re: Poker & Gnaw on this... its about the rigged thingy
You can test whether you're getting too few or to many aces or any other hand using the following:
Take the number of sample hands you have (N) and multiply it by the probability of getting that hand (eg 1/221 for pocket Aces). Call the result L. This is the mean of the distribution (expected number).
The variance of the distribution is also equal to L.
To get your test statistic z, take your actual number of that hand and subtract L. Then devide this by the standard deviation, which is the square root of the variance, i.e. sqr(L).
Now decide on a significance level, e.g. 1%, and look the significance limits up on a Normal (z) distribution table such as this
one. To save you the bother:
At 1% the limits are -2.58 < z < 2.58
At 5% the limits are -1.96 < z < 1.96
So, from my database, under one of my aliases I got AA 23 times in 7487 hands.
L = (1/221)*7487 = 33.88 (I should get on average this many)
z = (23 - 33.88)/sqr(33.88) = -1.87
At 5% significance, -1.87 is within the limits above, so I reject the hypothesis that the rate I'm getting aces is not equal to (1/221). In other words, although I'd expect to get Aces 34 times but only got them 23 times, this doesn't show that I'm not actually getting them at the "proper" rate.
Try it yourself for your stats! Don't forget that even if they are complying to the correct mean value, 1 time in 20 on average they will be outside the 5% significance bands (that's why they're 5% significance).
Particular pocket pair - expect 1/221
AK suited - 1/332
AK offsuit - 1/110
More probs here (http://www.poker1.com/mcu/tables/Table18.asp)