Bell curve for poker pairs in NL texas hold em over 100 hands

Does anyone have a bell curve for how many of times you should expect to get pocket pairs per 100 hands. I know averages tell you that you should get dealt pocket pairs 5.9 times out of 100 hands. What I'd like to know is how rare is it to get dealt pocket pairs only 3 times in 100 hands.

Quote: photoz223

Does anyone have a bell curve for how many of times you should expect to get pocket pairs per 100 hands. I know averages tell you that you should get dealt pocket pairs 5.9 times out of 100 hands. What I'd like to know is how rare is it to get dealt pocket pairs only 3 times in 100 hands.

I get that the probability of getting 3 or fewer pocket pairs in 100 hands is 15.38%.

In Excel's notation, the probability of getting exactly x pocket pairs in 100 hands =combin(100,x) * (1/17)^x * (16/17)^(100-x), where 1/17 is the probability of getting a pocket pair as a hand.

Here is what I get for the probabilities for various values of x:
0 0.23%
1 1.46%
2 4.50%
3 9.19%
4 13.93%
5 16.72%
6 16.55%
7 13.89%
8 10.09%
9 6.45%
10 3.67%
11 1.87%
12 0.87%
13 0.37%
14 0.14%
15 0.05%
16 0.02%
17 0.01%
18 0.00%

Quote: photoz223

Does anyone have a bell curve for how many of times you should expect to get pocket pairs per 100 hands. I know averages tell you that you should get dealt pocket pairs 5.9 times out of 100 hands. What I'd like to know is how rare is it to get dealt pocket pairs only 3 times in 100 hands.

If ANYTHING happened over only 100 hands, including your getting two black aces each time and one of the players at the table dropping dead of a heart attack at the end of every deal, it wouldn't be statistically significant. (However, if in addition to the above, a naked sumo wrestler--a different one each time--hopped up on the table and did the can-can dance while singing a Top 40 hit in Korean, then you would probably have entered the realm of statistical anomalies.)

For what it's worth, I've gone an entire hour or more without getting dealt a pocket pair, more times than I can remember.