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Message: [QUOTE="zachvac, post: 688074, member: 26306"] Really wish I remembered stat, but wikipedia refreshed my memory. How about a test to see just how likely it is that poker is rigged. Null hypothesis: AA(expected) = AA(actual) Pokerstars: AA(expected) = 1497.14 AA(actual) = 1491 Total hands = n = 330869 P = .0045063152 P(hat) = .0045248724 One proportion Z-test z = (P(hat) - P)/sqrt((P(1-P))/n) z = 0.159 P = .8736 In English, if we assume poker is not rigged, there is an 87.36% chance of seeing these results or stranger (further away from the mean). If this were to be under 5%, we would say it was sufficient evidence to show that online poker is indeed rigged. Since you cannot prove a negative, you can simply say that this data fails to reject the null hypothesis that poker is not rigged. There is no reason to believe that poker is rigged based on this data. For full tilt, I'll spare all the calculations, but P=.061, 6.1% chance of seeing data like this or stranger. This is awfully close to say we are bordering on being able to claim that full tilt is rigged by giving less action hands (or perhaps because the sample is skewed towards better players, they don't need to give action to get them to keep coming back... I'm kidding :)) For ipoker: P=0.69 = 69%. Total: P=.2816=28.16% Note that for example 28.16% has nothing to do with the fact that there's a 28% sites are on the up-and-up. It's just that IF poker sites are not rigging, and we did this sample an infinite amount of times, we'd see this much variation from the mean 28% of the time, certainly not low enough to conclude the site is rigged. Full tilt's 6.1% is rather low though. As mentioned, usually 5% is the threshold of suspicion, and almost all confidence intervals (ever see the + or - after the Presidential polls? Most likely they use a 95% confidence interval, which would get a P of 5%). So it's low enough to raise suspicion. Note that just because the number of hands at full tilt is lower does not make this number less reliable, because n is factored into the z formula. As n gets higher for the z to stay the same the mean has to get closer and closer to the expected mean. There is also the assumption with this test of independence that p*n > 10 and (1-p)*n > 10. The first is basically the expected is > 10 because p can be expressed as expected/n, and the multiplication cancels the n's out. All expected values are over 10, so the samples can be said to be independent. Or normal, or whatever that's supposed to conclude. Also I believe there's a restriction about the sample being a sufficiently small sample (at most 1/10 or something) of the entire population. I think we can safely conclude that CC members have not been involved in over 1/10 of all hands at pokerstars, full tilt, ipoker, or all combined. So in conclusion there is no evidence whatsoever that pokerstars or ipoker are rigging their sites, and there's no evidence there's a mass collusion against the poker players by the sites. BUT, there is some evidence that full tilt gives less AA hands than it should. But also remember this is hardly even close to conclusive proof. If we took 17 samples of this size from full tilt, we'd expect to see this one even if they weren't rigged. More data would surely help determine if they're RNG is in fact rigged intentionally or not to give players less AA hands than it should. [/QUOTE]

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