Quote:
Originally Posted by franknagaijr
Its been a while. Here is a little more to amuse myself.
If you have A2HH in hand and only care about the other six ranks
LLL (distinct) = c(24,1) * c(20,1) * c(16,1)
LLH (distinct) = c(24,1) * c(20,1) * c(18,1)
LLL (one pair on board) = (c(4,2) * 6) + c(20,1)
Since you know your own hand, the flop denominator is c(48,3)
I got a little bit of the math wrong in my original response, fwiw.
some assistance (for reference as you amuse yourself)
when holding A2HH ie. A2KQ
there are 38 distinct flop textures when considering the ranks as either low cards (Ace thru 8) and high cards (9 thru king) as well as the flops intersection with the hand
flop quads
LLL ie. AAA,222 2/17296 =.01%
HHH ie. KKK,QQQ 2/17296 =.01%
flop boat
LLL ie. AA2,22A 18/17296 =0.1%
LLH ie. AAK,AAQ,22K,22Q 36/17296 =0.21%
LHH ie. AKK,2KK,AQQ,2QQ 36/17296 =0.21%
HHH ie. KKQ,KQQ 18/17296 =0.1%
flop set
LLL ie. AA[3-8],22[3-8] 144/17296 =0.83%
LLH ie. AA[j-9],22[j-9] 72/17296 =0.42%
LHH ie. [3-8]KK,[3-8]QQ 144/17296 =0.83%
HHH ie. KK[j-9],QQ[j-9] 72/17296 =0.42%
flop 2pr
LLL ie. A2[3-8] 216/17296 = 1.25%
LLH ie. A2K,A2Q 54/17296 = 0.31%
LLH ie. AK[3-8],AQ[3-8],2K[3-8],2Q[3-8] 864/17296 = 5.0%
LLH ie. A2[j-9] 108/17296 = 0.62%
LHH ie. AKQ,2KQ 54/17296 = 0.31%
LHH ie. AK[j-9],AQ[j-9],2K[j-9],2Q[j-9] 432/17296 = 2.5%
LHH ie. [3-8]KQ 216/17296 = 1.25%
HHH ie. KQ[j-9] 108/17296 = 0.62%
flop 1 pr. paired flop
LLL ie. A[33-88],2[33-88] 216/17296 = 1.25%
LLH ie. [33-88]K,[33-88]Q 216/17296 = 1.25%
LHH ie.A[jj-99],2[jj-99] 108/17296 = 0.62%
HHH ie.K[jj-99],Q[jj-99] 108/17296 = 0.62%
flop 1 pr. unpaired flop
LLL ie. A[3-8][3-8],2[3-8][3-8] 1440/17296 = 8.33%
LLH ie. [3-8][3-8]K,[3-8][3-8]Q 1440/17296 = 8.33%
LLH ie. A[3-8][j-9],2[3-8][j-9] 1728/17296 = 10%
LHH ie. [3-8][j-9]K,[3-8][j-9]Q 1728/17296 = 10%
LHH ie. A[j-9][j-9],2[j-9][j-9] 288/17296 = 1.66%
HHH ie. K[j-9][j-9],Q[j-9][j-9] 288/17296 = 1.66%
flop nothing trips flop
LLL ie. 333-888 24/17296 = 0.14%
HHH ie. 999-jjj 12/17296 = 0.07%
flop nothing paired flop
LLL ie. [3-8][33-88] 720/17296 = 4.16%
LLH ie. [33-88][j-9] 432/17296 = 2.5%
LHH ie. [3-8][jj-99] 432/17296 = 2.5%
HHH ie. [j-9][jj-99] 144/17296 = 0.83%
flop nothing unpaired flop
LLL ie. [3-8][3-8][3-8] 1280/17296 = 7.4%
LLH ie. [3-8][3-8][j-9] 2880/17296 = 16.65%
LHH ie. [3-8][j-9][j-9] 1152/17296 = 6.66%
HHH ie. [j-9][j-9][j-9] 64/17296 = 0.37%
17296/17296 =100%
(annoyingly there is no tab to help with formatting and not inspired to make edit it into table. sorry)