probability of pairs

[kirisim]

I think I am missing something fairly simple here, but please help me out:

The probably of getting a specific pair (say, AA) is 221-1.

However, after 5,000 hands, I have been dealt each specific pair between 40 and 65 times. For example, I had AA 41 times. This is about twice what I would expect if it was 221-1 against getting AA.

(That is to say, 5000/221 = 22)

What very simple thing am I missing?

[gaming_mouse]

Actually, 220 to 1, but you are correct in that you have observed an unlikely number of AA.

There is some natural variance, of course, but you have observed more than can be expected.

The number of AA dealt in 5000 hands is distributed according to the binomial distribution with n=5000 and p=.0045.

Plugging the calculation into excel, we get:

BINOMDIST(41,5000,0.0045,TRUE)= .99985

This means that the chances of seeing 41 or more AA dealt in 5000 hands is about .00015, very unlikely.

I would guess that there is a mistake somewhere in your book keeping. Where does the data come from?

gm