What are the chances of.....

[antifish225]

Playing live for 16 hours (assume 50 hands per hour = 800 hands) and never once gettig AK, AQ or AA - I only ask because this actually happened last night - I know that mathematically' I should get AA about 4 times, AK ~10 times, AQ ~10 times over 800 hands - but what are the odds of getting none? (I know small sample size.....but still curious)

[MickeyHoldem]

This is another one of those looks rare after the fact situations... but if you sat down specifically looking for AA, Ak & AQ and then went 800 hands without seeing any, you would be looking at odds of about 12.5 billion to 1 against.

That's pretty rare... but it's gotta be more common than seeing 800 hands in 16 hours of live play. /images/graemlins/grin.gif (atleast in any B&M I've been in)

[deadmoney314]

It is no where near billions to one odds just so you know. There are 38 different ways you can get AA, AK, or AQ out of an order and suit specific total possible hands 2652. So on any given hand your probability of getting those specific hands are 38/2652 = ~0.014. Here's the important part, the possibilty that you WONT be dealt the hand is then 1-0.014 or ~0.986. The probability of not getting it in 800 tries is ~0.986^800 = 0.000009675. Hence your "odds" of this happening are (1/0.000009675)-1 to 1, or ~103358 to 1. This is more probable than getting a straight flush and most of us have had at least one straight flush so this happening to you is _not_ that out of the ordinary. I do agree that I doubt the actual # of hands were 800 and I find it very possible that you got an AK that won preflop or shortly thereafter that you forgot about. Anyway, there ya go.

[shday]

(1 - 38/1326)^800, or one in 12.7 billion.

...you should play the lottery.

[antifish225]

Thanks for the math - and 50 may be a little higher per hour I agree! It was a miserable night, with very few high card power hands....somehow I eeked out a small win though (and no - I NEVER had those hands all night - after about 2 hours I started really keeping track!) - thanks again

[MickeyHoldem]

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So on any given hand your probability of getting those specific hands are 38/2652 = ~0.014.

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If your going to use 2562 as the total number of ordered hands, you might want to use 76 as the possible ways to get dealt AA, AK & AQ in an ordered fashion.

There are 38 ways to get these 3 hands unordered...
and (52 choose 2) = 1326 ways to get any hand unordered.

1 - 38 / 1326 = 0.971342383
0.971342383^800 = 0.00000000007904441034

Hence your "odds" of this happening are
(1/0.00000000007904441034)-1 to 1,
or ~12651115945 to 1.

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...just so you know

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