It's not a fallacy; it's that using a purely probabilistic approach here is not warranted. It requires some Bayesian reasoning.
The main difference is in the SIDS case, you have a sample size of 2.
In the Postle case, we have hundreds of hands he is involved in; dozens of sessions. Multiple instances of where he makes incredibly good reads, contrary to optimal theoretical play. (the article also notably does not detail any incorrect reads).
We also have a good understanding of how playing lots (50 %) of hands should affect his variance, yet he seems to come out of almost every session a winner. He should be coming away a loser a lot more.
The idea in popular culture that great poker players can "read" other players like a book is overblown, and a bit obsolete. Modern live players have learned to conceal their intentions much better than in the past. Yes some players may still have slight tells, but unless his opponents' eyes are bulging out of their head like a cartoon wolf when they get a flush, that can only account for a slight edge.
So sure, if you take a purely probabilistic approach and say "well, somebody somewhere could go on that sort of run", then it looks like a fallacy. But if you take the other data: That he doesn't play in other cash games, that he cashes almost every time despite a high variance style, that he makes theoretically unsound plays at critical times and they always turn out to be correct, that other legendary players do not have these sorts of results...then it seems to me there is a very high likelihood that he is cheating.
The main difference is in the SIDS case, you have a sample size of 2.
In the Postle case, we have hundreds of hands he is involved in; dozens of sessions. Multiple instances of where he makes incredibly good reads, contrary to optimal theoretical play. (the article also notably does not detail any incorrect reads).
We also have a good understanding of how playing lots (50 %) of hands should affect his variance, yet he seems to come out of almost every session a winner. He should be coming away a loser a lot more.
The idea in popular culture that great poker players can "read" other players like a book is overblown, and a bit obsolete. Modern live players have learned to conceal their intentions much better than in the past. Yes some players may still have slight tells, but unless his opponents' eyes are bulging out of their head like a cartoon wolf when they get a flush, that can only account for a slight edge.
So sure, if you take a purely probabilistic approach and say "well, somebody somewhere could go on that sort of run", then it looks like a fallacy. But if you take the other data: That he doesn't play in other cash games, that he cashes almost every time despite a high variance style, that he makes theoretically unsound plays at critical times and they always turn out to be correct, that other legendary players do not have these sorts of results...then it seems to me there is a very high likelihood that he is cheating.