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Old 11-26-2003, 02:26 AM
BruceZ BruceZ is offline
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Join Date: Sep 2002
Posts: 1,636
Default Re: Tough question???

Probability you will be dealt a pair is 1*3/51 = 1/17.

With a flop of AAX, and you don't have an A, the probability that at least one of your N opponents has an A assuming random hands is 1 minus the probability that there are no aces out. This is 1 - C(45,2N)/C(47,2N). That is, there are 47 cards remaining, and 45 of them are not an A, so there are C(45,2N) ways to choose 2N cards without an A, and C(47,2N) total ways to choose 2N cards.

For example, if you have 4 opponents, 1 - C(45,8)/C(47,8) = 1 - (45*44*43*..*38/8!) / (47*46*45*...*40/8!) = 1 - 39*38/(47*46) = 31.5%.

Here are the solutions for different numbers of opponents.

<font class="small">Code:</font><hr /><pre>
opponents P(A out)

1 8.4%
2 16.5%
3 24.1%
4 31.5%
5 38.4%
6 45.0%
7 51.2%
8 57.0%
9 62.4%
10 67.5%</pre><hr />
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