Quote:
Originally Posted by DarkMagus
unpaired, rainbow: 13c3 = 286
unpaired, 2-flush: 13c3 * 3 = 858
unpaired, 3-flush: 13c3 = 286
paired, rainbow: 13*12 = 156
paired, 2-flush: 13*12 = 156
trips: 13
total: 1755
not sure how useful this number is, as the different types of flops have different probabilities.
I get also 1755 – but a little bit more detailed:
3-Straight-Flush = 12
Trips = 13
3-Straight 2-flush = 12 * 3 = 36
3-Straight rainbow = 12
3-Flush = c(13,3)-12 = 274
Paired rainbow = 13 *12 = 156
Paired 2-flush = 13 * 12 = 156
High-Card-Flops 2-flush: [c(13,3)-12] * 3 = 822
High-Card-Flops Rainbow: [c(13,3)-12] = 274
As DarkMagus already said, this consideration makes not much sense. A split-up of the c(52,3) = 22,100 different flop combinations looks as follows:
3-Straight-Flush = c(12,1) * c(4,1) = 12 * 4 = 48
Trips = c(13,1) * c(4,3) = 13 * 4 = 52
3-Straight 2-flush = c(12,1) * c(4,1)*c(3,1)^3 = 12 * 36 = 432
3-Straight rainbow = c(12,1) * c(4,1)*c(3,1)*c(2,1) = 12 * 24 = 288
3-Flush = [c(13,3)-12] * c(4,1) = 274 * 4 = 1,096
Axx = (c(12,2) - 2 ) = 64 *4 = 256
Kxx = (c(11,2) – 1) = 54 * 4 = 216
Qxx = (c(10,2) – 1) = 44 * 4 = 176
Jxx = (c(9,2) – 1) = 35 * 4 = 140
Txx.= (c(8,2) – 1) = 27 * 4 = 108
9xx = (c(7,2) – 1) = 20 * 4 = 80
8xx = (c(6,2) – 1) = 14 * 4 = 56
7xx = (c(5,2) – 1) = 8 * 4 = 36
6xx = (c(4,2) – 1) = 5 * 4 = 20
5xx = (c(3,2) – 1) = 2 * 4 = 8
Paired rainbow = c(13,1) * c(4,2) * c(12,1) * c(2,1) = 78 * 24 = 1,872
Paired 2-flush = c(13,1) * c(4,2) * c(12,1) * c(2,1) = 78 * 24 = 1,872
High-Card-Flops = [c(13,3)-12] * [c(4,1)^3 - 4] = 274 * 60 = 16,440
High-Card-Flops 2-flush: 274 * 36 = 9,864
Axx = (c(12,2) - 2 ) * c(4,1)*c(3,1)^3 = 64 *36 = 2,304
Kxx = (c(11,2) – 1) = 54 * 36 = 1,944
Qxx = (c(10,2) – 1) = 44 * 36 = 1,584
Jxx = (c(9,2) – 1) = 35 * 36 = 1,260
Txx.= (c(8,2) – 1) = 27 * 36 = 972
9xx = (c(7,2) – 1) = 20 * 36 = 720
8xx = (c(6,2) – 1) = 14 * 36 = 504
7xx = (c(5,2) – 1) = 8 * 36 = 288
6xx = (c(4,2) – 1) = 5 * 36 = 180
5xx = (c(3,2) – 1) = 2 * 36 = 72
High-Card-Flops rainbow: 274 * 24 = 6,576
Axx = (c(12,2) - 2 ) * c(4,1)*c(3,1)*c(2,1) = 64 *24 = 1,536
Kxx = (c(11,2) – 1) = 54 * 24 = 1,296
Qxx = (c(10,2) – 1) = 44 * 24 = 1,056
Jxx = (c(9,2) – 1) = 35 * 24 = 840
Txx.= (c(8,2) – 1) = 27 * 24 = 648
9xx = (c(7,2) – 1) = 20 * 24 = 480
8xx = (c(6,2) – 1) = 14 * 24 = 336
7xx = (c(5,2) – 1) = 8 * 24 = 192
6xx = (c(4,2) – 1) = 5 * 24 = 120
5xx = (c(3,2) – 1) = 2 * 24 = 48
After we know our 2 hole-cards only C(50,3) = 19,600 flop combos are possible. 2,500 less than shown above.
Last edited by McSeafield; 10-25-2008 at 04:45 PM.