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Old 11-23-2002, 03:30 PM
Jim Brier Jim Brier is offline
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Join Date: Sep 2002
Location: Las Vegas, NV
Posts: 189
Default My Calculation

Rather than focusing on flopping exactly one pair, I would focus on flopping one pair or better. This is simply one minus the probability of not having either an A or a K flop and it ignores the remote possibility of a flop containing a Q-J-T which is very small anyway.

If you have A-K, then there are 3 aces and 3 kings from 50 unseen cards. The probability of flopping a pair or better (ignoring flopping a straight) is 1 - (44/50)*(43/49)*(42/48) which is about 32%.

If you have nine opponents, one of whom has an ace and the other a king than you have 32 unknown cards of which 2 are aces and 2 are kings. The probability of flopping a pair or better (but ignoring flopping a straight) is 1-(28/32)*(27/31)*(26/30) which is 34%.

So, I believe you are correct. The probability of flopping one pair or better has increased from 32% to 34%.
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