99.99890581% chance that cheaters were operating on Absolute?

[Josem]

Dear Probability Gurus,

I'm just a lowly internet gambling/stt/bbv poster. i have no qualifications in statistics, so could someone please check my reasoning at http://forumserver.twoplustwo.com/sh...umber=12202343 and http://forumserver.twoplustwo.com/sh...umber=12202371 ?

Essentially, it is my contention that there is a logically provable 99.99890581% chance that players on Absolute Poker were able to see the cards of others. Am I right? Am I wrong?

I've also reproduced my posts below:

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Assumption: cheater plays with 90% VPIP.

In the 25 hands analysed by Adanthar (the first ones listed in the cliff notes) the cheater folds whenever another player - and only when another player - has AA, KK, QQ, JJ. There is another hand analysed, but it involves a re-raise squeeze, which is a slightly wider range, and we can ignore it for this analysis.


So - what are the chances that a player who plays 90% of hands will randomly fold the 4 precise hands that someone else has AA, KK, QQ, or JJ, and none others?

I think the mathematics can be written out like this:

.1^4 * .9^21

ie, it is .1 * .1 * .1 * .1 * .9* .9* .9* .9* .9* .9* .9 etc.
^--these are the four premium hands ^--these are the rest

chucking that into excel provides the following answer:

0.00109419% chance of occuring.

in other words, a 1 in 100,000 chance of occuring randomly.

hopefully this methodology is right. can someone who is smarter than me (ie, almost anyone) confirm or correct me?

does this then mean that we can say with 99.99890581% certainty that the cheater was cheating in these hands? the more i think about it, i think not, but i feel that there is a calculation somewhere here that would give us the probability that this was cheating - can someone who knows mathematics/statistics well chime in?

[i]incidentally, the figures vary a bit depending on what the cheater's VPIP is. if the VPIP is .95, then there is a 0.00021285% and a 99.99978715% chance respectively. if the VPIP is .8, 0.00147574% and 99.99852426%)

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in answer to my own question in bold, i think the following analogy is fair and reasonable. i've been thinking about this, and I am increasingly confident that if the cheater had a VPIP of 90%, then there is a 99.99890581% chance that he is cheating.


Let's say, hypothetically speaking, someone had a secret way to win the lottery (a 1 in 100,000 chance in this particular lottery). You say to this person, "prove it."

So, this person goes away, picks their numbers, and wins the 1 in 100,000 lottery.

Thus, either they won the lottery randomly (ie, it really was a 1 in 100,000 chance) or they cheated. 99.99890581% of the time they will have cheated.


I think the same thing applies here - because the cheater was accused before the data became available.

Obviously, it is not reasonable to accuse someone of winning the lottery of being a cheater after they have won the suspicious - at that time, the lottery win is in the past, and thus has a 100% chance of having occurred (it already did).

However, because the cheater was accused before the data became available - and we then tested the data on our existing hypothesis, I'm now confident, with a 99.99890581% certainty, that the accused cheater was actually cheating

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