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[pineapple888]

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Dude, I'm sorry, but this is out of left field.

I stand by my post, and will really have to stop there with any further odds discussions.


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Just let me know whats wrong with my calculation and I will correct it.

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Dude, it's not your calculation, it's your methodology.

But in other news.

I AM WRONG ABOVE.

JOSEM IS RIGHT.

The methodology should be to go hand-by-hand, look at the cards, define what "perfect play" means for that hand for Villain, and look at the chance that he does that with just blind luck, then multiply all those together.

My apologies. [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img]

[knappis]

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Dude, it's not your calculation, it's your methodology.

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NP m8. But I like my methodology since it focuses on the statitsical properties behind the mechanisms generating the bet/fold pattern.

[flight2q]

Either Potripper cheats or not, it's 50%. I'm not saying this is good math, but it's as good as what Josem and pineapple were arguing over.

knappis, you are much closer to the truth. First, you had some problem entering the numbers into calculator or something. The expression calculates to 1/12,650 [lol, I had problems too]. The odds are much less severe than this, of course. One factor is you need to figure out a fair way to deal with the fact that we don't know if there were other hands where Potripper did vpip while a JJ+ hand was out there. Another factor is that the JJ+ range was chosen on the basis of examining the data. Then there is the data selection bias problem.

Your approach is not perfect, but at least it is trying to compare the probability of events with and without knowledge of hole cards.

And people, please stop saying I'm 99.999% sure. You can't say that without an a priori distribution.

[Tartufo]

I'm mainly lurking at this site, but I just wanted to let the people who invest time in sorting this out and post their findings and summaries know it is very much appreciated.

Just one suggestion: can the HH's be formatted? This would not only shorten the threads but also make the evidence more accessible and perspicuous...

[nath]

Can we edit the images in this thread so they don't break it

[Josem]

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One factor is you need to figure out a fair way to deal with the fact that we don't know if there were other hands where Potripper did vpip while a JJ+ hand was out there.

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I wanted to apply this methodology to something relatively short and simple first.

I next intend on applying it to some HU hand histories, where we can see 100% of the hands held by the cheaters' opponent.

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Another factor is that the JJ+ range was chosen on the basis of examining the data. Then there is the data selection bias problem.

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Correct. The difficulty is that we don't know what the opponent's strategy is. The only way to determine their strategy is to look at what they do, and use that to create some mathematically "testable" rules.

Eg, if villain has AK vs QQ, does he fold? probably not...also, if villain has AA vs opponent's KK, obviously he wouldn't fold, but this is not inconsistent with the meaning behind the general rule.

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And people, please stop saying I'm 99.999% sure. You can't say that without an a priori distribution.

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What is a priori distribution?

[flight2q]

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What is a priori distribution?

[/ QUOTE ]An a priori distribution is an assumed or known probability distribution for the object of study in advance of looking at the data.

For example, tonight I hear a wolf howling. About 10% of nights this is so. I don't say, okay I'm 90% convinced that there's a full moon tonight (even without a model of the relationship between howling and full moons!).

But suppose I knew that wolf always howls when there is a full moon, and sometimes at other times. But I still don't know how likely it is that there is a full moon tonight. Now I add an a priori distribution that moon is full 1/28th of the time. Now I can deduce a posteriori that there is a 35.7% probability that the moon is full based on my knowledge of wolves, moons, hearing the howling, and assuming I have no other information such as whether I heard howling last night.

[Josem]

So what would a priori distribution be for a heads up game vs one of the alleged cheaters?

[flight2q]

Say a few weeks ago you sat down at a table with Graycat HU, and after the session you asked yourself did that guy see my holecards. The a priori distribution is whatever probability you thought he had of seeing your hole cards before you sat down with him. 1 in a million? 1 in a billion? or whatever.

Then you analyze the session to adjust that a priori probability based on the data. But in doing so, you need to realize that your data is biased, because you don't do this analysis after every session. But if you sit at a table with Graycat right now and play until he quits you (or play until a prescribed number of hands, and throw out the sample if he quits you earlier), and analyze based on those results, good or bad, then you won't have selection bias.

[knappis]

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knappis, you are much closer to the truth. First, you had some problem entering the numbers into calculator or something. The expression calculates to 1/12,650 [lol, I had problems too]. The odds are much less severe than this, of course. One factor is you need to figure out a fair way to deal with the fact that we don't know if there were other hands where Potripper did vpip while a JJ+ hand was out there. Another factor is that the JJ+ range was chosen on the basis of examining the data. Then there is the data selection bias problem.

Your approach is not perfect, but at least it is trying to compare the probability of events with and without knowledge of hole cards.

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Thanks. My mistake. It was pretty late and I was tired [img]/images/graemlins/blush.gif[/img].

The correct calculation is as follows:

(4/25)*(3/24)*(2/23)*(1/22) = 1:12650

If we also factor in the likelihood that folding 4 hands of 25 is part of villains distribution of bet/fold patterns we would know the odds of this to happen by chance. The problem is that we don't kow his distribution of bet/fold patterns but I would say the likelihood is probably pretty high, maybe 33%ish. That would give odds in the 50k range indicating that similar "coincidences" probably happens every day in online poker.