Odds of 3 consecutive 2 & 1?
Anne O'Rexic
Michael Petch
On 03/01/10 12:54 AM, in article
W2Y%m.21381$Ym4....@text.news.virginmedia.com, "Anne O'Rexic"
<postm...@127.0.0.1> wrote:
> http://img194.imageshack.us/img194/7453/bnucheat.jpg
Odds of getting 3 2-1's (or any SPECIFIC non double) In a row are 5831:1
against. Probability is (2/36*2/36*2/36) or 1 in 5832.
If your instinct says that - it shouldn't happen because 5831:1 is not very
likely, I can only say that it would be a problem if it never happened as
well. I did a study of about 10,000,069 regular rolls (Regular rolls are any
roll that wasn't the first roll of a game) using GnuBG and Mersenne Twister
(Default dice algorithm). I had GnuBG play 38571 11ptrs against itself. The
result are here:
http://www.capp-sysware.com/analysis/gnubg-10millrolls-11ptrs-mt.txt
There is a chart at the bottom where it shows how many times 2-1 was rolled
consecutively (including 3 in a row). In 10,000,069 rolls it happened 1795
times or about 1 in every 5571 rolls. The two tailed p-value for this was
about 5%. Anything higher than 1% is considered good. This means that
getting 1795 2-1's 3 times in a row in 10,000,069 likely would have occurred
if the source of rolls was random.
Over time the more you play the more likely you are going to see what you
believe are unusual events actually occur. In GnuBG (Or Extreme Backgammon)
these occurrences are likely to happen around the expected frequency over a
large sample of rolls.
tc...@lsa.umich.edu
You would probably have noticed if it had been three consecutive instances
of any other roll (double 6's or 5-3 or ...). If we assume that in an
average game, both players roll the dice 18 times, then you should expect
to observe three consecutive occurrences of the same roll every ten games
or so. (I'm not counting cases where I roll 2-1, my opponent immediately
rolls 2-1, and I roll 2-1 again right after that. If that counts then you
should expect to see one or the other happen once every five games or so.)
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
muratk
>
> <postmas...@127.0.0.1> wrote:
> >http://img194.imageshack.us/img194/7453/bnucheat.jpg
>
> Odds of getting 3 2-1's (or any SPECIFIC non double) In a row are 5831:1
> against. Probability is (2/36*2/36*2/36) or 1 in 5832.
>
> If your instinct says that - it shouldn't happen because 5831:1 is not very
> likely, I can only say that it would be a problem if it never happened as
> well. I did a study of about 10,000,069 regular rolls (Regular rolls are any
> roll that wasn't the first roll of a game) using GnuBG and Mersenne Twister
> (Default dice algorithm). I had GnuBG play 38571 11ptrs against itself. The
> result are here:
>
> http://www.capp-sysware.com/analysis/gnubg-10millrolls-11ptrs-mt.txt
>
> There is a chart at the bottom where it shows how many times 2-1 was rolled
> consecutively (including 3 in a row). In 10,000,069 rolls it happened 1795
> times or about 1 in every 5571 rolls. The two tailed p-value for this was
> about 5%. Anything higher than 1% is considered good. This means that
> getting 1795 2-1's 3 times in a row in 10,000,069 likely would have occurred
> if the source of rolls was random.
A lot of work that accomplishes nothing in regards to gnubg's cheating
or not.
More useful experiments maybe to have gnubg play 38571 11ptrs against
other
robots, once using Mersenne Twister and once using other robots' dice
rollers,
and observe for anything unexpected.
Even then a human's experience will be very different, in part because
all
robots are alike in skill and style.
The opposite of random is predictable. Thus the only valid test of
cheating
by the robots would be to observe if its dice rolls are predictable or
not.
Personally, I never made a prediction against gnudung as specific a
rolling
2-1 three times in a row but bets can be made against similarly high
odds by
making more generalized predictions such as one side not rolling
anything
higher than a 3 for the next six rolls, etc.
It would only take a few such predictions coming through before
bettors
defending rigged bots start shitting in their pants... ;)
Let's all remember once more that rigged robot defenders have never
been
able to put their money where their mouth is, on this issue... :)
MK
muratk
> In article <W2Y%m.21381$Ym4.14...@text.news.virginmedia.com>,
>
> Anne O'Rexic <postmas...@127.0.0.1> wrote:
> >http://img194.imageshack.us/img194/7453/bnucheat.jpg
>
> You would probably have noticed if it had been three consecutive instances
> of any other roll (double 6's or 5-3 or ...). If we assume that in an
> average game, both players roll the dice 18 times, then you should expect
> to observe three consecutive occurrences of the same roll every ten games
> or so. (I'm not counting cases where I roll 2-1, my opponent immediately
> rolls 2-1, and I roll 2-1 again right after that. If that counts then you
> should expect to see one or the other happen once every five games or so.)
This makes it a little easier to understand but add nothing more in
terms
of proof that gnudung doesn't cheat.
The magic roll can be 4-3 instead of 2-1 and it has to occur at the
magic
moment instead of at just any moment during the game, etc...
But let's skip all that. What your saying is this: "Too bad it
happened to
you on the first game. If you had gone on to play 9 more games, it
would
not have happened again"...
And you get away with this bullshit simply because nobody can possibly
have
enough time to prove that every first instance of an unlikely sequence
will
not happen again during the following games any more than
statistically
expected.
Again, all one has to do is bet a dollar against one in five hundred,
one
in two thousand, one in six thousand, etc. odds and hit a few of them
before mathshitters start shitting in their pockets... :))
MK
tc...@lsa.umich.edu
muratk <mu...@compuplus.net> wrote:
>Let's all remember once more that rigged robot defenders have never
>been able to put their money where their mouth is, on this issue... :)
This is the part of your challenge that I was most interested in taking
you up on, but you were unwilling to say ahead of time exactly what kind
of predictions you would make and how often you would make them, so I
couldn't calculate my expected payoff to see if I would make enough money
to make it worthwhile.
>Personally, I never made a prediction against gnudung as specific a
>rolling 2-1 three times in a row but bets can be made against similarly
>high odds by making more generalized predictions such as one side not
>rolling anything higher than a 3 for the next six rolls, etc.
Ah, now this is interesting! I don't recall your getting this specific
before. How many times during a game, on average, do you expect to be
able to make a prediction of this precise form? That is,
Side X will not roll anything higher than Y for the next Z rolls,
where Y <= 3 and Z >= 6?
postm...@127.0.0.1
>In article <W2Y%m.21381$Ym4....@text.news.virginmedia.com>,
>Anne O'Rexic <postm...@127.0.0.1> wrote:
>>http://img194.imageshack.us/img194/7453/bnucheat.jpg
>
>You would probably have noticed if it had been three consecutive instances
>of any other roll (double 6's or 5-3 or ...). If we assume that in an
>average game, both players roll the dice 18 times, then you should expect
>to observe three consecutive occurrences of the same roll every ten games
>or so. (I'm not counting cases where I roll 2-1, my opponent immediately
>rolls 2-1, and I roll 2-1 again right after that. If that counts then you
>should expect to see one or the other happen once every five games or so.)
Actually, just looking at that screen capture I realise I got lumbered
with 4 2&1's in six rolls.
Anyone want to do the maths on that?
Michael Petch
On 04/01/10 12:19 PM, in article gnf4k5dn2k3r4uepp...@4ax.com,
"postm...@127.0.0.1" <postm...@127.0.0.1> wrote:
>
>
> Actually, just looking at that screen capture I realise I got lumbered
> with 4 2&1's in six rolls.
>
> Anyone want to do the maths on that?
Simple Math sure. 4 2-1's in 6 rolls would be:
(6 choose 4) * (2/36)^4*(34/36)^2 =
15*(1/18)^4*(17/18)^2 = 7845.96
Probability of rolling specifically 4 2-1's in 6 rolls Is approximately 1 in
7855 rolls. Not a whole lot higher than 3 in a row.
Michael Petch
(Double or Non Double as Tim described it) It is about 1 in 510. And if you
use Tim's example of a game being average 18 rolls for each player (and you
view each players rolls independently) then you'd expect to see this happen
about 1 in every 14 games.
On 04/01/10 12:51 PM, in article C76794EE.21343%mpe...@capp-sysware.com,
Walt
> If you follow the math more and reduce it to seeing ANY roll 4 times in 6
> (Double or Non Double as Tim described it) It is about 1 in 510. And if you
> use Tim's example of a game being average 18 rolls for each player (and you
> view each players rolls independently) then you'd expect to see this happen
> about 1 in every 14 games.
Or in other words, "unusual sequences are quite common". That's because
there are so many unusual sequnces that something unusual is bound to
come along before long.
The fact is that you can take any four rolls and calculate the
probability of getting those exact four rolls in that order and arrive
at the same number as for consecutive 2-1.
//Walt
Michael Petch
On 04/01/10 3:10 PM, in article
wHt0n.6282$o06....@en-nntp-08.dc1.easynews.com, "Walt"
<walt_...@SHOESyahoo.com> wrote:
>
> The fact is that you can take any four rolls and calculate the
> probability of getting those exact four rolls in that order and arrive
> at the same number as for consecutive 2-1.
>
That was not the question that was asked, and I don't dispute that all! I
didn't say anything to the contrary. 2 specific questions were posed, I
answered both questions as asked.
muratk
> In article <211809cb-81cb-4a8a-a37c-00e6ba8f0...@v25g2000yqk.googlegroups.com>,
>
> muratk <mu...@compuplus.net> wrote:
> >Let's all remember once more that rigged robot defenders have never
> >been able to put their money where their mouth is, on this issue... :)
>
> This is the part of your challenge that I was most interested in taking
> you up on, but you were unwilling to say ahead of time exactly what kind
> of predictions you would make and how often you would make them, so I
> couldn't calculate my expected payoff to see if I would make enough money
> to make it worthwhile.
I thought you weren't in this for the money... :)
But when betting money proportionate to the odds, it won't matter what
kind of predictions I make and how often, will it..??
You need to consider that I want to make money also and am not willing
to give you an edge.
If all works out as you all claim, we will both break even.. :))
> >Personally, I never made a prediction against gnudung as specific a
> >rolling 2-1 three times in a row but bets can be made against similarly
> >high odds by making more generalized predictions such as one side not
> >rolling anything higher than a 3 for the next six rolls, etc.
>
> Ah, now this is interesting! I don't recall your getting this specific
> before. How many times during a game, on average, do you expect to be
> able to make a prediction of this precise form? That is,
>
> Side X will not roll anything higher than Y for the next Z rolls,
>
> where Y <= 3 and Z >= 6?
I had specifically stated that I would make complex predictions,
scenario
like predictions if you will, which could lead to the predicted
results
in more ways than one and inquired about any software tools I could
use
to make such betting practical.
In the above example, the prediction can come true by any series of 6
dice rolls made of any combination of numbers 1, 2 and 3.
I have no idea how often I may be able to make any kind of prediction
on
a per game basis. I don't know what's the significance of this either?
How would it matter if I don't make any predictions for 5 games and
then
make 3 predictions in a single game?
I don't know if you will answer but let me be nice and give you a big
hint ;) most of the time there will be only one such bet per game and
later and earlier in the game. If my prediction fails, I may get to
make
another one/s yet before the end of the game, but if I succeed, after
that point on the game kinds of switches to "autopilot", leaving very
little more to predict.. :)))
Have fun assessing your expected payoff... ;)
MK
tc...@lsa.umich.edu
I'm not into *backgammon* for the money. Testing crazy claims is another
matter.
>But when betting money proportionate to the odds, it won't matter what
>kind of predictions I make and how often, will it..??
It matters because of the variance. Too small a number of trials and
anything can happen.
>You need to consider that I want to make money also and am not willing
>to give you an edge.
>
>If all works out as you all claim, we will both break even.. :))
Ah, well, then you don't *really* want to make money. You have to offer an
apparent edge to me in order to get me to play. Why else would I bother
wasting my time proving to you what I already know to be true, that you're
an idiot?
postm...@127.0.0.1
Thanks for that; so are you saying that in the space of 6 rolls I
experienced not only a 1-in-5832 event but a 1-in-7855 event?
(Bearing in mind we're talking about "what good is that" 2 and 1
rolls?)
tc...@lsa.umich.edu
<postm...@127.0.0.1> wrote:
>On Mon, 04 Jan 2010 12:51:58 -0700, Michael Petch
><mpe...@capp-sysware.com> wrote:
>>(6 choose 4) * (2/36)^4*(34/36)^2 =
>>15*(1/18)^4*(17/18)^2 = 7845.96
>>
>>Probability of rolling specifically 4 2-1's in 6 rolls Is approximately 1 in
>>7855 rolls. Not a whole lot higher than 3 in a row.
Probably you should have computed the probability of *at least* four
2-1's in 6 rolls.
>Thanks for that; so are you saying that in the space of 6 rolls I
>experienced not only a 1-in-5832 event but a 1-in-7855 event?
In fact, in the space of *any* 6 rolls you experience an event with
probability 1 in 34 million (at least).
Michael Petch
On 05/01/10 3:40 PM, in article
4b43bfe7$0$502$b45e...@senator-bedfellow.mit.edu, "tc...@lsa.umich.edu"
<tc...@lsa.umich.edu> wrote:
> Probably you should have computed the probability of *at least* four
> 2-1's in 6 rolls.
>
Wasn't what was asked for specifically, nor did I think it would be too
large a difference. If they would have asked I could have provided that too.
1 in 7664 chances to get 4 or more 2-1's in 6 rolls. About 1 in 498 rolls
for any roll (doubles and non doubles) appearing 4 or more times - which
translated into about 1 in every 13.83 games (based on an average of 18
rolls per player per game, and player rolls being looked at independently).
postm...@127.0.0.1
>In fact, in the space of *any* 6 rolls you experience an event with
>probability 1 in 34 million (at least).
Yep, nicely blurred, you're not a politician are you?
How about five doubles in seven rolls? Anyone want to do the maths on
that?
postm...@127.0.0.1
Even better:
http://img695.imageshack.us/img695/9459/bnucheatagain2thisisget.jpg
how about the lack of a single 5 in 8 rolls when that's the key die?
What's disturbing is that these "anomalies" are occurring in the very
few matches I'm playing? It isn't as if I'm playing 40,000 matches
and picking the odd roll?
WTF is going on with GNUBG?
postm...@127.0.0.1
Here's another one, the chances of being stuck on the bar 14, yep 14,
times in a row?
http://img141.imageshack.us/img141/6203/bnucheatagain3thisisget.jpg
tc...@lsa.umich.edu
tc...@lsa.umich.edu
<postm...@127.0.0.1> wrote:
>What's disturbing is that these "anomalies" are occurring in the very
>few matches I'm playing? It isn't as if I'm playing 40,000 matches
>and picking the odd roll?
The probabilities that you're asking for are not the right ones to capture
what you're confused about. What you should be asking for is the probability
of the following: "Given that I find the following set of events surprising
[list here everything that you would find worthy of commenting on], what is
the expected number of such events I would find in X games?" If you wait
until you observe something surprising and then ask for the probability
*after the fact*, then you're committing the "politician" fallacy. You
need to specify ahead of time what you're looking for and wait for it to
happen.
David C. Ullrich
What's going on is you're looking at what happened, noticing
something funny, and computing (or asking about) the probability
of that particular thing happening. That's cheating, because
you don't specify what sort of "anomaly" you're looking for
in advance.
Hence the relevant probability is the probability that there will
be _some_ "anomaly" in n rolls. That probability is much higher
than any of the numbers that have been calculated here, because
there are so many different possible "anomalies". It would be
very surprising to play a "very few" matches and never notice
_something_ "surprising".
Tim's comment was not blurring, it was right on the money.
_Any_ given sequence of n rolls is very unlikely. I just
tossed a coin 20 times. I got THHTHHTTHTHHTTHTHHHH.
The probability of getting THHTHHTTHTHHTTHTHHHH
in 20 coin tosses is less than one in a million...
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
postm...@127.0.0.1
>The probabilities that you're asking for are not the right ones to capture
>what you're confused about. What you should be asking for is the probability
>of the following: "Given that I find the following set of events surprising
>[list here everything that you would find worthy of commenting on], what is
>the expected number of such events I would find in X games?"
Given that I observed that GNUBG rolled itself five doubles in seven
rolls, what is the expected number of such an event I would find in
(a) 1 game, (b) 10 games, (c) 30 games?
Given that I observed that I was unable to roll a single 5 in 8 rolls,
what is the expected number of such an event I would find in (a) 1
game, (b) 10 games, (c) 30 games?
tc...@lsa.umich.edu
<postm...@127.0.0.1> wrote:
>Given that I observed that GNUBG rolled itself five doubles in seven
>rolls, what is the expected number of such an event I would find in
>(a) 1 game, (b) 10 games, (c) 30 games?
>
>Given that I observed that I was unable to roll a single 5 in 8 rolls,
>what is the expected number of such an event I would find in (a) 1
>game, (b) 10 games, (c) 30 games?
You've got the question phrased almost right now...the only distinction
you still need to make is whether the 1/10/30 games *includes* the one
where you made the observation, or whether it *doesn't* include it.
Given that you observed five out of seven doubles, what is the probability
of observing five out of seven doubles in 1/10/30 games *including* the one
you observed it in? Obviously, the probability is 1: we are given that you
observed it.
Given that you observed five out of seven doubles, what is the probability
of observing five out of seven doubles in 1/10/30 games *not including* the
one you observed it in? This is a standard calculation of the type Michael
Petch was showing you how to do. The probability is low, and to confirm
this, you should examine your games *starting from now on*, to see if you
get an unusually high number of five doubles in seven rolls. It's no fair
including the games that you examined *before* formulating your hypothesis
that there was something wrong with the dice, and it's also no fair, when
you start observing games *from now on*, suddenly saying that other kinds
of "anomalies" (like dancing 10 times in a row) are occurring. If you want
to show that there is a bias in the dice, you have to say ahead of time what
kinds of anomalies you're looking for, and stick firmly to that script.
Otherwise, you're playing politics and not doing science.
tc...@lsa.umich.edu
>If you want to show that there is a bias in the dice, you have to say
>ahead of time what kinds of anomalies you're looking for, and stick firmly
>to that script. Otherwise, you're playing politics and not doing science.
By the way, just in case you think I'm blindly parroting the "party line"
and would not accept anything as evidence of biased dice no matter how
strong it was, let me mention a recent case where someone demonstrated
conclusively that there was something wrong with the dice on a certain
backgammon website:
http://backgammoncamp.wordpress.com/2009/10/11/safe-harbor-games-dice/
This is a stellar example of how to do this kind of thing correctly. If
you think there is something wrong with GNU's dice, then you would do well
to study Womack's example carefully.
Michael Petch
Thanks Tim and David for your posts - they are bang on.
On 07/01/10 3:03 PM, in article
4b465a48$0$512$b45e...@senator-bedfellow.mit.edu, "tc...@lsa.umich.edu"
<tc...@lsa.umich.edu> wrote:
> By the way, just in case you think I'm blindly parroting the "party line"
> and would not accept anything as evidence of biased dice no matter how
> strong it was, let me mention a recent case where someone demonstrated
> conclusively that there was something wrong with the dice on a certain
> backgammon website:
>
> http://backgammoncamp.wordpress.com/2009/10/11/safe-harbor-games-dice/
>
Just as an update to this the data is now at about 1.7 million rolls and I
have combined the rated room, Doubling Cube and Gammonzone room (All use the
fixed dice) into one analysis here:
http://www.capp-sysware.com/analysis/shgnewall36_stats.txt
If people are curious about the analysis on the data in the rooms that
haven't been changed here are the original ~580,000 regular rolls that made
it clear there was an issue.
http://www.capp-sysware.com/analysis/shgolddice_stats.txt
From a statistical perspective there is no comparison. The old dice were/are
bad. Most of the P-values for the data points are 0 (Nonsensical from a
randomness perspective). The one thing about the old dice on SHG though is
that your chances of rolling a 1,2,3,4,5,6 on any given die are
statistically fine. It that when the dice are laid end to end, the expected
patterns paint a picture of non randomness.
I have concluded that Doubles have been skewed to the low side, inflating
the expected non double sequences. Other analysis indicate the old dice on
SHG are likely random and fair to both players (but don't represent a 6
sided set of precision dice).
SHG is a great site, it has its growing pains and Jim Borror has been trying
to make every effort to fix the problems. SHG uses both the old set and new
sets of dice. Rooms tagged with Yellow dice use the statistically normal
dice, and the red dice use the old dice (Which have doubles about 9.2% of
the time rather than 16.67%). The old dice are preferred by Social players
(and social tournament groups) - as they appear to be "fairer" (less Jokers
in the way of doubled).
* Regular roll = any roll that was not first roll.
Michael Petch
On 07/01/10 4:16 PM, in article C76BB95A.21422%mpe...@capp-sysware.com,
"Michael Petch" <mpe...@capp-sysware.com> wrote:
> All use the
> fixed dice) into one analysis here:
OUCH I should have said:
" All use the
Statistically correct dice) into one analysis here:"
"Fixed" was a bad choice of terms. I meant "Fixed" in terms of them being
"corrected" not "Fixed" as being "manipulated". Sorry for that.
I also forgot to mention that Will Womack and I shared the workload in doing
this study, and I thank him for maintaining the blog posts on the subject
and all his work and input on the data collection. It was a very time
consuming task - especially when you factor in the time trying to explain
why the new dice appear fine (compared to the old). I am sure that Will and
I should probably buy shares in the hair club for men!
postm...@127.0.0.1
>Given that you observed five out of seven doubles, what is the probability
>of observing five out of seven doubles in 1/10/30 games *not including* the
>one you observed it in? This is a standard calculation of the type Michael
>Petch was showing you how to do. The probability is low, and to confirm
>this, you should examine your games *starting from now on*, to see if you
>get an unusually high number of five doubles in seven rolls. It's no fair
>including the games that you examined *before* formulating your hypothesis
>that there was something wrong with the dice, and it's also no fair, when
>you start observing games *from now on*, suddenly saying that other kinds
>of "anomalies" (like dancing 10 times in a row) are occurring. If you want
>to show that there is a bias in the dice, you have to say ahead of time what
>kinds of anomalies you're looking for, and stick firmly to that script.
>Otherwise, you're playing politics and not doing science.
Not my intention, honestly :-)
Some background; I've been playing computer versions of backgammon for
the best part of 30 years.
I started with a ZX Spectrum version and, horrified by the amazing
good fortune of the computer, purchased a very good disassembler which
enabled me to establish, fairly quickly, that the code was programmed
to cheat.
I could even state, before a match started, exactly when and why the
computer would cheat. For example, the code had a flag named
"matchstate", if that flag was negative then one of the user's dice
rolls was fixed at 1. So you'd be well on top and your dice rolls
were restricted to 1 1, 2 1, 3 1, 4 1, 5 1 or 6 1.
My first exposure to computer backgammon and the machine was cheating;
that stays with you, believe me. Of course, the cheating was quite
basic in those days.
Note: I've not suggested GNU is cheating; when I have some time, I'll
grab the source code and have a look.
I've simply asked for the odds of some v-e-r-y dodgy looking rolls.
And the 5 doubles in 7 rolls probability?
tc...@lsa.umich.edu
<postm...@127.0.0.1> wrote:
>Note: I've not suggested GNU is cheating; when I have some time, I'll
>grab the source code and have a look.
You will discover that GNU has an option to enable cheating dice. This
is not turned on by default, of course. I think it was put in to demonstrate
what it would be like if GNU really *were* cheating.
Thanks for mentioning your experience with cheating dice in the past.
You are hopefully aware that this experience may lead you to be overly
suspicious of GNU. If you are subconsciously biased towards thinking
that there may be something wrong, then you are likely to pick up on
"patterns" and "anomalies" when they occur and ascribe significance to
them. When no anomalies occur, you don't pay any attention, and fail
to factor in the "non-events" correctly when assessing the likelihood
of the anomalies.
It is extremely difficult for human beings to develop an accurate feeling
for true randomness. The book "Judgment Under Uncertainty: Heuristics
and Biases" by Tversky and Kahneman documents many instances of this.
Even experienced scientists can fall into this trap if they are not
paying attention. Here's a short article giving you a flavor for the
book (I hope you don't need a subscription to view this):
http://psiexp.ss.uci.edu/research/teaching/Tversky_Kahneman_1974.pdf
If you Google "Roshambot" then I think you will be able to find programs
that play rock-paper-scissors against you. The programs will probably
beat you a surprisingly high percentage of the time if you play against
them long enough. They pick up on your human biases rather accurately
and use them against you.
tc...@lsa.umich.edu
Michael Petch <mpe...@capp-sysware.com> wrote:
>SHG uses both the old set and new sets of dice. Rooms tagged with Yellow
>dice use the statistically normal dice, and the red dice use the old dice
>(Which have doubles about 9.2% of the time rather than 16.67%). The old
>dice are preferred by Social players (and social tournament groups) -
>as they appear to be "fairer" (less Jokers in the way of doubled).
This is amusing. It would be interesting to further tinker with the dice
to make them seem "even more fair." For example, one could bias the dice
to make consecutive rolls be less likely to be equal to each other. I bet
that such dice would be preferred by the social players even more.
I think I mentioned here before that on a Continental Airlines flight, there
was a backgammon game on the console that seemed to me to be cheating with
the dice *so as to favor the player*. There was no way, of course, to
collect enough data to be sure about this, but from a customer-satisfaction
point of view, such a "feature" does make a lot of sense.
postm...@127.0.0.1
>Thanks for mentioning your experience with cheating dice in the past.
>You are hopefully aware that this experience may lead you to be overly
>suspicious of GNU. If you are subconsciously biased towards thinking
>that there may be something wrong, then you are likely to pick up on
>"patterns" and "anomalies" when they occur and ascribe significance to
>them. When no anomalies occur, you don't pay any attention, and fail
>to factor in the "non-events" correctly when assessing the likelihood
>of the anomalies.
>
You are, of course, right.
I also play a pc vs human version of Spades (a card game). It's
partners so you end up cohabiting with a bot but hey ho.
The best bid you can make against the computer is nil since this gets
you 100 points........what you therefore don't need is the Ace of
Spades.
I get that very same card on probably 50% of deals.......given that
there are four players, I reckon I'm hard done by since the most
damaging bid I can make is, on every other occasion, denied to me.
The company who've written the software deny cheating but won't
release the source code........go figure?
Shocking.
tc...@lsa.umich.edu
<postm...@127.0.0.1> wrote:
>The best bid you can make against the computer is nil since this gets
>you 100 points........what you therefore don't need is the Ace of
>Spades.
>
>I get that very same card on probably 50% of deals.......given that
>there are four players, I reckon I'm hard done by since the most
>damaging bid I can make is, on every other occasion, denied to me.
This is a simple enough thing to test. Starting now, keep track of how
often you get the Ace of Spades. The MOST IMPORTANT THING is to be
absolutely anal about keeping track of EVERY DEAL you get. Repeat:
every deal. No excuses about how sometimes you're playing just for
fun and can't be bothered to track this particular game. Any excuses
you invent just introduce the possibility that you are biasing yourself
towards counting deals that are favorable to your cause and ignoring
those that aren't.
After you have tracked literally every deal (repeat: literally, literally
EVERY DEAL) you get for a while, look at your statistics. If it is true
that you're getting the Ace of Spades much more often (twice as often?)
than you should, then it shouldn't take too many deals to demonstrate
that. If you need help with the probabilities, post here.
Oh, one more thing...did I mention that you need to track EVERY DEAL?
muratk
> If you follow the math more and reduce it to seeing ANY roll 4
> times in 6 (Double or Non Double as Tim described it) It is
> about 1 in 510. And if you use Tim's example of a game being
> average 18 rolls for each player (and you view each players
> rolls independently) then you'd expect to see this happen
> about 1 in every 14 games.
Sorry for not paying attention to detail. I had said Chow's
comment was easier to understand because it was based on a
smaller number of games, but where do you guys get this "18
rolls per player per game" figure...? Did Chow pull it out
of his mathshitter ass...??
Already in 1998, I was observing that games against jellyshit
were lasting shorter than in real life and questioning why!
http://groups.google.com/group/rec.games.backgammon/msg/65b45243f420558d?dmode=source
In that article I was pointing out that in 100 games, average
rolls per game was 26.5 giving average rolls per player 13.25.
I have since commented time and again that while playing against
bots, including gnudung, games don't seem to lat as long since
the dice rolled seem to "plop into plce" (like bullshit)...
Do you all remember Patch's analysis of the 11 matches of 31
points and 10 matches of 33 points I had played against gnudung?
http://www.capp-sysware.com/analysis/murat/index.html
Total moves = 760 in 14 matches, averaging 53 moves per game or
26.6 moves per player per game.
We seem to be a problem here, "non"...?? :)
MK
muratk
> In article <6549e321-0459-4232-9d21-6d290afc4...@m3g2000yqf.googlegroups.com>,
>
> muratk <mu...@compuplus.net> wrote:
>>I thought you weren't in this for the money... :)
>
> I'm not into *backgammon* for the money. Testing crazy claims is another
> matter.
Same here. I wouldn't mind a bit spending all the time needed to stick
my crazy claims up your ass whenever you feel ready... :))
>>But when betting money proportionate to the odds, it won't matter what
>>kind of predictions I make and how often, will it..??
>
> It matters because of the variance. Too small a number of trials and
> anything can happen.
We don't have all day to prove that some alleged world-class robot is
actually a poor product of some sick mother fucking scum, do we...? ;)
>>If all works out as you all claim, we will both break even.. :))
>
> Ah, well, then you don't *really* want to make money.
That's right cocksucking matshitter, my claim is more honest than
yours...! :)
> You have to offer an apparent edge to me in order to get me to play.
Why...??
> Why else would I bother wasting my time proving to you what I already
> know to be true, that you're an idiot?
Your knowing it alone is not enough, prof, you need to prove it to me
and to the spectators... :))
MK
muratk
> On 05 Jan 2010 22:40:39 GMT, tc...@lsa.umich.edu wrote:
>
> >In fact, in the space of *any* 6 rolls you experience an event with
> >probability 1 in 34 million (at least).
>
> Yep, nicely blurred, you're not a politician are you?
You may be on to something there... :) I hear that six politicians
are worth half of a dozen mathshitters... :))
MK
muratk
> Tim's comment was not blurring, it was right on the money.
> _Any_ given sequence of n rolls is very unlikely. I just
> tossed a coin 20 times. I got THHTHHTTHTHHTTHTHHHH.
> The probability of getting THHTHHTTHTHHTTHTHHHH
> in 20 coin tosses is less than one in a million...
Here comes the math-kisser with his coins... :) Because he is
tooooo stupid to speak to the subject without some irrelevant
mathshit...
It's not always an issue of whether what you are saying is
correct mathematically (or whateverically) but it is also
an issue of whether what you are saying is pertinent to the
subject...
Too many math-oil peddlers and their ass-kissers here... :))
MK
tc...@lsa.umich.edu
muratk <mu...@compuplus.net> wrote:
>Sorry for not paying attention to detail. I had said Chow's
>comment was easier to understand because it was based on a
>smaller number of games, but where do you guys get this "18
>rolls per player per game" figure...? Did Chow pull it out
>of his mathshitter ass...??
Yes.
>Already in 1998, I was observing that games against jellyshit
>were lasting shorter than in real life and questioning why!
This is an interesting question. Did you ever try playing the games with
manually entered dice to see if the average game length changed?
muratk
>>Already in 1998, I was observing that games against jellyshit
>>were lasting shorter than in real life and questioning why!
>
> This is an interesting question. Did you ever try playing the games with
> manually entered dice to see if the average game length changed?
Almost 12 years ago.. I don't remember how I compared what but
somehow I had come to make that observation and it remained an
issue that bothered me ever since.
Maybe others can share their similar experiences/statistics??
MK
Paul
> I think I mentioned here before that on a Continental Airlines flight, there
> was a backgammon game on the console that seemed to me to be cheating with
> the dice *so as to favor the player*. There was no way, of course, to
> collect enough data to be sure about this, but from a customer-satisfaction
> point of view, such a "feature" does make a lot of sense.
> --
> Tim Chow
I believe that non-precision dice are seriously biased towards a 6.
The pips are drilled in making the 1 side the heaviest, giving 6's
significantly more often than precision dice would.
I don't think this is a problem commercially, because 6 is a good
number in most dice games. Yes, that means that your opponent will
also get 6's more often. However, the bias still might have a good
effect commercially because players are more sensitive to their own
dice than their opponents' dice. Furthermore, dice games are often
played in a non-competitive context where players actually want their
"competitors" to do well. (For example, a parent of a young child.)
Paul Epstein