This post is addressed to any of the high-stakes players that are convinced cheating took place on AP. Would any of you be interested in trying to transform your thought process which leads from the HHs to your conclusion into some kind of probability model? I am a professional mathematician whose research area is probability theory. I would be willing to work with you on trying to do this.
I have my doubts about the feasibility of this idea, since there are so many assumptions to be made, but I think it is worth at least an initial attempt. See my post
here for my initial comments on this subject.
If we focus for the moment on POTRIPPER, then what we need for this model are three things: (1) p_0 = the probability a randomly selected player from among all online players can see hole cards, (2) p_f = the probability that the HHs we have for POTRIPPER would look the way they do if POTRIPPER could not see hole cards, and (3) p_c = the probability that the HHs we have for POTRIPPER would look the way they do if POTRIPPER could see hole cards. According to Bayes Theorem, if these 3 quantities are given, then the probability that POTRIPPER could see hole cards, given the HHs, would be
p_0*p_c/[p_0*p_c + (1 - p_0)*p_f].
What I need from you, if you want to do this, is an estimate of p_f and p_c. That is, I would need you to walk me through the HHs -- once under the assumption there is no cheating and once under the assumption there is cheating -- and estimate all the probabilities of seeing the various actions that POTRIPPER took on the various streets.
This is the part where many assumptions would have to be made. In the end, whatever numbers we come up with will just be the opinions of the high-stakes players in this forum. But at least those opinions will be formulated numerically (possibly with some stated margin of uncertainty). If the opinions are expressed numerically, then someone who wants to raise an objection can be challenged to come up with their own numbers. They could not as easily get away with only addressing AP's lack of motive or appealing to the ubiquitousness of claims that online poker is rigged.
As for p_0, I have proposed to use p_0 = 1/(N + 2), where N is the total number of players who have ever played online poker. This is based on a well-established statistical model, so I think it is a reasonable place to start. We could, if you want, discuss other possibilities for p_0. But if we use my suggestion, then we would also need an estimate for N, and I would need your help coming up with that estimate.
If you would like to contact me privately, send email to
anonymous.investigator@yahoo.com