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Multi-Strike Poker Appendix 3
Introduction
The purpose of this page is to show my detailed calculations for the Full Pay Deuces Wild (FPDW) pay table in Multi-Strike Poker.
The following table shows the probability of getting a free ride at each level.
FPDW Free Ride Probabilities
| Level | Probability |
|---|---|
| 3 | 7.80% |
| 2 | 7.80% |
| 1 | 8.25% |
The following table shows the return table for playing level 4 of FPDW. This also reflects the probabilities for conventional FPDW, and for any level where a Free Ride card was awarded. This wins are 16 times those of level 1. The lower right cell shows the value of attaining level 4 is 8.060957 times the bet per line.
FPDW — Level 4 Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural royal flush | 6400 | 440,202,756 | 0.000022 | 0.141337 |
| 4 deuces | 1600 | 4,060,462,824 | 0.000204 | 0.325925 |
| Wild royal flush | 200 | 35,796,957,696 | 0.001796 | 0.359169 |
| 5 of a kind | 120 | 63,818,309,856 | 0.003202 | 0.384192 |
| Straight flush | 72 | 82,122,481,680 | 0.004120 | 0.296631 |
| 4 of a kind | 40 | 1,294,427,430,576 | 0.064938 | 2.597527 |
| Full house | 24 | 423,165,297,240 | 0.021229 | 0.509499 |
| Flush | 16 | 330,506,232,804 | 0.016581 | 0.265291 |
| Straight | 16 | 1,127,512,239,276 | 0.056564 | 0.905031 |
| 3 of a kind | 8 | 5,671,888,316,712 | 0.284544 | 2.276355 |
| Nothing | 0 | 10,899,492,585,780 | 0.546800 | 0.000000 |
| Total | 19,933,230,517,200 | 1.000000 | 8.060957 |
The following table shows the return table for playing level 3 of FPDW, when a Free Ride was not awarded. The wins are 4 times those of level 1, plus the expected value of 8.060957 of level 4 for any paying hand. The lower right cell shows the value of attaining level 3 with no Free Ride is 15.044824 times the bet per line.
FPDW — Level 3 Return Table — No Free Ride
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural royal flush | 3208.060957 | 417,777,504 | 0.000021 | 0.067237 |
| 4 deuces | 808.0609569 | 4,110,107,700 | 0.000206 | 0.166617 |
| Wild royal flush | 108.0609569 | 32,932,616,280 | 0.001652 | 0.178533 |
| 5 of a kind | 68.0609569 | 64,358,413,080 | 0.003229 | 0.219748 |
| Straight flush | 44.0609569 | 76,886,019,288 | 0.003857 | 0.169951 |
| 4 of a kind | 28.0609569 | 1,311,734,068,716 | 0.065806 | 1.846590 |
| Full house | 20.0609569 | 427,803,152,904 | 0.021462 | 0.430544 |
| Flush | 16.0609569 | 315,562,064,400 | 0.015831 | 0.254260 |
| Straight | 16.0609569 | 1,048,879,491,840 | 0.052620 | 0.845122 |
| 3 of a kind | 12.0609569 | 5,825,829,039,480 | 0.292267 | 3.525022 |
| Nothing | 0 | 10,824,717,766,008 | 0.543049 | 0.000000 |
| Total | 19,933,230,517,200 | 1.000000 | 7.703625 |
The following table shows the return table for playing level 4 of FPDW, when a Free Ride was awarded. The wins are 8 times those of level 1, plus the expected value of 8.060957 of level 4 for any hand. The lower right cell shows the value of attaining level 3 with a Free Ride is 23.523527 times the bet per line.
FPDW — Level 3 Return Table — Free Ride
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural royal flush | 3208.060957 | 440,202,756 | 0.000022 | 0.070846 |
| 4 deuces | 808.060957 | 4,060,462,824 | 0.000204 | 0.164605 |
| Wild royal flush | 108.060957 | 35,796,957,696 | 0.001796 | 0.194061 |
| 5 of a kind | 68.060957 | 63,818,309,856 | 0.003202 | 0.217904 |
| Straight flush | 44.060957 | 82,122,481,680 | 0.004120 | 0.181526 |
| 4 of a kind | 28.060957 | 1,294,427,430,576 | 0.064938 | 1.822227 |
| Full house | 20.060957 | 423,165,297,240 | 0.021229 | 0.425877 |
| Flush | 16.060957 | 330,506,232,804 | 0.016581 | 0.266301 |
| Straight | 16.060957 | 1,127,512,239,276 | 0.056564 | 0.908479 |
| 3 of a kind | 12.060957 | 5,671,888,316,712 | 0.284544 | 3.431877 |
| Nothing | 8.060957 | 10,899,492,585,780 | 0.546800 | 4.407732 |
| Total | 19,933,230,517,200 | 1.000000 | 12.091435 |
The next table is a weighted average of the two level 3 tables, according to the Free Ride probability. The lower right cell shows the value of attaining level 3 is 8.045874 times the bet per level, before it is determined if a Free Ride is awarded.
FPDW — Level 3 Combined Return Table
| Free Ride | Probability | Expected Return | Expected Value |
|---|---|---|---|
| Yes | 0.078 | 12.091435 | 0.943132 |
| No | 0.922 | 7.703625 | 7.102742 |
| Total | 1 | - | 8.045874 |
The following table shows the return table for playing level 2 of FPDW, when a Free Ride was not awarded. The wins are 2 times those of level 1, plus the expected value of 8.045874 of level 3 for any paying hand. The lower right cell shows the value of attaining level 2 with no Free Ride is 5.688897 times the bet per line.
FPDW — Level 2 Return Table — No Free Ride
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural royal flush | 1608.045874 | 352,599,540 | 0.000018 | 0.028445 |
| 4 deuces | 408.0458742 | 4,135,053,204 | 0.000207 | 0.084647 |
| Wild royal flush | 58.04587425 | 28,881,001,728 | 0.001449 | 0.084102 |
| 5 of a kind | 38.04587425 | 64,679,487,096 | 0.003245 | 0.123452 |
| Straight flush | 26.04587425 | 75,959,998,392 | 0.003811 | 0.099254 |
| 4 of a kind | 18.04587425 | 1,319,770,944,444 | 0.066210 | 1.194810 |
| Full house | 14.04587425 | 429,993,794,952 | 0.021572 | 0.302993 |
| Flush | 12.04587425 | 308,214,731,724 | 0.015462 | 0.186258 |
| Straight | 12.04587425 | 1,049,449,618,236 | 0.052648 | 0.634194 |
| 3 of a kind | 10.04587425 | 5,854,925,226,024 | 0.293727 | 2.950743 |
| Nothing | 0 | 10,796,868,061,860 | 0.541652 | 0.000000 |
| Total | 19,933,230,517,200 | 1.000000 | 5.688897 |
The following table shows the return table for playing level 2 of FPDW, when a Free Ride was awarded. The wins are 2 times those of level 1, plus the expected value of 8.045874 of level 3 for any hand. The lower right cell shows the value of attaining level 2 with a Free Ride is 10.061113 times the bet per line.
FPDW — Level 3 Return Table — Free Ride
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural royal flush | 1608.045874 | 440,202,756 | 0.000022 | 0.035512 |
| 4 deuces | 408.045874 | 4,060,462,824 | 0.000204 | 0.083120 |
| Wild royal flush | 58.045874 | 35,796,957,696 | 0.001796 | 0.104241 |
| 5 of a kind | 38.045874 | 63,818,309,856 | 0.003202 | 0.121808 |
| Straight flush | 26.045874 | 82,122,481,680 | 0.004120 | 0.107306 |
| 4 of a kind | 18.045874 | 1,294,427,430,576 | 0.064938 | 1.171866 |
| Full house | 14.045874 | 423,165,297,240 | 0.021229 | 0.298182 |
| Flush | 12.045874 | 330,506,232,804 | 0.016581 | 0.199729 |
| Straight | 12.045874 | 1,127,512,239,276 | 0.056564 | 0.681368 |
| 3 of a kind | 10.045874 | 5,671,888,316,712 | 0.284544 | 2.858497 |
| Nothing | 8.045874 | 10,899,492,585,780 | 0.546800 | 4.399485 |
| Total | 19,933,230,517,200 | 1.000000 | 10.061113 |
The next table is a weighted average of the two level 2 tables, according to the Free Ride probability. The lower right cell shows the value of attaining level 2 is 6.029930 times the bet per level, before it is determined if a Free Ride is awarded.
FPDW — Level 2 Combined Return Table
| Free Ride | Probability | Expected Return | Expected Value |
|---|---|---|---|
| Yes | 0.078 | 10.061113 | 0.784767 |
| No | 0.922 | 5.688897 | 5.245163 |
| Total | 1 | - | 6.029930 |
The following table shows the return table for playing level 1 of FPDW, when a Free Ride was not awarded. The wins include the expected value of 6.029930 of level 2 for any paying hand. The lower right cell shows the value of attaining level 1 with no Free Ride is 3.765257 times the bet per line.
FPDW — Level 1 Return Table — No Free Ride
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural royal flush | 806.02993 | 311,564,400 | 0.000016 | 0.012599 |
| 4 deuces | 206.02993 | 4,137,281,292 | 0.000208 | 0.042763 |
| Wild royal flush | 31.02993004 | 27,031,420,440 | 0.001356 | 0.042080 |
| 5 of a kind | 21.02993004 | 64,785,708,888 | 0.003250 | 0.068350 |
| Straight flush | 15.02993004 | 74,427,700,308 | 0.003734 | 0.056120 |
| 4 of a kind | 11.02993004 | 1,322,859,685,584 | 0.066365 | 0.731996 |
| Full house | 9.02993004 | 431,437,958,172 | 0.021644 | 0.195445 |
| Flush | 8.02993004 | 304,697,744,388 | 0.015286 | 0.122745 |
| Straight | 8.02993004 | 1,048,553,327,628 | 0.052603 | 0.422401 |
| 3 of a kind | 7.02993004 | 5,871,597,609,348 | 0.294563 | 2.070759 |
| Nothing | 0 | 10,783,390,516,752 | 0.540976 | 0.000000 |
| Total | 19,933,230,517,200 | 1.000000 | 3.765257 |
The following table shows the return table for playing level 1 of FPDW, when a Free Ride was awarded. The wins include the expected value of 6.029930 of level 2 for any hand. The lower right cell shows the value of attaining level 2 with a Free Ride is 7.037550 times the bet per line.
FPDW — Level 1 Return Table — Free Ride
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural royal flush | 806.029930 | 440,202,756 | 0.000022 | 0.017800 |
| 4 deuces | 206.029930 | 4,060,462,824 | 0.000204 | 0.041969 |
| Wild royal flush | 31.029930 | 35,796,957,696 | 0.001796 | 0.055725 |
| 5 of a kind | 21.029930 | 63,818,309,856 | 0.003202 | 0.067330 |
| Straight flush | 15.029930 | 82,122,481,680 | 0.004120 | 0.061921 |
| 4 of a kind | 11.029930 | 1,294,427,430,576 | 0.064938 | 0.716263 |
| Full house | 9.029930 | 423,165,297,240 | 0.021229 | 0.191698 |
| Flush | 8.029930 | 330,506,232,804 | 0.016581 | 0.133142 |
| Straight | 8.029930 | 1,127,512,239,276 | 0.056564 | 0.454209 |
| 3 of a kind | 7.029930 | 5,671,888,316,712 | 0.284544 | 2.000327 |
| Nothing | 6.029930 | 10,899,492,585,780 | 0.546800 | 3.297166 |
| Total | 19,933,230,517,200 | 1.000000 | 7.037550 |
The next table is a weighted average of the two level 1 tables, according to the Free Ride probability. The lower right cell shows the value of attaining level 1 is 4.035221 times the bet per level, before it is determined if a Free Ride is awarded.
FPDW — Level 1 Combined Return Table
| Free Ride | Probability | Expected Return | Expected Value |
|---|---|---|---|
| Yes | 0.0825 | 7.037550 | 0.580598 |
| No | 0.9175 | 3.765257 | 3.454623 |
| Total | 1 | - | 4.035221 |
The player must bet four lines, so to get the expected return of the game divide the total return of 4.035221 by 4 to get 1.008805. In single-level mode the return for FPDW is 1.007620. So, betting all five levels increases the return by 0.12%.
More Information
- Main Multi-Strike Poker page.
- Multistrike Poker appendix 1 shows the strategy for Multistrike full pay deuces wild.
- Multistrike Poker appendix 2 shows the strategy for Multistrike full pay jacks or better.
Links
- multistrikepoker.com. Official Multi Strike Poker web site. Includes a very well done practice game.
- Bob Dancer article on Mutlistrike poker. Includes expected return for all available pay tables.