photoz223
photoz223
  • Threads: 1
  • Posts: 1
Joined: Mar 27, 2011
March 28th, 2011 at 1:35:43 PM permalink
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.
ChesterDog
ChesterDog
  • Threads: 8
  • Posts: 1479
Joined: Jul 26, 2010
March 28th, 2011 at 2:53:14 PM permalink
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%
mkl654321
mkl654321
  • Threads: 65
  • Posts: 3412
Joined: Aug 8, 2010
March 28th, 2011 at 5:52:29 PM permalink
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.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
  • Jump to: