couple of odds questions

[aroddolla]

Is it true that in a 9 handed holdem game 53% of the time someone is going to be dealt a pair?

and

If you have no A or K in your hand and you have 4 players behind you, CO button SB BB. Will one of these players have an A or K in thier hand 82% of the time?

[BruceZ]

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Is it true that in a 9 handed holdem game 53% of the time someone is going to be dealt a pair?

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This is well-approximated by 1 - (16/17)^9 =~ 42%. Your estimate apparently came from 9*(1/17) which is high since it over counts the deals with multiple pairs. In fact, the exact answer is between 41.9% and 42.1% by the formula I derived in this post with 4 terms of the inclusion-exclusion principle for X = 9.


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If you have no A or K in your hand and you have 4 players behind you, CO button SB BB. Will one of these players have an A or K in thier hand 82% of the time?

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This is exactly 1 - C(42,8)/C(50,8) = 78.0%.