the
>>expected value was 278.69. The variance of this number (the sum of the
>>variances of each case) is 74.45. By probability theory and by the central
>>limit theorem, we would expect the statistic
>>
>> (T-E[T])
>>-------------
>>(Var(T))^0.5
>>
>>to have an approximately normal distribution of mean 0 and variance 1. The
>>value of this statistic is -2.28. Looking up in a standard normal
>>probability table there is a probability of 1.1% that this statistic will
>>have a value of -2.28 or smaller if the probability distribution is
>>correct. The difference between observation and theory is therefore
>>statistically significant at the 0.011 level.
>>
Chuck Bower replied:
> I have two technical concerns about this analysis. Again--disclaimer
>--I could be wrong on both (and thus Rob right on both). Let's hear from
>you other pencil pushers!
>1) If Rob would have also made a similar post if the number of entries
>had been TOO LARGE by 2.28 standard deviations, then you must multiply
>the 1.1% by 2. The jargon used here is "two-tailed" versus "one-tailed"
>analysis. The Gaussian (normal, bell-shaped, etc.) distribution mentioned
>by Rob above is symmetric. He took only the area under to LOW SIDE tail
>to come up with his number. (That is, there is a 1.1% chance of getting
>too few entries by this amount.) BUT, the HIGH SIDE tail represents the
>chance of getting too many entries. Thus if this would garner equal
>eyebrow raising, it is only fair to say "the chances of the number of
>entries being off by 2.28 standard deviations or more is 2.2%").
I agree completely.
>2) I see another way to analyze the data. (NOTE: SINCE MY ANSWER
>DISAGREES WITH ROB, AT MOST ONE OF US IS DOING IT CORRECTLY! I challenge
>all of you to find out which one (IF EITHER) is doing the analysis right.)
>The sum of the expected outcomes is 278.69 Entries (and 152.31 Wiffs).
>So the standard deviation (for a binomial distribution) for 431 trials is:
> srqt( e*w/n ) = sqrt( 278.69 * 152.31 / 431) = 9.92
>(NOTE that Rob's method gets sqrt(74.45) = 8.63 for the standard dev.)
>Now, dividing this into the difference (278.69 - 259)/9.92 = 1.98
>standard deviation result (instead of the 2.28 s.d. result Rob indicates).
>Although this doesn't seem like much of a difference, in fact it results
>in another factor of two (because the Gaussian distribution is non-linear).
Rob did it correctly and Chuck has errored.
The key probability fact which Rob used is that the variance
of a sum of independent variables equals the sum of the variances.
To see your error Chuck imagine the following experiment.
100 trials are conducted of an experiment in which the probability
of success is 100%. Then 100 trials are conducted of an experiment
in which probability of success is 0. Obviously the net result will
be always 100 successes out of the 200 trials. The variance is 0.
Chuck's technique says variance would be same as 200 trails of a
50% chance of success variable.
,Bob Koca
bobk on FIBS
BobKoca on GamesGrid
Andy Germain
Well, there is certainly another possibility:
The random number generator could have an error.
This could be thought of as a variant on #3 below, but implies no evil
on marvin's part.
Chuck Bower
Dear r.g.bg reader,
Does the following scenario sound familiar?
1) Someone makes a statement you don't agree with.
2) You think that the statement can be refuted rationally.
3) Before you get a chance to state your case, someone who supports
YOUR side of the argument (that is, disagrees with the original
statement) begins to spout off using inaccurate, incorrect logic.
4) An arguent ensues, with much chest-beating, name-calling, and
general authoritarianism. Reason is deemed to be irrelevant.
That is a simplified view of most of the "random dice" threads
on this newsgroup. "Belief" is justification enough (for both sides).
That may be true of religion, politics, kangaroo courtrooms, and SOME
philosophies. It's not enough for me.
What follows are some clips from various posts made since my LONG
reply to Rob Smith's original post. Included are my rebuttals. (surprise!)
Before that, though, I thank both Rob Smith and Bob Koca for pointing
out the error of my "alternate analysis" of Rob's data.
In Article: 15525 of rec.games.backgammon
From: so...@concentric.net (Steve Mellen)
Subject: Re: Randomness and FIBS dice (with DATA)
Date: Sun, 30 Mar 1997 16:41:32 -0500
Message-ID: <solon-30039...@61021d0001dt.concentric.net>
Steve Mellen said:
(snip)
>The problem I have with the original post is not so much that it questions
>the randomness of the FIBS dice (after all, if someone can show an
>unintentional bias in the dice, I am sure marvin would want to know about
>it and correct it). On the contrary, the original post, while thoughtful
>and detailed, proffers a hypothesis that, if valid, can only be explained
>by an intentional (and utterly inexplicable) act by marvin in constructing
>the random number generator.
(snip)
I had to look up the word "proffer" and found the following definition:
"to offer, usually something intangible, for acceptance." I have reread
Rob's original post many times. I see no mention of this "intentional...
act". I can only surmise that this is Steve's profference.
I see a dangerous flaw. Steve (or I, or anyone else) thinks about
how such an apparent skewed situation can occur. The MOST LIKELY
EXPLANATION (or the one which most easily comes to mind) is mistakenly
taken as the ONLY POSSIBLE EXPLANATION. Later in this article I illustrate
a simple-minded alternative. It's not likely, but it should illustrate
my point.
In Article: 15532 of rec.games.backgammon
From: Alexander Nitschke <nits...@mailszrz.zrz.tu-berlin.de>
Subject: Re: Randomness and FIBS dice (with DATA)
Date: Mon, 31 Mar 1997 17:54:41 +0200
Message-ID: <333FDE...@mailszrz.zrz.tu-berlin.de>
(snip)
>Now the surprise: Peter Fankhauser (funk) already did exactly this for
>the huge number of matches recorded by BigBrother. I haven't his numbers
>at hand but he posted them to rgb. He even listed the entering
>probabilities sorted after players and there was nothing unusual. There
>were some players who danced often and some players who danced few but
>overall the distribution was fairly normal.
(snip)
I got on the WEB and looked for this data in DejaNews. I found an
article dated 23 Aug 1996 in which Peter stated that he had done such
a study and found the expected result. BUT NO DETAILS WERE PRESENT.
(That is: no mean, std. dev., expected, actual, etc.) Can someone find
or resurrect the details?
Article: 15543 of rec.games.backgammon
From: Robert-Jan Veldhuizen <veld...@xs4all.nl>
Subject: Re: Randomness and FIBS dice (with DATA)
Date: 01 Apr 97 01:50:07 +0100
(snip)
> Patti's own sampled data of 5 million randomly chosen FIBS rolls show
> an amount of doubles that has an unlikeliness of 0.1%.
(snip)
I did find this on the web (http://www.gammon.com/fibs_dice/results.txt).
I plugged in the numbers and got 0.36%. That's an exaggeration of a factor
of 3.6. Anyone surprised about the direction of the error? Regardless of
that, I felt at the time (and still do) that this unlikely result deserves
another look. I believe someone (Stephen Turner) is doing that, but I have
yet to see his work. I suspect it's not a simple exercise...
Article: 15551 of rec.games.backgammon
From: Andy.G...@gsfc.nasa.gov (Andy Germain)
Subject: Re: Randomness and FIBS dice
Date: Tue, 01 Apr 1997 16:36:27 GMT
Organization: NASA Goddard Space Flight Center -- Greenbelt, Maryland USA
Message-ID: <5hrdib$b...@post.gsfc.nasa.gov>
(snip)
>Well, there is certainly another possibility:
>
> The random number generator could have an error.
>
>This could be thought of as a variant on #3 below, but implies no evil
>on marvin's part.
>
>kwoo...@netcom.com (Kit Woolsey) wrote:
>
(snip)
>>3) Marvin, that evil man, intentionally subverts his own product, for no
>>apparent reason whatsoever. Considering that Marvin wrote FIBS not for
>>profit but for his own ego satisfaction and to supply a working
>>backgammon server for the internet, I guess we can estimate this
>>probability at .0001%.
(snip)
An interesting idea of Andy's. In further support of this, and
as a continuation of my rebuttal to Steve Mellen's post, try this
(simple-minded, and almost certainly wrong!) scenario:
Suppose the FIBS random number generator always gave the same number on
both dice! Then there are only six (equally likely) possible rolls.
WOULD THIS MANIFEST ITSELF IN A STUDY SUCH AS ROB'S WHERE YOU LOOK AT
ENTRIES FROM THE BAR? I reproduce most of Rob's original table, except
that now I put in "mean" entries based on the above dice generator.
Since Rob doesn't know about this problem, he assumes that he should
enter 11/36 on a five-point board, 20/36 on a four-point board, etc.
landing Total Expected
spaces rolls Successes Failures successes Variance
1 106* 18 88 32.39 22.49
2 97 32 65 53.89 23.95
3 108 54 54 81 20.25
4 63 42 21 56 6.22
5 57 48 9 55.42 1.54
total 431 194 237 278.69 74.45
So the actual "entries" disagree with "expected" by
(194 - 278.69)/sqrt(74.45) = -9.8 standard deviations.
Now we are talking SERIOUS discrepancy (2-tailed likelihood much
less than one chance in 10^22. Of course not quite the one
chance in 10^166 of my first scenario! Hey, I'm getting better...)
So, Rob's test found a flaw in the random number generator,
and it probably wasn't an intentional design flaw, but a careless
programming error. (Oh, no! Now it looks like I'm calling Marvin
stupid. Is that worse than calling him evil?)
I reiterate that I'd like to see a more systematic study done.
(That is, DON'T record numbers by hand, on the fly, in games you are
playing in. Recall what Sagan said--see my earlier post.) Hopefully
someone will do this, or find Funk's data. Hey, don't look at me!
I'm too busy getting on and off my soapbox.
Donald Kahn
>Well, there is certainly another possibility:
>
> The random number generator could have an error.
>
>This could be thought of as a variant on #3 below, but implies no evil
>on marvin's part.
You mean, for instance, that it produced a disproportionate number of
6's, which would of course bias toward entry-failure?
That would be the easiest thing in the world to check.
Otherwise, the program employing the 'faulty' generator would need to
be aware of the fact that a piece was on the bar, in order to produce
its faulty results at just those times. That could only come about
through evil intent and an operative subroutine. I go along with
Kit's estimate of its likelihood.
Donald Kahn
Tom Keith
Chuck Bower wrote:
>
> I reiterate that I'd like to see a more systematic study done.
> (That is, DON'T record numbers by hand, on the fly, in games you are
> playing in. Recall what Sagan said--see my earlier post.) Hopefully
> someone will do this, or find Funk's data. Hey, don't look at me!
> I'm too busy getting on and off my soapbox.
Ok, I wrote a program to collect more data. Here's what
it came up with.
The following data is taken from the archive of matches
collected by Mark Damish's Big Brother program and stored
at "http://www.gammon.com/". A total of 2553 matches were
analyzed (8463 games), and in those matches the player
on roll had a checker (or checkers) on the bar 91503 times.
The following table summarizes how often that player was
able to enter at least one of his checkers, classified
according to the number of points that were open in the
opponent's home board. I leave it to more statistically-
inclined readers to interpret this data.
Points Open Successes / Attempts Rate*36 (Expect)
0 0 / 6486 0.00 (0)
1 4973 / 16910 10.59 (11)
2 10802 / 19529 19.91 (20)
3 14170 / 18972 26.89 (27)
4 14953 / 16847 31.95 (32)
5 12288 / 12629 35.03 (35)
6 130 / 130 36.00 (36)
Total 57316 / 91503
Tom
Chuck Bower
In article <334363...@bkgm.com>, Tom Keith <t...@bkgm.com> wrote:
(snip)
>
>The following data is taken from the archive of matches
>collected by Mark Damish's Big Brother program and stored
>at "http://www.gammon.com/". A total of 2553 matches were
>analyzed (8463 games), and in those matches the player
>on roll had a checker (or checkers) on the bar 91503 times.
>The following table summarizes how often that player was
>able to enter at least one of his checkers, classified
>according to the number of points that were open in the
>opponent's home board. I leave it to more statistically-
>inclined readers to interpret this data.
>Points Open Successes / Attempts Rate*36 (Expect) expected variance
> entries
> 0 0 / 6486 0.00 (0)
> 2 10802 / 19529 19.91 (20) 10849.44 4821.98
> 3 14170 / 18972 26.89 (27) 14229.00 3557.25
> 4 14953 / 16847 31.95 (32) 14975.11 1663.90
> 5 12288 / 12629 35.03 (35) 12278.19 341.06
> 6 130 / 130 36.00 (36)
>
>CRB Total 57186 / 84887 57498.60 13972.34
The last two columns were added by me. I don't count the first
and last rows, which are a good "sanity check" on the programming but
of doubtful use statistically. (If you do the statistics with them,
I think you'd get the same answer... Check me, please!)
So the discrepancy (in standard deviations) using Rob' method is:
(57186 - 57498.6)/sqrt(13972.34) = -2.64
For a 2-tailed experiment, this has a probability of 0.8% of being
consistent with random dice. I BEG ALL OF YOU TO PLEASE CHECK MY
ANALYSIS!!
So, the plot thickens. I think there are a couple things worth
emphasizing:
1) In this experiment, as in Rob's, there was a big discrepancy for
entering on a five point board, with not much on the other size
boards. This may be a clue IF there is a problem. It may also be
just a coincidence.
2) The RATIO's of expected/actual have gotten closer to 1, BUT, the
much larger number of trials (84,887 compared to 431) is more sensitive
and thus the discrepancy in terms of number of standard deviations is
larger than before. This shouldn't be too surprising.
3) It would be interesting to see the case--ONLY one checker on the
bar--enumerated separately. This might or might not tell something.
In particular, if there is a "programming" error in Tom's data
collection (no offense, PLEASE!) it might show up. Also, if there
really is a random number generator problem in FIBS, this extra
piece of info might be another clue.
Out of curiosity, did anyone take you up on your bet, Kit?
Andy Germain
In response to problems (real or imagined) with software random number
generators, I am developing a product. It is a Hardware Random number
generator, based on a truly chaotic physical process. It is intended
to be completely unpredictable and unguessable.
It is is targeted primarily at commercial uses, such as generating
random keys for RSA encryption, but I expect it will also be useful
for games such as BG.
Anyway, if the FIBS community and the FIBS operators are interested, I
would like to offer a beta model to FIBS at no charge.
Andy Germain (Andy_Germain on FIBS) (AndyG on GG)
Andy.G...@gsfc.nasa.gov
Jennifer Griffin
Steve Mellen (so...@concentric.net) wrote:
: It is so implausible to me that someone would program the random number
: generator on a backgammon server to scan the board before each roll to see
: if a player has men on the bar, determine which points are open, and
: reduce the chance of rolling those numbers by some small percentage, that
: it really blows my mind that people waste time on exercises like this.
Ah...but you seem to have forgotten that FIBS is all a psychological
experiment ;))
intern
: In article <smith-ya02408000...@news.u.washington.edu>,
: sm...@ieng.washington.edu (Robert P. Smith) wrote:
: > In article <333280...@cam.ac.uk>, Stephen Turner <sr...@cam.ac.uk> wrote:
: >
: > >
: > > When was the last time you heard a competent mathematician or a good player
: > > who thought that FIBS dice were non-random?
: > >
: >
: > Let me offer my opinion. I am not here to trumpet academic credentials,
: > but I believe that I do understand probability and statistics enough to
: > make reasonable statements. I also am a competent (but not expert)
: > backgammon player (FIBS rating of ~1670).
: >
: > For the past week or so I have been collecting data to see if FIBS produces
: > outcomes that are consistent with expected random behavior. Specifically,
: > I have been observing whether getting men off the bar is more difficult
: > than one would expect. Every time there were men on the bar I observed how
: > many possible landing spaces there were (open, blots or held by friendly
: > troops) and whether or not the roll succeeded in landing at least one man
: > off the bar. (I did not concern myself with the issue of more than one man
: > on the bar.)
: >
: > Probability theory suggests that if there is one landing pace, there will
: > be a successful roll 11/36 of the time; 2 spaces 20/36; 3 spaces 27/36; 4
: > spaces 32/36; 5 spaces 35/36. I observed the following data:
: >
: > landing Total Expected
: > spaces rolls Successes Failures successes Variance
: > 1 104 21 85 32.39 22.49
: > 2 97 46 51 53.89 23.95
: > 3 108 83 25 81 20.25
: > 4 63 53 10 56 6.22
: > 5 57 56 1 55.42 1.54
: >
: > As you can see from the data there were fewer successes than expected for
: > the instances when there were 1, 2 and 4 landing spaces, and basically
: > matching the expectation if there were 3 or 5 landing spaces. The question
: > then is whether the difference between the observation and the expectation
: > is statistically significant.
: >
: > I will aggregate the data together: total number of successes was 259, the
: > expected value was 278.69. The variance of this number (the sum of the
: > variances of each case) is 74.45. By probability theory and by the central
: > limit theorem, we would expect the statistic
: >
: > (T-E[T])
: > -------------
: > (Var(T))^0.5
: >
: > to have an approximately normal distribution of mean 0 and variance 1. The
: > value of this statistic is -2.28. Looking up in a standard normal
: > probability table there is a probability of 1.1% that this statistic will
: > have a value of -2.28 or smaller if the probability distribution is
: > correct. The difference between observation and theory is therefore
: > statistically significant at the 0.011 level.
: >
: > There are (at least) three possible hypotheses that can explain this result:
: >
: > A) FIBS dice are non-random.
: > B) I happened to observe a non-typical series of rolls, and additional
: > data will cause the observed data to lose their statistical significance.
: > C) I was not diligent in my observations, and I incorrectly recorded
: > actual behavior.
: >
: > I do not entirely discount hypothesis (C), but I was trying to be fair and
Robert P. Smith
We are now left with three active hyptoheses:
A) FIBS dice are non-random.
B) There was a programming error by Tom Keith.
C) Big_Brother happened to observe an extended set of unlikely events
(correctly calculated by Chuck Bower to be <0.8% probability).
Also, for the one-point open case the observation is 3.24 standard
deviations away from the expected value, which has a two-tailed probability
of 0.12%.
Explanations anyone?
Rob Smith
In article <5i0kll$1...@dismay.ucs.indiana.edu>,
bo...@bigbang.astro.indiana.edu (Chuck Bower) wrote:
Ole Jensen
Tom Keith <t...@bkgm.com> writes:
> The following data is taken from the archive of matches
> collected by Mark Damish's Big Brother program and stored
> at "http://www.gammon.com/". A total of 2553 matches were
> analyzed (8463 games), and in those matches the player
> on roll had a checker (or checkers) on the bar 91503 times.
> The following table summarizes how often that player was
> able to enter at least one of his checkers, classified
> according to the number of points that were open in the
> opponent's home board. I leave it to more statistically-
> inclined readers to interpret this data.
>
> Points Open Successes / Attempts Rate*36 (Expect)
>
> 0 0 / 6486 0.00 (0)
> 1 4973 / 16910 10.59 (11)
> 2 10802 / 19529 19.91 (20)
> 3 14170 / 18972 26.89 (27)
> 4 14953 / 16847 31.95 (32)
> 5 12288 / 12629 35.03 (35)
> 6 130 / 130 36.00 (36)
>
> Total 57316 / 91503
For the total number of entries from the bar I get an expected value
of 57628.69 and a standard deviation of 118.20. The actual number of
entries is 312.69 short of the expected number, which is 2.65 standard
deviations out. The probability of being this far away (in either
direction) is 0.8 percent. In other words, assuming uniformly random
dice, a data set as "bad" as this has only 0.8 percent chance of
occuring.
More water on the conspiracy theory mill? Or can some explanation be
found in the method of data collection?
As a possible candidate for a methodological explanation, could there
be some significance to the fact that non-entries are handled by the
server, whereas entries typically are non-forced moves that require
input from the player? Interaction across the network carries the
risk of disconnections after lag or other network problems, so things
would tend to go wrong slightly more often after entries than after
non-entries. I am not sure whether matches that got disrupted in this
manner have been eliminated from the Big_Brother data or not. Even if
they have, it is questionable whether this effect would have enough
significance to account for all of the discrepancy. However, there
seems to be some scope for "natural" explanations of this kind.
-- Ole Hoegh Jensen
Kit Woolsey
: A) FIBS dice are non-random.
: B) There was a programming error by Tom Keith.
: C) Big_Brother happened to observe an extended set of unlikely events
: (correctly calculated by Chuck Bower to be <0.8% probability).
: Also, for the one-point open case the observation is 3.24 standard
: deviations away from the expected value, which has a two-tailed probability
: of 0.12%.
: Explanations anyone?
: Rob Smith
Yeah, I think I can give it a try. There is a fourth possible
hypothesis: That the Big_Brother data isn't complete!
Not complete, you ask? In what way? Doesn't Big_Brother record the full
games? Maybe not.
Consider the following (all-too-familiar) scenario: You are stuck on the
bar against a closed board, and your opponent starts peeling his
checkers off. The situation is such that you MUST hit a shot to have a
chance, either because you are stone cold gammoned if you don't or
because your opponent doesn't need a gammon to win the match.
Eventually, you enter. What do you do? You don't play the move -- you
resign! We would have to check it out, but my guess is that when this
happens Big_Brother doesn't record that last entering dice roll or the
entrance which was never made. Note that if you had stayed on the bar,
the roll would have been recorded. Consequently, some of the entering
numbers which should be in the data simply aren't there, while all of the
flunking numbers are. Granted this only occurs occasionally, but it
doesn't have to happen very often to cause the apparently skewed results
Tom's survey got us.
Great programming job, Tom. However, if I happen to be correct about the
missing data do you think you could tweak your program a bit to take
these last rolls which were not recorded into account (if you already did
so, my hypothesis goes down the drain, of course).
Kit
Phill Skelton
Tom Keith wrote:
>
> The following data is taken from the archive of matches
> collected by Mark Damish's Big Brother program and stored
> at "http://www.gammon.com/". A total of 2553 matches were
> analyzed (8463 games), and in those matches the player
> on roll had a checker (or checkers) on the bar 91503 times.
> The following table summarizes how often that player was
> able to enter at least one of his checkers, classified
> according to the number of points that were open in the
> opponent's home board. I leave it to more statistically-
> inclined readers to interpret this data.
>
> Points Open Successes / Attempts Rate*36 (Expect)
>
> 0 0 / 6486 0.00 (0)
> 1 4973 / 16910 10.59 (11)
> 2 10802 / 19529 19.91 (20)
> 3 14170 / 18972 26.89 (27)
> 4 14953 / 16847 31.95 (32)
> 5 12288 / 12629 35.03 (35)
> 6 130 / 130 36.00 (36)
>
> Total 57316 / 91503
<Sarcasm mode ON>
But the Big Brother matches are almost entirely those played by the top
ranked players, and they are the people conspiring with Marvin to fix
the ratings system. It's the low rated players that the RNG picks on...
<Sacrasm mode OFF>
These data fit the expectations of a random distribution pretty well.
Nothing is more than 3 standard deviations from what you'd expect.
Somehow, I doubt that mere *data* is going to dissuade those who
'know' - deep down in their hearts - that the RNG is stacked (against
them).
Phill
Phill Skelton
Ole Jensen wrote:
>
> For the total number of entries from the bar I get an expected value
> of 57628.69 and a standard deviation of 118.20. The actual number of
> entries is 312.69 short of the expected number, which is 2.65 standard
> deviations out. The probability of being this far away (in either
> direction) is 0.8 percent. In other words, assuming uniformly random
> dice, a data set as "bad" as this has only 0.8 percent chance of
> occuring.
In the happy world of data analysis where I spend most of my days,
any effect of less than 3 standard deviations is ignored. They come up
far to often. When you get to 4 SD you get interested, but need more
data. When you get to 5 SD you have a result that is worth something,
but not until then. I would not think that 2.65 SD was at all
significant.
Phill
Robert-Jan Veldhuizen
On 02-apr-97 02:04:57, Chuck Bower wrote:
[big snip]
I feel with you, Chuck. It happens all the time; discussions get more "intense"
if the participants know too little of the subject. In this thread, it's
sometimes the statistics which are not right but mainly, as I see it, it's all
due to the fact that it's impossible to examine the way FIBS "rolls" its dice
*yourself*. What remains then is discussing about a "black box" by seeing what
comes out of it. A guarantee for heated debates ;^)
I couldn't resist commenting your comments on my comments though: ;)
>> Patti's own sampled data of 5 million randomly chosen FIBS rolls show
>> an amount of doubles that has an unlikeliness of 0.1%.
CB> (snip)
CB> I did find this on the web
CB> (http://www.gammon.com/fibs_dice/results.txt).
CB> I plugged in the numbers and got 0.36%.
Well I actually got 0.18% back then, I didn't remember the figure exactly and
erroneously wrote 0.1%. I get this figure by testing H0: The prob. of a double
is 1/6 against H1: The prob. of a double is more than 1/6.
You can discuss endlessly about one- or two-sided tests, not much use I guess.
CB> That's an exaggeration of a
CB> factor of 3.6. Anyone surprised about the direction of the error?
:) Well a few notes: with my method my error is a factor 1.8 instead of 3.6,
but, more importantly, you should compare the probabilities that FIBS rolls a
too high amount of doubles ! That's what I was testing.
In that case you see that it doesn't matter really: 99.9% against 99.82% or
99.64%. So I'm only exaggerating by 0.26% at most... ;^)
CB> Regardless of that, I felt at the time (and still do) that this unlikely
CB> result deserves another look. I believe someone (Stephen Turner) is
CB> doing that, but I have yet to see his work. I suspect it's not a simple
CB> exercise...
Well, the best (if not the only) way to really "solve" this argument would be if
the people who are convinced FIBS's dice are random would define a test with
only two outcomes: 1.They're most probably right 2. They're most probably wrong.
Stephen Turner's (in)famous bet springs to mind...;^)
[snip]
CB> Suppose the FIBS random number generator always gave the same number on
CB> both dice! Then there are only six (equally likely) possible rolls.
CB> WOULD THIS MANIFEST ITSELF IN A STUDY SUCH AS ROB'S WHERE YOU LOOK AT
CB> ENTRIES FROM THE BAR?
Well this was exactly what I thought when I saw the table. A too high amount of
doubles on FIBS would give one a smaller chance of entering, was my intuition.
Of course, the table is not very convincing in this respect, but at least it
supports the hypothesis that FIBS rolls too many doubles (FWIW...)
[snip]
CB> I reiterate that I'd like to see a more systematic study done.
CB> (That is, DON'T record numbers by hand, on the fly, in games you are
CB> playing in. Recall what Sagan said--see my earlier post.) Hopefully
CB> someone will do this, or find Funk's data. Hey, don't look at me!
CB> I'm too busy getting on and off my soapbox.
I just started writing a program to extract my and my opponent's rolls out of
FIBS output. Of course, it'll take quite a while to acquire enough data to
analyze, but I'll let you know if there's something to say.
--
<tsb>Zorba
Greycat Sharpclaw
Meow, all...
==== First, allow me to add a few more small stats to a previous
experiement:
Table from Tom Keith & Chuck Bower trimmed, and data added:
<---- tom's data (trimmed) ------> <- Chuck's stats-> < I add >
Points Open Successes / Attempts expected variance "zeta"
entries (standard
deviations
from mean)
0 0 / 6486
1 4973 / 16910 5166.94 3588.66 - 3.24
2 10802 / 19529 10849.44 4821.98 - 0.68
3 14170 / 18972 14229.00 3557.25 - 0.99
4 14953 / 16847 14975.11 1663.90 - 0.54
5 12288 / 12629 12278.19 341.06 + 0.53
6 130 / 130
Two things of note...
Only the "1 roll enters" case is as much as 1 full standard deviation
off of the expected mean for true dice. This seems to be pulling the
rest down. It is, however, over 3 standard deviations itself!
There is a trend towards the negative zeta increasing with smaller
numbers. The "roughness" in this trend is well within statistical
fluctuations. On the other hand, the trend itself is not well enough
defined to claim that it is itself significant.
Here we have some hard data that suggests a dice bias, and which
significantly *agrees* with the earlier (less precise) experiment in
the nature of the bias... it's seems harder than it should be to get
off the bar.
This data is not beyond the streach of a "fluke", but it's got my
attention. So I went to the next step.
OK... theory time: why might this bias exist?
I will arbitrarily discount the possibility that the dice are
correlated to the board position... almost any (even poor) attempt at
a RNG would prevent this... it's hard to accidently produce a RNG that
*would* have a correlation; while it's easy to accidently create a RNG
with other problems. OK... this arguement is semi-philosophical and
based on programmer's experience rather than hard data, but it seems
fairly clear to me, at least.
**** Pure Speculation Follows **** (I prefer quotes include this
disclaimer)
--Hypothesis 1) the dice are biased towards certain numbers,
particularly those numbers likely to be covered.
- hey, a slight bias towards 6's would give this.
--Hypothesis 2) the dice favor doubles... and doubles are less likely
to get you off the bar.
**** end speculation ****
==== now the promised new experiment.
Test: I look at dicetest on FIBS:
870404 rolls of two dice:
We expect on the average:
each number occurs on 290134.7 dice (var. 241779, std dev 491.7)
each number occurs at least once on 266048.4 rolls (var. 184692, std
dev 429.8)
actual data from the dicetest: Note the two columns of data are *not*
independent, so may not be simply combined.
num. occurs "zeta" occurs "zeta"
on die on roll
1 289962 - .35 265782 - .62
2 289285 -1.72 265441 -1.41
3 289704 - .88 265589 -1.07
4 291152 +2.06 266795 +1.73
5 290504 + .75 266346 + .69
6 290201 + .13 266004 - .10
all 1740808 .00 1595957 - .31
2-3 of 6 cases outside 1 standard deviations (about 2 is average).
But note that the high rolls are more common. Is this significant?
1-3 868951 -1.71
4-6 871857 +1.71
This suggests that high rolls are more common, but at less than 2
standard deviations, we get poor confidence. Note... if high rolls
are more common, then it's harder to get off of the bar... the higher
points are occupied more often (I say this from personal experience in
backgammon & backgammon strategy, but have no statistics to back it up
with... sorry).
So, it appears that there may indeed be a bias in the dice, but the
evidence is inconclusive. More testing (and *hard*, i.e. numeric)
testing) is called for.
The experiment I performed, however, seems to show *no* significant
results for the "more doubles" hypothesis:
number of doubles: 144851
expected value: 145067.3
difference - 216.3
varience: 120889
standard deviation: 347.7
results: - .62 standard deviations fron unbiased expectation
(well within normal fluctuations)
=== back to quoting chuck
>3) It would be interesting to see the case--ONLY one checker on the
>bar--enumerated separately. This might or might not tell something.
>In particular, if there is a "programming" error in Tom's data
>collection (no offense, PLEASE!) it might show up. Also, if there
>really is a random number generator problem in FIBS, this extra
>piece of info might be another clue.
I second this proposal. It would give clues as to what the bias, if
it exists for real, might be. It might pertain to my results, too
Chuck Bower
In article <kwoolseyE...@netcom.com>,
Kit Woolsey <kwoo...@netcom.com> wrote:
>hypothesis: ...the Big_Brother data isn't complete!
>
>Not complete, you ask? In what way? Doesn't Big_Brother record the full
>games? Maybe not.
>
>Consider the following (all-too-familiar) scenario: You are stuck on the
>bar against a closed board, and your opponent starts peeling his
>checkers off. The situation is such that you MUST hit a shot to have a
>chance, either because you are stone cold gammoned if you don't or
>because your opponent doesn't need a gammon to win the match.
>Eventually, you enter. What do you do? You don't play the move -- you
>resign! We would have to check it out, but my guess is that when this
>happens Big_Brother doesn't record that last entering dice roll or the
>entrance which was never made. Note that if you had stayed on the bar,
>the roll would have been recorded. Consequently, some of the entering
>numbers which should be in the data simply aren't there, while all of the
>flunking numbers are. Granted this only occurs occasionally, but it
>doesn't have to happen very often to cause the apparently skewed results
>Tom's survey got us.
>
I've been trying to find a possible correlation between Patti's
study which showed a small (but potentially statistically significant)
overage in number of doubles and Rob's and Tom's entry failure tests.
Kit's expanation could account for both IF Patti's data collection
also suffers a similar bias. She used "dicetest". Is this independent
of what goes on in the actual matches?
(BTW, the scenario--resign the game if you DON'T get doubles in
the bearoff--would give too many doubles, or not enough non-doubles,
whichever way you want to think of it.)
Chuck
Robert-Jan Veldhuizen
On 03-apr-97 09:01:15, Tom Keith wrote:
TK> The following data is taken from the archive of matches
TK> collected by Mark Damish's Big Brother program and stored
TK> at "http://www.gammon.com/". A total of 2553 matches were
TK> analyzed (8463 games), and in those matches the player
TK> on roll had a checker (or checkers) on the bar 91503 times.
TK> The following table summarizes how often that player was
TK> able to enter at least one of his checkers, classified
TK> according to the number of points that were open in the
TK> opponent's home board. I leave it to more statistically-
TK> inclined readers to interpret this data.
Thanks Tom !
Well I'll have a try at this. I'll leave most of the calculations out of here,
because it's too much and too boring B-)
I will test the hypothesis H0: FIBS rolls random against H1: FIBS rolls
non-random in such a way that one can enter less often from the bar than one
could with random dice. I give the probability values for H0 being true instead
of H1 for each of the different cases and for the all the cases combined:
Points Open Successes / Attempts Rate*36 (Expect) P(H0 is true)
0 0 / 6486 0.00 (0) -
1 4973 / 16910 10.59 (11) 0.0006 !
2 10802 / 19529 19.91 (20) 0.2483
3 14170 / 18972 26.89 (27) 0.1635
4 14953 / 16847 31.95 (32) 0.2981
5 12288 / 12629 35.03 (35) 0.7123
6 130 / 130 36.00 (36) -
(The cases 0/6 points open don't contribute to the analysis and are ignored)
The total is more complex; we first have to find the average probability of
entering for all of the attempts:
16910*11/36 + 19529*20/36 + 18972*27/36 + 16847*32/36 + 12629*35/36 successes in
total would be expected, that's 57498.69444 out of 16910+19529+18972+16847+12629
= 84887 attempts. Average probability: 0.677355713. The actual number of
successes was 4973+10802+14170+14953+12288 = 57186.
That yields P(H0 is true) = 0.0110 !
(I hope I did all the calculations right...)
Conclusion: In this sample, entering from the bar occured less often than one
would expect; the chances of this happening with random dice in a sample of
this size are 1.1%
Not /that/ small, but small enough "to raise an eyebrow" ;) I would say.
Everyone can draw their own conclusions from this conclusion now... ;^)
Cheers and good luck,
--
Zorba/Robert-Jan
Patti Beadles
It would be easy to test this hypothesis by modifying the analysis
program to diregard the last roll of each game.
-Patti
--
Patti Beadles |
pat...@netcom.com/pat...@gammon.com |
http://www.gammon.com/ | "I trust you. It's just
or just yell, "Hey, Patti!" | that I'm scared of you."
Patti Beadles
Dicetest is entirely independent of the state of the game.
Tom Keith
Kit Woolsey wrote:
>
> There is a fourth possible hypothesis: That the Big_Brother data isn't
> complete!
> ...
> Great programming job, Tom. However, if I happen to be correct about the
> missing data do you think you could tweak your program a bit to take
> these last rolls which were not recorded into account (if you already did
> so, my hypothesis goes down the drain, of course).
Good thinking! I checked the BB data. In 500 games, the game ended
when
a player resigned while he had a checker on the bar. It seems likely in
the vast majority of those cases that the resigning player actually
rolled
first and then resigned when he saw that he was forced to enter his
checker.
BB does not seem to record the roll if no play is made. Here's a
breakdown
of those games:
Points Open Games Resigned With
a Checker on the Bar
0 5
1 37
2 126
3 155
4 113
5 52
6 12
Total 500
If we assume that all these games represent rolls that enter (probably
not quite true), then the previous totals can be revised as follows:
Points Open
0 5/ 6491 = 0.03/36 <-(Obviously false assumpt
here)
1 5010/16947 = 10.64/36
2 10928/19655 = 20.02/36
3 14325/19127 = 26.96/36
4 15066/16960 = 31.98/36
5 12340/12681 = 35.03/36
6 142/ 142 = 36.00/36
E&OE :)
Tom
Ole Jensen
pat...@netcom.com (Patti Beadles) writes:
> Dicetest is entirely independent of the state of the game.
I'm not sure whether this statement answers the question brought up by
Chuck. I believe the relevant question is: Does dicetest record all
rolls generated by the RNG, irrespective of whether those rolls are
subsequently played or not? I presume the answer is yes -- it's hard
to imagine how or why one would have programmed dicetest otherwise.
If that presumption is correct, then Kit's suggestion, that Tom's
entry-from-bar data could be skewed by certain entries never being
played, would not be applicable as an explanation of the small
over-frequency of doubles present in Patti's data.
-- Ole Hoegh Jensen
Stephen Turner
Robert-Jan Veldhuizen wrote:
>
> Well, the best (if not the only) way to really "solve" this argument would be if
> the people who are convinced FIBS's dice are random would define a test with
> only two outcomes: 1.They're most probably right 2. They're most probably wrong.
>
> Stephen Turner's (in)famous bet springs to mind...;^)
>
I agree, but no-one's taken me up on it yet. Let me remind you/tell newcomers
of the conditions:
------------------------------------------------------------------------------
From: Stephen Turner <sr...@statslab.cam.ac.uk>
Subject: WIN 200 POUNDS ($300)!! (was Re: FIBS Rigged?)
Date: Fri, 23 Aug 1996 09:54:16 +0100
I challenge you, and anyone else, to the following proposition. We agree any
scientific test of FIBS dice which is verifiable and which will succeed only 1%
of the time if FIBS is unbiased. You pay me 10 pounds sterling (or US$15 if you
prefer). We conduct the test, with a disinterested referee if you like. If it
succeeds, I pay you 200 pounds (or US$300, respectively). If FIBS is really
biased, you should make money out of me pretty quickly. Put your money where
your mouth is.
-------------------------------------------------------------------------------
--
Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, England
"This store will remain open during modernisation. We apologise
for any inconvenience this may cause" Topshop, Cambridge
Stephen Turner
Chuck Bower wrote:
>
> I felt at the time (and still do) that this unlikely result [too many doubles
> in Patti's 5 million rolls] deserves another look. I believe someone
> (Stephen Turner) is doing that, but I have yet to see his work.
And you need wait no longer. Executive summary: FIBS dice appear fair on the
tests I carried out. Details follow.
First some background. Patti's sample of 5,530,616 rolls showed 924,319
doubles. If the dice were fair, this many doubles or more would only come up
1 in 530 times (0.189%), so there was some cause for concern.
Just before Robert-Jan Veldhuizen noticed this, the FIBS command 'matrix' was
also pointed out to me by someone else, and I had started collecting data
from it. Here is my original post:
-------------------------------------------------------------------------------
From: Stephen Turner <sr...@statslab.cam.ac.uk>
Subject: Re: 5 million rolls
Date: Tue, 29 Oct 1996 11:31:53 +0000
I too have been carrying out some tests of the FIBS dice in the last couple
of weeks, using the FIBS matrix command. You probably don't know about this
command because it's not on the list of commands, but it produces data not
only on the frequency of rolls, but on the frequency of each of the possible
1296 possible pairs of consecutive rolls. So seeing whether these data are
fair will test both whether some rolls come up more than others, and whether
some rolls are more likely than others to come up after specific rolls.
I won't bore you with the details of another statistical test, except to say
for the benefit of statisticians that it's a simple chi squared test on 1295
degrees of freedom, which I approximate by N(1295,2590). All everyone else
needs to know is that it comes out at the end with a number, which we hope
is near 0. A number greater than 2 indicates that the dice are biased in some
way (too many of one roll or of one pair of consecutive rolls at the expense
of another). A number less than -2 indicates that the dice are too good -- in
the sense that it looks as if they're fixed to try and get the right
proportions, and there's actually too little statistical variation.
I shall continue to collect more rolls until I have reached 10 million.
Overall, I think we can say that the jury is still out. There may be a
deviation from unskewed-ness, but if so, it is slight, and more data are needed
to be sure. I think that it probably wouldn't affect the game, UNLESS there
is some reason why any imperfections are more likely to occur at certain
times, such as during races, doubles after doubles, etc.
-------------------------------------------------------------------------------
In the end, the data took me longer to collect than I had hoped because I
didn't log on to FIBS very often. I collected 14 sets of data over nearly
6 months from 11th October to 5th April. This was a total of 10,593,121
rolls, so 10,593,107 pairs of consecutive rolls.
I can supply the data on request, but the chi-squared statistic gave an
answer of -0.355521, showing no evidence of bias. As I said above, this
test will check both whether some rolls come up more than others, and
whether some rolls are more likely than others to come up after specific
rolls. As a check, the number of doubles in the sample was 1763911, or
16.651%, fractionally less than expected, but well within normal statistical
variation (1.32 s.d.s from the mean, in fact).
Of course this doesn't check for every possible bias in the data, but it
checks for the most plausible and most widely suggested ones.
Any questions?
Chuck Bower
>hypothesis: That the Big_Brother data isn't complete!
>
>Not complete, you ask? In what way? Doesn't Big_Brother record the full
>games? Maybe not.
>
>Consider the following (all-too-familiar) scenario: You are stuck on the
>bar against a closed board, and your opponent starts peeling his
>checkers off. The situation is such that you MUST hit a shot to have a
>chance, either because you are stone cold gammoned if you don't or
>because your opponent doesn't need a gammon to win the match.
>Eventually, you enter. What do you do? You don't play the move -- you
>resign! We would have to check it out, but my guess is that when this
>happens Big_Brother doesn't record that last entering dice roll or the
>entrance which was never made. Note that if you had stayed on the bar,
>the roll would have been recorded. Consequently, some of the entering
>numbers which should be in the data simply aren't there, while all of the
>flunking numbers are. Granted this only occurs occasionally, but it
>doesn't have to happen very often to cause the apparently skewed results
>Tom's survey got us.
My cat woke me up at 3 AM with the following observation: isn't
there another kind of "resignation" which is even more common than the
one Kit mentioned? It goes like "double--pass". This can occur with
checkers on the bar (by either/both sides).
Both Kit's theory and this modification would likely happen more
often for a five point board than with fewer points made (for different
reasons, maybe).
Unfortunately now I have a bigger problem--convincing people my cat
figured this out...
Ole Jensen
bo...@bigbang.astro.indiana.edu (Chuck Bower) writes:
> [...] isn't there another kind of "resignation" which is even more
> common than the one Kit mentioned? It goes like "double--pass".
> This can occur with checkers on the bar (by either/both sides).
>
> Both Kit's theory and this modification would likely happen more
> often for a five point board than with fewer points made (for
> different reasons, maybe).
How would "double-pass"es skew the data? Since one must double before
rolling, no dice rolls go unrecorded in this case. Kit's scenario is
different, because a roll that was actually produced by the server
gets left out of Big_Brother's data.
And btw, as Tom's reply to Kit's suggestion shows, the resign happened
more often for three and four point boards than for five point boards.
In fact, with Tom's revised data, the five point case is now the only
one that has any noticable discrepancy (about 2.8 standard deviations).
-- Ole Hoegh Jensen
Chuck Bower
In article <yvtlo6x...@iris.cl.cam.ac.uk>,
Ole Jensen <oh...@cl.cam.ac.uk> wrote:
>bo...@bigbang.astro.indiana.edu (Chuck Bower) writes:
>
>> [...] isn't there another kind of "resignation" which is even more
>> common than the one Kit mentioned? It goes like "double--pass".
>> This can occur with checkers on the bar (by either/both sides).
>>
>> Both Kit's theory and this modification would likely happen more
>> often for a five point board than with fewer points made (for
>> different reasons, maybe).
>
>How would "double-pass"es skew the data? Since one must double before
>rolling, no dice rolls go unrecorded in this case. Kit's scenario is
>different, because a roll that was actually produced by the server
>gets left out of Big_Brother's data.
>
This sounds familiar. I recall someone trying to explain skewed
number of doubles by arguing that doubles are more likely to end the
game. I think I may have fallen into a similar trap... No, I mean
"my cat" screwed up. No "fishy treats" for one week!
>And btw, as Tom's reply to Kit's suggestion shows, the resign happened
>more often for three and four point boards than for five point boards.
>In fact, with Tom's revised data, the five point case is now the only
>one that has any noticable discrepancy (about 2.8 standard deviations).
>
On this point, I'm not sure what you say is relevant. I think it
is the percentage effect that is important and not the raw numbers.
(Sorry, but I don't have the data in front of me to check this... shame,
shame). There were fewer cases studied with a five point board, as
compared to the four and three point boards. It seems to me what should
be compared are the ratios (games ended by resignation with checkers on
the bar) divided by (total games in the study) as a function of numbers
of home board points closed. For example if there were 10,000 rolls where
a checker was on the bar with a 5 point board of which 100, were resigned
with the floater (apparently on roll) and 20,000 games studed with a four
point board (otherwise similar conditions) of which 150 ended in similar
type resignations, we'd both be right. Am I making any sense here?
Stephen Turner
OK, I'll analyse Tom Keith's data with the Woolsey Correction:
>
> Points Open observed expected variance
> 1 5010/16947 5178.3 3596.0
> 2 10928/19655 10919.4 4853.1
> 3 14325/19127 14345.3 3586.3
> 4 15066/16960 15075.6 1675.1
> 5 12340/12681 12328.8 342.5
----- ----- -----
57669 57847 14053
(57847-57669)/sqrt(14053) = 178/118.5 = 1.5
This is well within normal amounts of randomness. The first row is a bit out,
but the other rows are now very close to their theoretical answers. It looks
as if Kit has hit the nail right on the head once again.
Ole Jensen
bo...@bigbang.astro.indiana.edu (Chuck Bower) writes:
> I recall someone trying to explain skewed
> number of doubles by arguing that doubles are more likely to end the
> game. I think I may have fallen into a similar trap...
Yes, if you were thinking along the more-likely-to-end-a-game line, I
think that *is* a trap. As an analogy, consider the expected
distribution of heads and tails in a "game" that simply consists in
throwing a coin repeatedly until a head shows up. It is easy to
calculate that the expected frequency of heads is still exactly 1/2.
> >And btw, as Tom's reply to Kit's suggestion shows, the resign happened
> >more often for three and four point boards than for five point boards.
> >In fact, with Tom's revised data, the five point case is now the only
> >one that has any noticable discrepancy (about 2.8 standard deviations).
>
> On this point, I'm not sure what you say is relevant. I think it
> is the percentage effect that is important and not the raw numbers.
I believe my statement is true even when percentages are considered.
In any case, what is really relevant is whether the corrected data
still give cause for concern about the fairness of the dice. My own
conclusion, based on the corrected data, is that only the case of a
five point board shows any discrepancy worth talking about. At 2.8
standard deviations it is not too unlikely to be a simple fluke, but
it is significant enough that it is worth thinking about possible
causes.
-- Ole
Robert-Jan Veldhuizen
On 04-apr-97 10:34:28, Phill Skelton wrote:
PS> In the happy world of data analysis where I spend most of my days,
PS> any effect of less than 3 standard deviations is ignored. They come up
PS> far to often.
With a normal distrubution and a z-value of -3 or +3 you're talking about 13
times out of 10,000. You call that "far too often" ? I think there's some
misunderstaning here. Confidence levels are usually chosen in the 0.1 to 5%
region, if I'm informed correctly by my study books.
PS> When you get to 4 SD you get interested,
My tables dont even go that far...they stop at z=3.69, where you can be 99.99%
sure of the outcome of your test.
PS> but need more
PS> data. When you get to 5 SD you have a result that is worth something,
PS> but not until then. I would not think that 2.65 SD was at all
PS> significant.
Well I wonder where you get these values from. Maybe some terms are interpreted
wrongly here ?
--
Zorba/Robert-Jan
Robert-Jan Veldhuizen
On 04-apr-97 09:31:07, Phill Skelton wrote:
PS> <Sarcasm mode ON>
PS> But the Big Brother matches are almost entirely those played by the top
PS> ranked players, and they are the people conspiring with Marvin to fix
PS> the ratings system. It's the low rated players that the RNG picks on...
PS> <Sacrasm mode OFF>
This is exactly the kind of remarks that should be avoided...
PS> These data fit the expectations of a random distribution pretty well.
No. Some quick calculations show the opposite. See other posts.
--
Zorba/Robert-Jan
Daniel Murphy
I'd like to single out this one sentence which gre...@tribeca.ios.com
(Greycat Sharpclaw) wrote ...
>Here we have some hard data that suggests a dice bias, and which
>significantly *agrees* with the earlier (less precise) experiment in
>the nature of the bias... it's seems harder than it should be to get
>off the bar.
... and suggest that regardless of whether *analysis* suggests a small
bias in the dice, such bias is *not* what any of our skeptics believe they
have noticed in play.
We've now seen Tom Keith's original statistics of games recorded by Big
Brother, and those figures revised to account for games ending with a
resignation but no move:
A B C D E F
Points Entry (*/36) Entry (*/36) Expected Entry B-D C-D
Open , Original Data Revised Data (3/36)
1 10.59 10.64 11 -0.41 -0.36
2 19.91 20.02 20 -0.09 +0.02
3 26.89 26.98 27 -0.11 -0.02
4 31.95 31.98 32 -0.05 -0.02
5 35.03 35.03 35 +0.03 +0.03
I'm rather skeptical that the differences from expected results as
reported in columns E or F above are so large that *it is this
difference* that anyone really notices while playing. I think
it's much more likely that we remember rolls that matter more, or
sequences of rolls that strike us as unusual, but in fact are
statistically utterly ordinary.
Daniel "No, I haven't noticed that I've been fanning 11.25% of the time,
not 11.11% of the time, on a 2-point board" Murphy
--
_______________________________________________________
Daniel Murphy | San Francisco | rac...@cityraccoon.com
Monthly tourneys in San Mateo: See www.gammon.com/bgbb/ for details
and some excellently annotated matches. On-line: telnet fibs.com 4321.
Lawrence J. Gier
This is all very well but tell me how statistics is going to answer
the question that FIBS might be training a program and giving the
program a number of random rolls to choose from in order to evaluate
game strategies? Until you answer this, all stats on this subject
are of secondary interest at best. (How's that for ranting, Daniel???)
On Sat, 05 Apr 1997 12:26:19 +0100, Stephen Turner <sr...@cam.ac.uk>
wrote:
>--
>Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
> Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, England
> "This store will remain open during modernisation. We apologise
> for any inconvenience this may cause" Topshop, Cambridge
Lawrence J. Gier
Peter Nau
Andy Germain wrote:
>In response to problems (real or imagined) with software random number
>generators, I am developing a product. It is a Hardware Random number
>generator, based on a truly chaotic physical process. It is intended
>to be completely unpredictable and unguessable.
>
>It is is targeted primarily at commercial uses, such as generating
>random keys for RSA encryption, but I expect it will also be useful
>for games such as BG.
>
>Anyway, if the FIBS community and the FIBS operators are interested, I
>would like to offer a beta model to FIBS at no charge.
Hey, Andy, I've got hardware random number generators, too. I call them
"dice." ;-)
Chris Wilson
In article <3347ddbf...@news.kdsi.net>, ljg...@kdsi.net (Lawrence J.
Gier) wrote:
>This is all very well but tell me how statistics is going to answer
>the question that FIBS might be training a program and giving the
>program a number of random rolls to choose from in order to evaluate
>game strategies? Until you answer this, all stats on this subject
>are of secondary interest at best. (How's that for ranting, Daniel???)
How many times are ignorant fools going to ask questions like this, when
the answer has been before them smack dab in the middle of their eyes. FIBS
is a psychological experiment, not a training program. I advise Lawrence to
go to his local university and do a computer search of research journals
with the keywords "backgammon" and "FIBS" and he will find out the truth.
Chris, Marvin_Gardens on FIBS
--
------------------------------------------------------------------------
| Chris Wilson "Why is med school such hard work?" |
|------------------------------------------------------------------------|
| http://www.iei.net/~wilson/work/biz.html for web design |
| http://www.iei.net/~wilson/boots.html for trading |
|------------------------------------------------------------------------|
| If you're bored enough to read this, you're bored enough to visit my |
| home page at <http://www.iei.net/~wilson> |
------------------------------------------------------------------------
Stephen Turner
Lawrence J. Gier wrote:
>
> This is all very well but tell me how statistics is going to answer
> the question that FIBS might be training a program and giving the
> program a number of random rolls to choose from in order to evaluate
> game strategies? Until you answer this, all stats on this subject
> are of secondary interest at best.
>
Yes, there are clearly all sorts of paranoid ramblings that can also account
for the data.
Robert P. Smith
> OK, I'll analyse Tom Keith's data with the Woolsey Correction:
> >
> > Points Open observed expected variance
> > 1 5010/16947 5178.3 3596.0
> > 2 10928/19655 10919.4 4853.1
> > 3 14325/19127 14345.3 3586.3
> > 4 15066/16960 15075.6 1675.1
> > 5 12340/12681 12328.8 342.5
> ----- ----- -----
> 57669 57847 14053
>
> (57847-57669)/sqrt(14053) = 178/118.5 = 1.5
>
> This is well within normal amounts of randomness. The first row is a bit out,
> but the other rows are now very close to their theoretical answers. It looks
> as if Kit has hit the nail right on the head once again.
>
> --
> Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
> Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, England
The first row has a statistic of (5178.3-5010)/sqrt(3596.0) = 168.3/59.97 =
2.8066
This is definitely "a bit out", with a two-tailed probability of occurance
of <0.5%.
I recognize that Kit Woolsey's correction may account for some of the
discrepency between the original Big Brother data and the assumption of
randomness, but I am not willing to say that the data are therefore
entirely consistent with the random hypothesis.
(1) We have to accept that the Woolsey correction always holds for
resignations that occur when men are on the bar (they only occur after the
roll occurs, and they always occur only if the roll is successful in
bringing at least one man in.)
(2) Current observations for the specific case of 1 point open are pretty
unlikely. I know that events with probabililty <0.5% do occur in 1 out of
200 observations, but I would prefer to see further investigation before I
accept that random chance explains these data. I don't know what this
further observation might consist of, since it is hard to imagine a larger
and better data set than the Big Brother data.
Before these data were available, there were statements such that "My money
says that when you have done this for, say, 5000 samples, the results will
be within two standard deviations of the norm. Anybody willing to bet
otherwise?" -- Kit Woolsey. Are you now willing to accept 2.8066 standard
deviations as being consistent with randomness?
Rob Smith
Greycat Sharpclaw
Meow, all...
There is an allegation that rac...@best.com (Daniel Murphy) wrote:
>A B C D E F
>Points Entry (*/36) Entry (*/36) Expected Entry B-D C-D
>Open , Original Data Revised Data (3/36)
>1 10.59 10.64 11 -0.41 -0.36
>2 19.91 20.02 20 -0.09 +0.02
>3 26.89 26.98 27 -0.11 -0.02
>4 31.95 31.98 32 -0.05 -0.02
>5 35.03 35.03 35 +0.03 +0.03
>I'm rather skeptical that the differences from expected results as
>reported in columns E or F above are so large that *it is this
>difference* that anyone really notices while playing. I think
>it's much more likely that we remember rolls that matter more, or
>sequences of rolls that strike us as unusual, but in fact are
>statistically utterly ordinary.
Agreed... as I stated in an earlier post, any process that _seems_ too
random is probably not... truely random processes don't seem random to
all but the most careful observers by their nature.
But to summarize my view on the data gathered to date: I believe
1. there _may_ be a bias in the dice. I stress _may_, as opposed to
_is_.
2. any bias is small. In reality, most real dice have biases in the
order we're talking about.
Patti Beadles
In article <3347ddbf...@news.kdsi.net>,
Lawrence J. Gier <ljg...@kdsi.net> wrote:
>This is all very well but tell me how statistics is going to answer
>the question that FIBS might be training a program and giving the
>program a number of random rolls to choose from in order to evaluate
>game strategies? Until you answer this, all stats on this subject
As someone who has spent a lot of time staring at the processes running
on fibs.com lately, and carefully monitoring memory utilization CPU
usage, let me assure you that there are no processes of this caliber
running on the machine.
-Patti
Kit Woolsey
.com>: <33459B...@bkgm.com> <33467E...@cam.ac.uk>
<smith-ya02408000...@news.u.washington.edu>
Organization: Netcom On-Line Services
Distribution:
Robert P. Smith (sm...@ieng.washington.edu) wrote:
: Before these data were available, there were statements such that "My money
: says that when you have done this for, say, 5000 samples, the results will
: be within two standard deviations of the norm. Anybody willing to bet
: otherwise?" -- Kit Woolsey. Are you now willing to accept 2.8066 standard
: deviations as being consistent with randomness?
: Rob Smith
The point is that you are now looking at a subset of entries from the bar.
Does this mean that you are changing your claim to non-randomness only vs
5-point boards, an after-the-fact modification of your original claim now
that you have seen the data? We are starting to get ridiculous. I am
sure that if I analyzed the data carefully I could come up with other
things which were over 2 standard deviations away from the norm (such as a
5-4 roll following a 4-3 roll), but that would mean nothing. If the
entries from the bar were 2.8 standard deviations from the norm for all
entries then it might be worth looking into. As it is, the overall
results are well within 2 standard deviations from the norm, as I
predicted, so in my opinion there is little reason to follow this further.
Kit
Stephen Turner
Kit Woolsey wrote:
>
> The point is that you are now looking at a subset of entries from the bar.
> Does this mean that you are changing your claim to non-randomness only vs
> 5-point boards, an after-the-fact modification of your original claim now
> that you have seen the data?
I'm with Kit on this one. The hypothesis was formulated as all rolls from
the bar. You can't change it after seeing the data. If you want to formulate
a new hypothesis having seen the data, you have to go and collect a new set
of data to test it on. [Aside: unfortunately too many statistics courses
concentrate simply on how to test the data. They ignore the underlying
philosophy of the classical scientific method. Unfortunately in this case
the philosophy is so fundamental that one cannot design any experiment or
test any hypothesis without knowing it. In brief, any test which is
formulated after seeing the data can never prove anything].
I'm reminded, probably unfairly, of a post a couple of years ago on the
subject of dice. It seems hard to believe, but the post appeared to be
serious. The author had noticed that certain rolls came up much too often
in games. For example, in one game, maybe 2-5 occurred half a dozen times
in just 20 rolls. These rolls were called "hot spots". But the hot spot was
different for each game.
--
Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, England
Peter Fankhauser
Patti Beadles wrote:
> There is a large database of saved matches on http://www.gammon.com/
> ... look for the Big Brother matches. It should be a relatively
> simple programming exercise to walk through all of the games, find
> positions where someone is entering from the bar, count the valid
> rolls, and keep track of whether or not he entered.
I've done that a while ago, and indeed it showed that the dice on
fibs show no bias with respect to that. More precisely, I've
counted all positions where a player needs to enter against a
4pt board or against a 5pt board (39060 positions). If the
player managed to enter I added 36/20 for the 4pt board case
and 36/11 for the 5pt board case, which should add up to
the number of investigated positions (btw. this test was once
suggested by Stephen Turner). The final sum was 38365.4. This
is a tad smaller than expected. I suspect the reason for this is that
sometimes a player doesnt get the full 3 rolls for entering against
a 5pt board, because the opponent has closed the board earlier.
funk
Phill Skelton
Robert P. Smith wrote:
>
> Before these data were available, there were statements such that
> "My money says that when you have done this for, say, 5000 samples,
> the results will be within two standard deviations of the norm.
> Anybody willing to bet otherwise?" -- Kit Woolsey. Are you now
> willing to accept 2.8066 standard deviations as being consistent
> with randomness?
But what is the total no of standard deviations away from the norm
for the whole dataset? It is not reasonable to just pick the one
result that best supports your idea.
If you took 10,000 observations, you would get some that were over
4 sigma from the norm with a purely random sample - that doesn't
mean that those aberrant observations are due to non-random effects.
Phill
Robert-Jan Veldhuizen
On 05-apr-97 01:22:39, Tom Keith wrote:
[snip]
TK> Points Open Games Resigned With
TK> a Checker on the Bar
TK> 0 5
TK> 1 37
TK> 2 126
TK> 3 155
TK> 4 113
TK> 5 52
TK> 6 12
TK> Total 500
TK> If we assume that all these games represent rolls that enter (probably
TK> not quite true), then the previous totals can be revised as follows:
Indeed not true, for sure. If 5 games were resigned with *all* points still
covered (so a fair hitting chance), then it could well be that many more of the
games with some points open were resigned *before* rolling.
Consider also the fact that 12 games were resigned with *all* points open, and I
think we cannot longer trust these data at all, corrected or not.
Guessing about errors in your data to correct them is not the way to do a proper
scientific test.
--
Zorba/Robert-Jan
Robert-Jan Veldhuizen
On 05-apr-97 17:32:13, Stephen Turner wrote:
ST> OK, I'll analyse Tom Keith's data with the Woolsey Correction:
I'm surprised that you analyze data that are humanly "corrected", based on some
assumptions which are not at all evident.
ST> This is well within normal amounts of randomness. The first row is a bit
ST> out, but the other rows are now very close to their theoretical answers.
ST> It looks as if Kit has hit the nail right on the head once again.
I can't find this very scientific, I'm sorry to say. You shouldn't have an
opinion about "the right outcome" of a test if you want to do it right.
I just consider Tom's data as unusable if it hasn't got all rolls in it.
--
Zorba/Robert-Jan
Stephen Turner
Robert-Jan Veldhuizen wrote:
>
> I'm surprised that you analyze data that are humanly "corrected", based on some
> assumptions which are not at all evident.
>
and again:
> Guessing about errors in your data to correct them is not the way to do a
> proper scientific test.
Fair point. I'll try and be clearer.
There are some games in which the game is resigned with men still on the
bar in the way we've discussed. If we assume that ALL of these were resigned
because the person on the bar entered and contact was broken, then the data
are insignificantly different from the theoretical answer assuming the
hypothesis of unbiased dice. That's what my previous post was about.
Now we don't know how many of the resignations were in fact of this sort --
our intuition says most of them, but let's not assume that. The only claim
I'm making is that if enough of them were resigned in the above way, there
isn't enough evidence to reject the hypothesis of unbiased dice. So the raw
data (in terms of this many entrances, this many failures and this many
resignations) don't provide enough evidence to reject the hypothesis of
unbiased dice, which is the strongest statement that a statistician is ever
prepared to make.
Ole Jensen
Robert-Jan Veldhuizen <veld...@xs4all.nl> writes:
> TK> If we assume that all these games represent rolls that enter (probably
> TK> not quite true), then the previous totals can be revised as follows:
>
> Indeed not true, for sure. If 5 games were resigned with *all*
> points still covered (so a fair hitting chance), then it could well
> be that many more of the games with some points open were resigned
> *before* rolling.
Agreed. But since we don't know how many, it seems reasonable to do
the analysis pretending that an entering roll was rolled in all of the
resigned games, except for the 5 where this isn't possible. We are
trying to see at which confidence level the data allows us to reject
the hypothesis that the dice are completely fair; therefore, to the
extent that the data are incomplete, we must give "the benefit of the
doubt" to the hypothesis. In this case that means counting as many
entries from the bar as the data allow.
> Consider also the fact that 12 games were resigned with *all* points
> open, and I think we cannot longer trust these data at all,
> corrected or not.
I don't find it so strange that a few games were resigned with all
points open. These will occur sometimes, when the player bearing out
has managaged to take off all checkers but one, and the opponent still
has one or more checkers on the bar. The opponent then rolls (against
a 0 point board), misses the blot, and resigns without completing the
move.
> Guessing about errors in your data to correct them is not the way
> to do a proper scientific test.
The problem is that these incomplete data are still the best we've
got. We are not guessing to correct the data, but merely trying to
see what conclusions can be reasonably drawn from the data, taking
their incompleteness into account.
-- Ole Hoegh Jensen
Richard Nelson
except for those overseas, all relevant parties are now in batf custody
on conspiracy charges, thanks all for your cooperation
"This redistribution of wealth is more tricky than I thought" - Dennis Moore
Phill Skelton
Robert-Jan Veldhuizen wrote:
>
> On 04-apr-97 10:34:28, Phill Skelton wrote:
>
> > In the happy world of data analysis where I spend most of my days,
>
> With a normal distrubution and a z-value of -3 or +3 you're talking > > about 13 times out of 10,000. You call that "far too often" ? I think
> there's some misunderstaning here. Confidence levels are usually
> chosen in the 0.1 to 5% region, if I'm informed correctly by my study
> books.
The reason we ignore anything with less than 3 sigma is that with 8000
odd data sets, and more being generated all the time, quite a few
spurious +/- 3 sigma significances appear. Admittedly, the FIBS data
isn't really comparable to this sort of thing, but these things *do*
happen.
What would be more convincing if is someone now collects another set
of data, and the analysis of that also shows the same bias. Don't know
if anyone has already done this.
A 2.8 (or whatever it was) sigma significance is interesting, and shows
that the FIBS dice probably *are* skewed, but it is far from conclusive.
Phill
Peter Fankhauser
Robert P. Smith wrote:
>
<referring to too few entering rolls against 5pt boards -PF>
> This is definitely "a bit out", with a two-tailed probability of occurance
> of <0.5%.
>
for the observation that (slightly) less rolls enter against a 5pt
board than expected that 5pt boards tend to become 6pt boards?
AFAIK, the test assumes that a 5pt board stays a 5pt board infinitely
long. This is not the case. Sure, resigns and double/pass might
add little more, but the "instability" of 5pt boards seems to
be the most compelling reason.
Hoping not to have made my misconception of probability theory too
obvious,
funk
Peter Fankhauser
Upon 6th thought or so, this hypothesis is of course rubbish.
Having overcome one of my misconceptions of prob-theory,
funk
Peter Fankhauser
Robert P. Smith wrote:
> The first row has a statistic of (5178.3-5010)/sqrt(3596.0) = 168.3/59.97 =
> 2.8066
>
> This is definitely "a bit out", with a two-tailed probability of occurance
> of <0.5%.
>
Well, just for fun I've kept an SGI busy during the weekend with
(a preliminary version of) my homegrown bg-nn, playing 500.000
matches and counting the number of enters against a five point
board (for the sake of completeness, I use drand48() as random
number generator).
The enter/dance ratio wanders quite a lot, even after
more than 250.000 positions. For example, for
259907 positions, I get only 78801 enters vs 79416 expected enters
(79416-78801)/sqrt(55150)=2.62 - again a "bit out", ain't it?
(and even beyond that there're often more than 2.5 standard deviations).
However, for the final number of 635296 positions I get
193706 enters vs 194118.2 expected
(194118.2-193706)/sqrt(134804.3)= 1.12.
So my conclusion is that 2.8 standard deviations for the fairly
small sample of 16000 positions is not at all unnatural. I guess,
if you just run some simulations rolling a specific
number with two dice you will get such large deviations eventually.
funk