As DrVanNostrin said, you are generating a misleading analysis by not utilizing all of your observations. You must not only use all the hands you observed, but also all aspects of those hands (not just the preflop anomaly). I think you
want to do that anyway. The preflop play is not what convinced the high-stakes players that cheating occurred. It was a combination of all the evidence that convinced them. I do not think they would have been convinced on the basis of this preflop play only. For that reason, your analysis does not accurately capture their reasoning process.
I also do not think you can avoid invoking some kind of prior probability. Before this scandal erupted, POTRIPPER was just another random online poker player. At that point (when there was no evidence) what was the probability he could see hole cards? I think I saw in the main thread that you were disputing the need for such a prior probability. But to illustrate its importance, suppose it was 0%. That is, imagine that somehow we had absolute certainty through whatever means that it is 100% impossible for anyone ever to see hole cards in online poker. In that case, the
only explanation for the HHs that were presented is that POTRIPPER is stupid and lucky.
There is a fairly common statistical method for getting a prior probability like this. Put yourself back in time before the scandal erupted. At that point, we had witnessed N people log in and play online poker since online poker was invented. (I do not know what N is, but maybe you can find some estimate of it.) Assume that none of them have ever been able to see hole cards. What is the probability that the next new online player we see will be able to view hole cards? A standard model says that the probability is 1/(N+2). The model I am referring to is described
here. Note that 1/(N+2), under this model, is the probability that POTRIPPER can see hole cards, calculated only on the basis that he is a random online poker player, without factoring in any evidence. The next step would be to factor in (all) the evidence in order to increase this probability.
There are two serious problems I see, which make me think that a statistical analysis might be a bit useless. First, I think it may be an intractable problem to incorporate ALL the evidence. Many assumptions would have to be made, and you run the risk of either making bad assumptions, or tailoring your assumptions to specifically generate the conclusion you want. Second, no matter what you do, someone will be able to question your methodology, your assumptions, your prior probabilities, etc. You will not be able to create a "bulletproof" analysis based only on statistics, which I assume is what you want.
From the main thread (
link):
[ QUOTE ]
I'll be honest, I haven't read every post in this newest thread, but what i've seen there hasn't been an attempt to unify the data. People are getting mathematically longwinded here with calculations that don't factor in EVERY PT stat.
It takes an understanding of poker, not statistics, to grasp this. Anybody that knows pokertracker well can see something isn't right with even a cursory glance at the data.
[/ QUOTE ]
Many of the high-stakes players are convinced beyond a reasonable doubt that cheating occurred. Their thought process which leads from the HHs to the conclusion of cheating is an intuitive one. I think the best you can hope to do with statistics is to (try to) model this intuitive thought process with a Bayesian analysis. I repeat that I think it may be intractable to do this, but if it were possible, and if it were done honestly, then it would capture the true arguments of these particular high-stakes players. Anyone who disputed the model would be directly contesting those arguments. Such an approach would probably be the one least likely to derail the discussion. However, I really think it would be very difficult if not impossible to do this.