% chance of flopping overpair?

[Small Stakes]

What percentage of the time will you flop an overpair with KK, QQ, JJ, tt, ect? Any help would be greatly appreciated.
Thanks

[Precision1C]

The basic formula for calculating the number of possible combinations drawing K objects from a pool of N is N!/[K!(N-K)!]. For instance the number of possible 3 card flops from a 50 card deck is N=50 K=3

Possible flops 50! divided by 3!*47!= 19,600

Now to get the chance of flopping an overpair you find the number of cards left in the deck that would give you the overpair and see how many possible combinations that gives and divide by the total number of flops.

For instance if you have KK there are 44 cards Q through 2 that would allow you to have an overpair. Note that this calculation neglects the chance of having a K flop. So the chance of flopping no card higher than a Queen is 44!/[3!*41!] =13,244. So the chances of flopping an overpair is 13,244/19,600=67.6%. The same method can easily be applied to the remaining pairs.

[cold_cash]

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[BruceZ]

I noticed that there is at least 1 error in these charts. The odds against flopping at least 2 of your suit when you hold 2 suited cards is [ C(11,2)*39 + C(11,3) ] / C(50,3) = 7.5:1, not 6.4:1.

[Lost Wages]

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