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Multi-Strike Poker Appendix 3
Introduction
This page serves to present my comprehensive calculations for the Full Pay Deuces Wild (FPDW) pay table used in Multi-Strike Poker.
The table below illustrates the likelihood of receiving a Free Ride at each level.
FPDW Free Ride Probabilities
| Level | Probability |
|---|---|
| 3 | 7.80% |
| 2 | 7.80% |
| 1 | 8.25% |
This table presents the return rates for playing level 4 of FPDW, which also indicates probabilities for standard FPDW and for any level where a Free Ride card is granted. Wins at this level are 16 times those at level 1. The value in the bottom right corner indicates that reaching level 4 is equivalent to 8.060957 times the wager 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 next table displays the return rates for level 3 of FPDW when no Free Ride card is received. Wins at this level are 4 times those at level 1, plus the expected value of 8.060957 for level 4 for any paying hand. The lower right corner reflects that the value of reaching level 3 without a Free Ride is 15.044824 times the wager per line.
Return Table for Level 3 of FPDW — Without 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 for level 4 of FPDW, when a Free Ride has occurred. The wins are 8 times those at level 1, in addition to the expected value of 8.060957 for level 4 on any hand. The value in the lower right indicates that reaching level 4 with a Free Ride yields 23.523527 times the line bet.
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 provides a weighted average of the two level 3 tables, based on the probability of getting a Free Ride. The bottom right corner shows that the value of reaching level 3 is 8.045874 times the wager per level, prior to determining a Free Ride award.
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 depicts the returns for playing level 2 of FPDW without receiving a Free Ride. Wins are twice those of level 1, plus the expected value of 8.045874 for level 3 across any paying hands. The lower right shows that achieving level 2 without a Free Ride has a value of 5.688897 times the line bet.
Return Table for Level 2 of FPDW — Without 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 |
This table illustrates the return rates for level 2 of FPDW when a Free Ride has been granted. The wins are twice those of level 1, plus the potential value of 8.045874 from level 3 on any hand. The bottom right indicates that level 2 with a Free Ride has a value of 10.061113 times the wager 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 following table presents a weighted average of the two level 2 scenarios based on Free Ride probabilities. The lower right cell indicates that the value of reaching level 2 is 6.029930 times the line bet before determining whether a Free Ride was 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 |
This table shows returns for level 1 of FPDW without a Free Ride. Wins include the expected value of 6.029930 from level 2 for any paying hand. The lower right section reveals that achieving level 1 with no Free Ride yields 3.765257 times the wager per line.
Return Table for Level 1 of FPDW — Without 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 |
This table illustrates the return for level 1 of FPDW when a Free Ride is granted. Wins encompass the expected value of 6.029930 from level 2 for any hand. The lower right indicates that reaching level 1 with a Free Ride gives a value of 7.037550 times the line bet.
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 |
Next, we present a weighted average of the two level 1 tables calculated on the basis of Free Ride probabilities. The lower right cell indicates that achieving level 1 results in 4.035221 times the wager per level before the Free Ride award is confirmed.
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 |
To determine the expected game return, since the player must place a bet on four lines, divide the total return of 4.035221 by 4, resulting in an expected return of 1.008805. In a single-level mode, FPDW returns 1.007620, indicating a 0.12% increase in return by betting across all five levels.
More Information
- Main Multi-Strike Poker page .
- Multistrike Poker appendix 1 Illustrates the strategy for Full Pay Deuces Wild in Multi-Strike.
- Multistrike Poker appendix 2 Illustrates the strategy for Full Pay Jacks or Better in Multi-Strike.
Links
- multistrikepoker.com The official website for Multi Strike Poker features an excellently designed practice game.
- Bob Dancer article On Multi-Strike poker, this includes the expected return for all the existing pay tables.