Sorry for taking so much time to get back to this. Hollidays and all. I hope you all understand that this is just for fun and that IF a site wanted to fiddle with their shuffling algorithm, there are other, less obvious ways they could and would do it. IMO, the action hand argument is the most widespread, probably because it's the easiest to understand.
Dispelling the notion that big rake generating hands like AA or KK are more prevalent should go a long way toward silencing all but the most hard core conpiracy theorists. Take away their biggest weapon and they might actually have to learn something about the issue to continue the debate, something they are unlikely to be qualified or inclined to do.
Very few of us have a DB big enough on its own to prove or disprove anything about the frequency of a given hand but many who don't understand this might think that their library of 20,000 hands is a sufficiently large enough sample to do just that. I'm no statistician, but it seems to me that any such assertion is meaningless with anything less than 10 times that number. If anyone knows something about statistics and standard deviations I'd be happy to hear from them.
But there's a better more satisfying reason for conducting this experiment than using it to defuse ignorant assumptions based on scant evidence. Even if there is no actual calculated ill intent on the part of the poker sites
, it would be interesting to see just how good their RNG's and shuffling algorithms are. with just short of 400,000 hands we are deviating from our expected result by just a little over .5%. Unfortunately, only the Poker Stars sampling is by itself large enough to have merit, thanks to big contributers like FP and TB. If we focus on that site alone the gap is MUCH smaller, about .1%. I wouldn't mind seeing some more stats from FTP as it is the probably the most played site after PokerStars. At this time it's deviation is high by about 4.35% but I suspect that given it's reputation, with a sufficienlty large sample it would approach that of PokerStars.
Wow, that's the most I've written in like a year. Time for some Data.