POCKET ACES BACK TO BACK AND 3/4

[skibandit]

Hi everyone,

I am a fairly new poker player and last night at a local casino playing 4/8 Limit, I had something that I have never seen before.

I was dealt pocket aces 2 times in a row, and then had them again one hand later. What are the odds of getting aces (or any specific pair) back to back, let alone three out of four hands?

And, just to let you all know, I won the pot all three times...

Thanks for your help.

CM

[SamIAm]

The odds of any independent event happening twice is just (the probability of it happening once)^2.

The chance of a good event happening = (# good ways to happen) / (# total ways to happen).

Hence your answer is (6/1326)^2.
-Sam

[AaronBrown]

SamIAm is correct. The chance of AA is 1/221, two in a row is (1/221)^2 = 1/48,841. Three times out of four is a bit tricky. If you don't count three in a row, there are only two ways to get three out of four, so it's 2*(1/221)^3 = 2/10,793,861. If you count three in a row there are two more ways to get it so you can double that probability.

However, if you ask, what are the chances that I will get the same pair twice in a row over an evening of 300 hands, it's not so astronomical. That will be about 1 time in 12.5 sessions. So if you play every week, it'll happen to you about four times a year.