What is proof?

[borisp]

I spend a lot of my idle time criticizing the lack of "proof" involved in various religious or social arguments. Being a mathematician, I hold the notion of proof, and more generally the notion of logical rigor, in an almost sacred regard. I admit that I am dogmatic with respect to its efficacy.

However, the recent info regarding the Absolute Poker superuser #363, etc., has forced me to question what it means to prove something. I am compelled to believe the "preponderance of evidence" that exists here on 2+2, whereas prior to this fiasco, I would have probably been more skeptical.

Here is a link to catch you up: cliff notes

Have the 2+2 detectives proven that cheating has occurred? And in the event that they have, will 2+2 react accordingly?

P.S. David Sklansky, if you can find time in your day to comment, then I believe your message will be well recieved.

[PairTheBoard]

If you've studied it, how about giving us a summary of the evidence. When I tried wading through the thread a while back it looked to me like a lot of the evidence was "take our word for it, we've gone over it". If that's the case, we need to see the actual evidence those guys say they've gone over. The few hands I saw posted were not sufficient in themselves imo. Misclicks alone can acccount for a small sample. And a witch hunt mentality can account for a small group of people reporting on unseen evidence.

You mentioned "prepoderance of evidence". That's the proof needed in a civil case as I understand it. I believe they translate that to better than 50%, although I wonder if they really mean that. Anyway, it's a lot less than the "beyond a reasonable doubt" measure for a criminal case. Both of which are far less than the rigorous kinds of mathematical proof you are used to. I don't think either legal definition translates well to a Sklansky Probability number.

PairTheBoard

[borisp]

Yes, the use of the phrase "preponderance of evidence" was deliberate. I'll try to post a "rigorous" summary ASAP.

The point is that I am personally questioning my own standards of rigor. In doing so, I may be forced to accept certain "real world" versions of rigor that may be uncomfortably close to "Sklansky" versions of rigor.

[borisp]

The situation as I see it:

There were some allegations that various accounts on Absolute Poker (potripper, doubledrag, etc.) were able to see hole cards, during the play of hands.

This was (circumstantially) confirmed by various pokertracker hand histories, compiled independently among various high stakes 2+2'ers.

INDEPENDENTLY, they each showed various statistical anomalies, among them, "infinite aggression factor" on the river. This means that the villians never called, but rather chose to raise or fold, EVERY time, on the river. Furthermore, they were correct an inordinate amount of the time. Their earn rate was a statistical anomaly.

So be it. Perhaps the sun shines on every dog's ass (or so my dad says). This was the official response from AP.

Fast forward to present day. Turns out that a victim of the AP "superuser" account was suspicious at a final table of a 1000$ buyin tournament (where the alleged cheater won), and he emailed for a hand history. Instead of getting the usual hand history, he instead got an indecipherable excel file.

Ultimately, after a month or so of translation, this file proved to contain the hole cards of every single player in the tournament, up to hand #100+, or thereabouts. Furthermore, this file contained the IP addresses and emails of everyone who OBSERVED (not who played) these tables. Anyone with an ounce of initiative can find the compiled video on PXF.

This is all for your entertainment. The real evidence has been uncovered by various posters, and I encourage you to start here link to p5s

The reason for the new post is that the IP address/excel file info was not available until recently.

[tpir]

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The reason for the new post is that the IP address/excel file info was not available until recently.

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The IP excel sheet would be pretty damning evidence if it was legit. I suppose someone could have access to a customer service account and be able to fake the excel sheet, but it matching up with the weird play of hands and other circumstances is preponderanceville imo.

All that being said, I find it hard to believe AP didn't figure this out by looking at the HHs and the account. Maybe they know about it and are trying to sweep it under the rug quietly(?)

[Jamougha]

Rigorous mathematical proof is in a category of its own. In the real world you have probability, evidence and so on. Not 'proof' in the same sense.

[Drag]

No one bothered to make a really compelling case, but IMO it can be created quite easily.

Something along this line:
If we assume that there were no cheating, and we futher assume that the players in question played bad and should be losing at a rate of about -20PTBB/100 in NL, -3PTBB/100 in Limit, and they have less than avrage probarility of winning a tournament (if there were 1000 palyers it would translate to 1/3000 probability of winning it). Then we take all the hands that they played in NL >1000, Limit >1000, and take into account a tourney won, we'll get a probaility of such an event of bein much less than 10^(-8).

We need to take into account that there is less than 10^3 players who play at these stakes, and high-stakes on-line poker exists for ~4 years, so there were about 4*12*1000 ~ 10^5 month of play (it's better to reformulate it in terms of hands played, though). So the probability of such an anomaly is less than 10^(-3).
And I am taking very conservative estimates.
So we can falsify a hypothesis that they played honestly.

So, what we get is that probability of someone having such a run by sheer luck during all time of on-line poker existence is less than 10^(-3). For me it is very compelling.

There is additional information that could be incorporated which will lower this probability even further, like the evidence about individual hands play, but I can't see an easy way to do so.

[BTirish]

I've always liked Aristotle's way of putting it on this point.

"It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs." Nicomachean Ethics, Book I, ch. 3.

[borisp]

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I've always liked Aristotle's way of putting it on this point.

"It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs." Nicomachean Ethics, Book I, ch. 3.

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This is a good quote, one that I should keep in mind more often. I guess I am questioning what level of precision the nature of this subject admits?

I'm also interested in polling SMP for opinions, since I generally distinguish SMP from the rest of the 2+2 mob. Partly wondering if anyone else is as convinced as I am, and partly surprised that I am as convinced as I am.

[madnak]

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I guess I am questioning what level of precision the nature of this subject admits?

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It's sad that no real "proof" can be had where empirical disciplines are concerned. After all, logic can only derive conclusions from initial premises - in math, these initial premises (axioms) are both "obvious" and well-defined. Theoretically, it is possible to establish an empirical discipline as "perfect" as mathematics, but you would have to have a rigorous set of logical assumptions about the world that everyone agrees with (probably impossible). The issue of limited information in the real world also implies that definite conclusions will always be probabilistic conclusions (ie never "this is true" but always "this is n% likely to be true"), and that some conclusions can never be definite (due to a potentially infinite range of possibilities in many cases). Intuition is a much better approach in the real world.

I'm not interested enough in this particular case to study everything, but based on your summary the evidence seems damning. The behavior of the alleged cheaters is very unusual (and thus unlikely to be coincidental). This behavior is also consistent with cheating - I can't think of any other hypothesis that would explain it. From the look of things, there are no other plausible explanations being presented. Furthermore, the circumstantial evidence supports the cheating explanation. Finally, there is no way for the situation to be engineered (to frame the cheaters, for instance) - the information itself seems reliable.

To get at your original question - other than an outright admission of cheating, what more evidence could there possibly be in a case like this? As a rule of thumb, if the information we have represents the highest standard of evidence that we can realistically apply (given our technological means), that generally indicates a "very high" level of precision relative to the subject. All the bases appear to be covered in this case.