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Mar 20, 1997, 3:00:00 AM3/20/97

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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

Mar 20, 1997, 3:00:00 AM3/20/97

to dh...@niteshift.com

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

Mar 20, 1997, 3:00:00 AM3/20/97

to

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 |

| fax : +31 (0)20 625 7435 The Netherlands |

+---------- It prevents everything from happening at once.-----------+

Mar 20, 1997, 3:00:00 AM3/20/97

to

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.

Mar 20, 1997, 3:00:00 AM3/20/97

to

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

Mar 21, 1997, 3:00:00 AM3/21/97

to

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

Mar 21, 1997, 3:00:00 AM3/21/97

to

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

Mar 21, 1997, 3:00:00 AM3/21/97

to

Richard McIntosh wrote:

>

> Stephen Turner wrote:

>

> > I don't know

> > what FIBS uses (marvin very sensibly hasn't published it)

>

> 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.

>

> 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

Mar 22, 1997, 3:00:00 AM3/22/97

to

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?

Mar 22, 1997, 3:00:00 AM3/22/97

to

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

Mar 22, 1997, 3:00:00 AM3/22/97

to

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

Mar 24, 1997, 3:00:00 AM3/24/97

to

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.

Mar 26, 1997, 3:00:00 AM3/26/97

to

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

Mar 26, 1997, 3:00:00 AM3/26/97

to

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

Mar 27, 1997, 3:00:00 AM3/27/97

to

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??

Mar 27, 1997, 3:00:00 AM3/27/97

to

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

Mar 27, 1997, 3:00:00 AM3/27/97

to

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

Mar 27, 1997, 3:00:00 AM3/27/97

to

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> |

------------------------------------------------------------------------

Mar 27, 1997, 3:00:00 AM3/27/97

to

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.

Mar 28, 1997, 3:00:00 AM3/28/97

to

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."

Mar 28, 1997, 3:00:00 AM3/28/97

to

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.

Mar 28, 1997, 3:00:00 AM3/28/97

to

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

Mar 29, 1997, 3:00:00 AM3/29/97

to

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

Mar 29, 1997, 3:00:00 AM3/29/97

to

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

Mar 30, 1997, 3:00:00 AM3/30/97

to

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?

Mar 30, 1997, 3:00:00 AM3/30/97

to

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

Mar 30, 1997, 3:00:00 AM3/30/97