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08-04-2005, 04:49 PM
What are the odds of being dealt AA three out of ten hands?
Sorry for being a moron, and thanks in advance for the replies.

jba
08-04-2005, 05:46 PM
[ QUOTE ]
What are the odds of being dealt AA three out of ten hands?
Sorry for being a moron, and thanks in advance for the replies.

[/ QUOTE ]

I assume you mean exactly three times, no more no less?

there's a couple steps to this.

1 - we need to know the odds of getting AA in one hand:

we find this by finding all combos of AA, and divide by all possible hands (all combos of 52 cards):

C(4,2)/C(52,2)

which is the same as :

(4*3/2!)/(52*51/2!)

6/1326, or 1/221

2 - we need to know the odds of not getting AA:

ok easy enough 220/221

3 - to get AA three times, then non-AA seven times, we say:

1/221*1/221*1/221*220/221*220/221*220/221*220/221*220/221*220/221*220/221
=8.97503248e-8 = 1/11,142,021

4 - but it's easier than that, cause we can also get non-AA the first seven times then AA the last three times, or AA/non-AA/AA/non-AA/AA/non-AA/......etc. I think the number of possible combos here can be written as 10!/(7!*3!) = 120. (If someone reading this can confirm, I'm a little shaky on this point.)

now we know there are 120 orders in which we can achieve the goal, so the final answer is:

120/11,142,021 = 1/92,850

Luzion
08-07-2005, 02:57 AM
Looks good to me.

C(10,7) * (1/221)^3 * (220/221)^7 was the answer.

So yeah, your lengthy explanation was spot on.