From your other comments, it is clear that you will not allow yourself to be wrong here no matter what anyone says to explain it to you.
that's how DNA evidence works, after all.
Just saying something is extremely unlikely to happen by itself does not constitute proof, after all it just could be that that extremely unlikely thing happened. You'd need to corroborate that with something else to meet the burden of proof that is normally used in a criminal case.
Different legal systems have different standards of evidence before being allowed to consider a defendant proven guilty, as far as I'm aware nobody ever got convicted on math alone. There always was something else.
sure it does.
statistics are a measurement of something in the real world. in the poker example you are measuring the possibility of a series of hands succeeding in a given episode of play. In court you are measuring the possibility of a given DNA sequence occurring by chance.
What distinction are you drawing between the statistical certainty in poker vs. the statistical certainty in court (or in medicine)?
There doesn't need to be anything else, if you have a sufficient statistical level of certainty.
In most cases there is corroborative evidence, but nobody thinks it's necessary when the DNA matches.
That is literally what it constitutes.
Sure, the chance is high. But if there is no conclusive evidence, then there's no conclusive evidence.
That might be enough for angry Twitter mobs, but I sure hope that it's not enough for court.
https://en.m.wikipedia.org/wiki/Sally_Clark
> Clark's first son died in December 1996 within a few weeks of his birth. Her second son died in similar circumstances in January 1998. A month later, Clark was arrested and tried for both deaths. The defence argued that the children had died of sudden infant death syndrome (SIDS). The prosecution case relied on flawed statistical evidence presented by paediatrician Professor Sir Roy Meadow, who testified that the chance of two children from an affluent family suffering SIDS was 1 in 73 million. He had arrived at this figure erroneously by squaring 1 in 8500, as being the likelihood of SIDS in similar circumstances. The Royal Statistical Society later issued a statement arguing that there was no statistical basis for Meadow's claim, and expressed concern at the "misuse of statistics in the courts".
There has been bad statistics in some completely different case. This argument uses statistics. We can conclude that this argument is also bad.
Consider if you had 1,000,000 people flipping coins. You'd expect one of them to flip 20 heads in a row. However, if you took the person who did it to court, you'd argue: it's highly unlikely this person could flip 20 heads in a row. They must be cheating!
I don't know enough about this case to say if it's correct, but OP is saying more than "dur people use bad statistics". They're saying it's the same fallacy. In the woman with the babies case, SIDS is rare, but in a country with millions of mothers it can happen to the same one twice. In this case, playing perfect hands is rare, but in a country of millions of players, you'd expect someone to, somewhere, maybe in a podunk town of small scale games.
Of course, the fallacy doesn't make forward predictions. If he continues to win improbably after he's been identified, then it's not that.
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.
I don't think that's the case.
Got a DNA match on a murder scene? Sadly a match isn't unique and several people can be matched.
Got your suspect caught on the crime scene? Might've just been at the wrong place at the wrong time.
A cop caught the suspect murdering? The cop might be the guilty one and just trying to frame an innocent.
This kind of statistic is as good as proof, proof isn't 100% reliable either.
Even if it's not given in mathematical form, common sense reasoning uses common sense statistics every day. You could always claim freak accident if that would not be the case.
If yes would you say that the chance of your being mistaken is higher or lower than one in 10^100s.
The widely shared preference for certain kinds of evidence over others has nothing to do with certainty and everything to do stubborn human biases.
CERN considers 5 sigma as the level where they are confident of announcing a discovery of new scientific result. 7 sigma for Higgs Boson. Statistical evidence against Mike Postle's game is stronger than that. It also only happens during streamed games with RFID chips in a single casino.
Either world's best player is playing for peanuts (relatively speaking) in single venue using high variance style without variance or he is cheating.