I have no idea if any of these are right btw :^)
flop example for R=A
flop1: AAA, AA2, A22, A43 (i.e. anything goes)
flop2: A22, A32 (i.e. not allowed to have AAx or AAA)
flop3: A32 (i.e. no pairs allowed)
.
Calculated via a script:
| Rank | flop1 (any) | flop2 (not paired R) | flop3 (not paired) | prob1 | prob2 | prob3 | |
|---|---|---|---|---|---|---|---|
| A | 4804 | 4512 | 4224 | 0.217376 | 0.204163 | 0.191131 | |
| K | 4052 | 3784 | 3520 | 0.183348 | 0.171222 | 0.159276 | |
| Q | 3364 | 3120 | 2880 | 0.152217 | 0.141176 | 0.130317 | |
| J | 2740 | 2520 | 2304 | 0.123982 | 0.114027 | 0.104253 | |
| T | 2180 | 1984 | 1792 | 0.098643 | 0.089774 | 0.081086 | |
| 9 | 1684 | 1512 | 1344 | 0.076199 | 0.068416 | 0.060814 | |
| 8 | 1252 | 1104 | 960 | 0.056652 | 0.049955 | 0.043439 | |
| 7 | 884 | 760 | 640 | 0.040000 | 0.034389 | 0.028959 | |
| 6 | 580 | 480 | 384 | 0.026244 | 0.021719 | 0.017376 | |
| 5 | 340 | 264 | 192 | 0.015385 | 0.011946 | 0.008688 | |
| 4 | 164 | 112 | 64 | 0.007421 | 0.005068 | 0.002896 | |
| 3 | 52 | 24 | 0 | 0.002353 | 0.001086 | 0.000000 | |
| 2 | 4 | 0 | 0 | 0.000181 | 0.000000 | 0.000000 |
cross-checked with spreadsheet
screenshot: http://imgur.com/6Q2phAS
formulas:
flop1 =COMBIN(4,1)*COMBIN(52-4*B3,2)/COMBIN(52,3)+COMBIN(4,2)*COMBIN(52-4*B3,1)/COMBIN(52,3)+COMBIN(4,3)/COMBIN(52,3)
flop2 =COMBIN(4,1)*COMBIN(52-4*B3,2)/COMBIN(52,3)
flop3 =COMBIN(4,1)*COMBIN(13-B3,2)*COMBIN(4,1)^2/COMBIN(52,3)