statistical tests to show that online poker is not rigged

[ianlippert]

Ok it took me a while to find it, but here is an RGP post from 2002, scroll down a bit to hand analysis, 2nd post from top.

http://www.playwinningpoker.com/rgp/02/

Not even 40K hands and everything seems to be pretty normal.

[AaronBrown]

Actually, it does not show that everything is normal. There is a serious deficit of Aces and Kings, more than can be plausibly explained by chance. If this is really a random sample of hands, then the site has serious problems.

The trouble with this post is that it gives no consideration to standard deviation. It shows the actual and expected numbers of various types of hands, and concludes that they look pretty close. But over 37,867 hands, things should be a lot closer than this.

For example, there were 2,264 paired starting cards. 2/13 or 348 of them should have been AA or KK. In fact, only 297 were. That may not seem to be a huge difference, but if everything is random, getting 297 or fewer AA or KK out of 2,264 paired hands would happen only one time in 780.

That's not conclusive proof that the site has random number generation problems, but I wouldn't tout it as evidence everything is working perfectly. Combined with the strong deficit of AKs, it looks funny.

Of course, there are a lot of card combinations cited, and some of them are going to differ from their expected frequency. But AA, KK and AKs are among the most important starting hands. Missing 67 of them, even over 37,867 hands, could make a significant difference. If you are a 2 BB/100 hand average player, you expect to make 757 BB over this many hands. Your AA, KK and AKs might average 5 BB wins eacy, the deficit of 67 means you lose about half your expected profit.