Okay, here's the deal: I've been playing on Pacific Poker for about seven or eight months now, mainly because it's the mother of all fish ponds. And I've been doing quite well. Got a SNG ROI of well over 30% with well over 50% at the 8$ 20 people SNGs which are my main source of income there. So I can't complain, right? Well ... Recently I did an extensive hand history analysis (if you play at Pacific you will understand how mindboggling this task is as their hand history support is a joke) and I came up with some troubling stats and numbers. Without further ado, here we go:

- Of the 70:30 hands (AK against AQ, KQ against KJ and so forth) I win about 55% in AI situations

- Of the 80:20 hands (AA against KK, QQ against 1010 and so forth), I win about 65% in AI situations.

- I hit a set on the flop about 7% of the time

- I pair on the flop about 18% of the time

Truth to be told, I've always had the impression that I'm getting sucked out way too often at Pacific but I ascribed that feeling to typical bad beat reaction. Now I'm not so sure. Yeah, I'm making solid money there, but ... I should be making a lot more, shouldn't I? Mind you, this is not a "online poker is rigged" kind of post ... I'm merely wondering about the probability of variance. I could understand if one or two of these stats were well below the average if another one or two were well above. But all of them? It just seems very odd to me and I'm having a hard time finding leaks when apparently I am getting my money in in the right spots.

Sample Size: About 800 SNGs and 200-300 MTTs. Not the largest of all sizes, I know, but with their software, it's hard to multi table effectively. I figure, however, it's large enough to evaluate.

Am I just dealing with a weird case of variance? Or is this perfectly normal? FYI: A friend of mine playing there with roughly the same ROI has surprisingly similar stats. We regularly share infos and try to plug leaks but came to the conclusion that we should have about 60-70% ROI if it weren't for this rather negative variance and that seems way, way off as well. Something just doesn't ring right here. Input is appreciated.

this can be easily calculated if you state your sample size for each of the numbers

It will also be believed a lot more if you have an actual database of hand histories that can be verified. A lot of people think they are not lucky because they remember the bad beats a lot more.

If an impartial party studied your data base, he would probably find many 70:30 hands where you won and forgot to include into your sample.

Yeah, your numbers suggest that you not analyzing your data correctly.

None of the statistics you cite are purely matters of mathematics, there can be slight differences depending on how you and others play. However, none of those differences are as large as the ones you describe.

If you have N examples of a situation in which you should win with probability p, you expect to win p*N and your standard deviation is [p*(1-p)*N]^0.5. So if you play 2,100 hands with a 70% chance of winning, you expect to win 0.7*2,100 = 1,470 times with a standard deviation of [0.7*0.3*2,100] = 21. If you win only 55%, 1,155 times, that's 315 fewer than expected. 315/21 = 15, so you're 15 standard deviations below the mean. The probability is close enough to zero to ignore. Either you counted wrong or something's wrong with the deal.

If you played on 140 of these hands and won 77 (55%) when you should have won 98 (70%), the standard deviation is 5.4, so you're 3.9 standard deviations below the mean. That's barely possible by luck (0.01% or 1 in 7,871). If you played 20 hands, and won 11 (55%) when you expected 14 (70%), the standard deviation is 2.0, so you're 1.5 standard deviations below the mean. The chance of that is 11%, or 1 in 9. So that's quite plausibly just bad luck.