[furyion21]

First, by no means am I a high-stakes player involved in this whole debacle. I'm just a player who's read the various posts about the AP deal and reviewed some of the HHs given as proof of cheating.

That said, any reasonable poker player (I think) can give you approximated quantities for your variables.

a. p_0 is not 100% accurate in assessing p(cheating) because higher-stakes players have more to gain in terms of monetary reward; thus, the incentive to cheat among immoral individuals is higher than that of a randomly selected poker player. I don't quite know what variable would replace it.

b. p_f is approaching zero given some HHs, and is quite high given other HHs.
e.g. p_f approaches 0 given highly improbable calldowns with T high on a scary, scary board.
p_f approaches 0 given highly improbable actions of raise/fold on the river; never calls (calling down is fairly standard on the river, so calling would be closer to a higher p_f than either raising/folding.)

The difficulty is taking every single HH since the AP patch and averaging the p_f given all of the HHs (is this even correct?). Some plays this player makes are normal-ish , assuming he is making reads (correct or incorrect) and acting on them. Sometimes HU limit play can appear to be a bit donkish/crazy, when there is a sound logic behind them.

c. Conversely, I assume p_c is 1 - p_f.

Regardless of the actual p(cheating) number generated by this application of Bayes Theorem, as we all know, events with a probability of approximately 0 occur more often than we would estimate. Even an infinitesimally small % would leave more than enough room for it to be very feasible that 1 player out of a large population could be cheating.