#1
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How many different flops can there be disregarding suits
I know there are 169 different possible pockets.
AA AKsuited AKoff KK KQsuited KQoff etc. etc. for a total of 169. Forget suits, how many different 3 card flops? |
#2
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Re: How many different flops can there be disregarding suits
If you don't care about suits and you don't care about cards in people's hands (including your own) then this is pretty easy:
number of no duplicate flops + number of paired flops + number of trips flops = 13*12*11/(3*2) + 13*12 + 13 = 13*11*2 + 13*12 + 13 = 13 * (22 + 12 + 1) = 13 * 35 = 455 |
#3
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Re: How many different flops can there be disregarding suits
There are 13 choose 3 = 286 unpaired flops.
There are 13*12 = 156 paired flops. There are 13 flops of one rank. Total: 286+156+13 = 455. If you want to distinguish suitedness of the flops, but not the particular suits, you can refine these: Each unpaired flop has 5 possible patterns (monochrome, rainbow, and 3 2-tone patterns). Each paired flop has 2 possible patterns (two-tone or rainbow). Each trips flop has 1 possible pattern (rainbow). Total: 5(286)+2(156)+1(13) = 1755. As a check, 286(4 + 24 + 3*12) + 156(12 + 12) + 13(4) = 52 choose 3. |
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