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View Full Version : which is more likely to flop top pair A4 or JT


BigBiceps
05-13-2004, 12:23 PM
which is more likely to flop top pair A4 or JT on a random flop (ie. not A4 vs. JT, the hands are against all other hands out there 9 handed)

Mano
05-13-2004, 01:55 PM
Number of ways A4 pairs the top board card on the flop (I am ignoring paired boards, trips, flushes, etc.):

The number of flops NOT containing an A is C(47,3) so there are C(50,3) - C(47,3) = 3385 flops containing an A. The 4 will be top pair when the board is precisely 4 3 2, and there are 3*4*4 = 48 ways this can come up. So there are 3433 ways that A4 pairs the top card on the flop.

For JT to be top pair, no A,K or Q can flop and we must flop a J or T. There are C(38,3) flops with no A,K or Q and C(32,3) flops with no A,K,Q,T or J. So there are C(38,3) - C(32,3) = 3476 flops containing at least one J or T and not containing an A,K or Q.

So in answer to your question, JT will pair the top card a bit more often than will A4.