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| Ultimate Texas Hold'em Return Table | ||||
| Event | Pays | Combinations | Probability | Return |
| Large raise, player wins with three of a kind or less, dealer qualifies | 5 | 3671050165880 | 0.131987 | 0.659933 |
| Large raise, player wins with straight, dealer qualifies | 6 | 246174692160 | 0.008851 | 0.053105 |
| Large raise, player wins with flush, dealer qualifies | 6.5 | 241047929080 | 0.008666 | 0.056332 |
| Large raise, player wins with full house, dealer qualifies | 8 | 295405180920 | 0.010621 | 0.084966 |
| Large raise, player wins with four of a kind, dealer qualifies | 15 | 23008208760 | 0.000827 | 0.012408 |
| Large raise, player wins with straight flush, dealer qualifies | 55 | 1818135760 | 0.000065 | 0.003595 |
| Large raise, player wins with royal flush, dealer qualifies | 505 | 596356920 | 0.000021 | 0.010828 |
| Large raise, player wins with three of a kind or less, dealer doesn't qualify | 4 | 1556797035840 | 0.055972 | 0.223888 |
| Large raise, player wins with straight, dealer doesn't qualify | 5 | 81416649960 | 0.002927 | 0.014636 |
| Large raise, player wins with flush, dealer doesn't qualify | 5.5 | 50874988680 | 0.001829 | 0.01006 |
| Large raise, player wins with full house, dealer doesn't qualify | 7 | 0 | 0 | 0 |
| Large raise, player wins with four of a kind, dealer doesn't qualify | 14 | 0 | 0 | 0 |
| Large raise, player wins with straight flush, dealer doesn't qualify | 54 | 229686840 | 0.000008 | 0.000446 |
| Large raise, player wins with royal flush, dealer doesn't qualify | 504 | 90386280 | 0.000003 | 0.001638 |
| Large raise, push | 0 | 285142270600 | 0.010252 | 0 |
| Large raise, player loses, dealer qualifies | -6 | 3931554359920 | 0.141353 | -0.848116 |
| Large raise, player loses, dealer doesn't qualify | -5 | 102655952400 | 0.003691 | -0.018454 |
| Medium raise, player wins with three of a kind or less, dealer qualifies | 3 | 2114839654764 | 0.076036 | 0.228107 |
| Medium raise, player wins with straight, dealer qualifies | 4 | 133100158992 | 0.004785 | 0.019142 |
| Medium raise, player wins with flush, dealer qualifies | 4.5 | 152618008784 | 0.005487 | 0.024692 |
| Medium raise, player wins with full house, dealer qualifies | 6 | 289401836880 | 0.010405 | 0.06243 |
| Medium raise, player wins with four of a kind, dealer qualifies | 13 | 18537793620 | 0.000666 | 0.008664 |
| Medium raise, player wins with straight flush, dealer qualifies | 53 | 2704129504 | 0.000097 | 0.005153 |
| Medium raise, player wins with royal flush, dealer qualifies | 503 | 112333500 | 0.000004 | 0.002031 |
| Medium raise, player wins with three of a kind or less, dealer doesn't qualify | 2 | 1083763469592 | 0.038965 | 0.07793 |
| Medium raise, player wins with straight, dealer doesn't qualify | 3 | 45053788356 | 0.00162 | 0.00486 |
| Medium raise, player wins with flush, dealer doesn't qualify | 3.5 | 38820798396 | 0.001396 | 0.004885 |
| Medium raise, player wins with full house, dealer doesn't qualify | 5 | 0 | 0 | 0 |
| Medium raise, player wins with four of a kind, dealer doesn't qualify | 12 | 0 | 0 | 0 |
| Medium raise, player wins with straight flush, dealer doesn't qualify | 52 | 358131456 | 0.000013 | 0.00067 |
| Medium raise, player wins with royal flush, dealer doesn't qualify | 502 | 8830620 | 0 | 0.000159 |
| Medium raise, push | 0 | 191611691060 | 0.006889 | 0 |
| Medium raise, player loses, dealer qualifies | -4 | 1841155221088 | 0.066196 | -0.264783 |
| Medium raise, player loses, dealer doesn't qualify | -3 | 7978353108 | 0.000287 | -0.000861 |
| Small raise, player wins with three of a kind or less, dealer qualifies | 2 | 1375033295072 | 0.049437 | 0.098874 |
| Small raise, player wins with straight, dealer qualifies | 3 | 395087247768 | 0.014205 | 0.042614 |
| Small raise, player wins with flush, dealer qualifies | 3.5 | 190959227136 | 0.006866 | 0.02403 |
| Small raise, player wins with full house, dealer qualifies | 5 | 43297986840 | 0.001557 | 0.007784 |
| Small raise, player wins with four of a kind, dealer qualifies | 12 | 859737984 | 0.000031 | 0.000371 |
| Small raise, player wins with straight flush, dealer qualifies | 52 | 1962591576 | 0.000071 | 0.003669 |
| Small raise, player wins with royal flush, dealer qualifies | 502 | 42135660 | 0.000002 | 0.00076 |
| Small raise, player wins with three of a kind or less, dealer doesn't qualify | 1 | 720579458748 | 0.025907 | 0.025907 |
| Small raise, player wins with straight, dealer doesn't qualify | 2 | 136018223484 | 0.00489 | 0.009781 |
| Small raise, player wins with flush, dealer doesn't qualify | 2.5 | 40911000804 | 0.001471 | 0.003677 |
| Small raise, player wins with full house, dealer doesn't qualify | 4 | 0 | 0 | 0 |
| Small raise, player wins with four of a kind, dealer doesn't qualify | 11 | 0 | 0 | 0 |
| Small raise, player wins with straight flush, dealer doesn't qualify | 51 | 269696304 | 0.00001 | 0.000495 |
| Small raise, player wins with royal flush, dealer doesn't qualify | 501 | 6109020 | 0 | 0.00011 |
| Small raise, push | 0 | 418339128088 | 0.015041 | 0 |
| Small raise, player loses, dealer qualifies | -3 | 2700150685692 | 0.097079 | -0.291238 |
| Small raise, player loses, dealer doesn't qualify | -2 | 47223220344 | 0.001698 | -0.003396 |
| Player folds | -2 | 5335144079760 | 0.191816 | -0.383633 |
| Total | 27813810024000 | 1 | -0.02185 | |
The lower right cell shows a house edge of 2.185% per ante bet. What this means, for example, is if you bet $1 and both the Ante and Blind initially you can expect to lose 2.185 cents on average. However for comparison to other games I believe the Element of Risk is more appropriate to look at. The average total amount bet by the end of the hand is 4.152252 times the ante bet. So the element of risk would be 2.185%/4.152252 = -0.526%.
The next table shows the average wager and return from each bet.
| Ultimate Texas Hold'em Return Table | |||
| Bet Type | Average Wager |
Average Pays |
Average Win |
| Ante | 1 | -0.165757 | -0.165757 |
| Blind | 1 | -0.314685 | -0.314685 |
| Play | 2.152252 | 0.213076 | 0.458593 |
| Total | 4.152252 | -0.02185 | |
The next table shows the probability of a large, medium, or small raise, or fold for each initial 2-card hand, as well as the expected value.
| Ultimate Texas Hold'em Return Table | |||||
| Initial Hand |
Probability Large Raise |
Probability Medium Raise |
Probability Small Raise |
Probability Fold |
Expected Value |
| 2/3 unsuited | 0 | 0.304286 | 0.243606 | 0.452109 | -0.925837 |
| 2/4 unsuited | 0 | 0.310306 | 0.241466 | 0.448228 | -0.87256 |
| 2/5 unsuited | 0 | 0.314337 | 0.242178 | 0.443485 | -0.823324 |
| 2/6 unsuited | 0 | 0.312194 | 0.233915 | 0.453891 | -0.861363 |
| 2/7 unsuited | 0 | 0.305357 | 0.231536 | 0.463107 | -0.882806 |
| 2/8 unsuited | 0 | 0.308878 | 0.237584 | 0.453539 | -0.820061 |
| 2/9 unsuited | 0 | 0.310612 | 0.28569 | 0.403698 | -0.758211 |
| 2/10 unsuited | 0 | 0.316633 | 0.38609 | 0.297277 | -0.659454 |
| 2/J unsuited | 0 | 0.322143 | 0.479439 | 0.198419 | -0.567216 |
| 2/Q unsuited | 0 | 0.333418 | 0.515782 | 0.1508 | -0.452218 |
| 2/K unsuited | 0 | 0.362551 | 0.525849 | 0.1116 | -0.311296 |
| 2/A unsuited | 1 | 0 | 0 | 0 | 0.04173 |
| 3/4 unsuited | 0 | 0.323163 | 0.243305 | 0.433532 | -0.760051 |
| 3/5 unsuited | 0 | 0.322857 | 0.24694 | 0.430202 | -0.708336 |
| 3/6 unsuited | 0 | 0.319745 | 0.23938 | 0.440875 | -0.745154 |
| 3/7 unsuited | 0 | 0.31949 | 0.231853 | 0.448657 | -0.767026 |
| 3/8 unsuited | 0 | 0.313163 | 0.233988 | 0.452848 | -0.784905 |
| 3/9 unsuited | 0 | 0.314745 | 0.28581 | 0.399445 | -0.708666 |
| 3/10 unsuited | 0 | 0.319082 | 0.386977 | 0.293941 | -0.610015 |
| 3/J unsuited | 0 | 0.323929 | 0.490041 | 0.186031 | -0.516712 |
| 3/Q unsuited | 0 | 0.335612 | 0.530447 | 0.133941 | -0.400884 |
| 3/K unsuited | 0 | 0.371224 | 0.528731 | 0.100045 | -0.258317 |
| 3/A unsuited | 1 | 0 | 0 | 0 | 0.147447 |
| 4/5 unsuited | 0 | 0.330102 | 0.253447 | 0.416451 | -0.597704 |
| 4/6 unsuited | 0 | 0.326939 | 0.24502 | 0.428041 | -0.631146 |
| 4/7 unsuited | 0 | 0.324184 | 0.239921 | 0.435895 | -0.652204 |
| 4/8 unsuited | 0 | 0.322398 | 0.238953 | 0.438649 | -0.670508 |
| 4/9 unsuited | 0 | 0.316939 | 0.28459 | 0.398471 | -0.674678 |
| 4/10 unsuited | 0 | 0.322449 | 0.388382 | 0.289169 | -0.561652 |
| 4/J unsuited | 0 | 0.328112 | 0.497765 | 0.174123 | -0.467023 |
| 4/Q unsuited | 0 | 0.340714 | 0.543068 | 0.116217 | -0.350343 |
| 4/K unsuited | 0 | 0.380714 | 0.531607 | 0.087679 | -0.206014 |
| 4/A unsuited | 1 | 0 | 0 | 0 | 0.249395 |
| 5/6 unsuited | 0 | 0.332041 | 0.25253 | 0.415429 | -0.520572 |
| 5/7 unsuited | 0 | 0.329694 | 0.246692 | 0.423614 | -0.538616 |
| 5/8 unsuited | 0 | 0.327347 | 0.246239 | 0.426414 | -0.556168 |
| 5/9 unsuited | 0 | 0.325153 | 0.289475 | 0.385372 | -0.560523 |
| 5/10 unsuited | 0 | 0.326224 | 0.385557 | 0.288218 | -0.527259 |
| 5/J unsuited | 0 | 0.333418 | 0.501255 | 0.165327 | -0.415855 |
| 5/Q unsuited | 0 | 0.348673 | 0.557868 | 0.093458 | -0.297525 |
| 5/K unsuited | 1 | 0 | 0 | 0 | -0.117582 |
| 5/A unsuited | 1 | 0 | 0 | 0 | 0.358541 |
| 6/7 unsuited | 0 | 0.335408 | 0.249535 | 0.415057 | -0.430923 |
| 6/8 unsuited | 0 | 0.33398 | 0.248153 | 0.417867 | -0.446264 |
| 6/9 unsuited | 0 | 0.33199 | 0.290571 | 0.377439 | -0.450033 |
| 6/10 unsuited | 0 | 0.333418 | 0.388159 | 0.278423 | -0.416729 |
| 6/J unsuited | 0 | 0.335918 | 0.495046 | 0.169035 | -0.382895 |
| 6/Q unsuited | 0 | 0.35352 | 0.558225 | 0.088255 | -0.24873 |
| 6/K unsuited | 1 | 0 | 0 | 0 | -0.020774 |
| 6/A unsuited | 1 | 0 | 0 | 0 | 0.339763 |
| 7/8 unsuited | 0 | 0.338469 | 0.252622 | 0.408909 | -0.340197 |
| 7/9 unsuited | 0 | 0.33699 | 0.293185 | 0.369826 | -0.341955 |
| 7/10 unsuited | 0 | 0.340714 | 0.388049 | 0.271237 | -0.305845 |
| 7/J unsuited | 0 | 0.344745 | 0.493503 | 0.161752 | -0.269829 |
| 7/Q unsuited | 0 | 0.363418 | 0.554881 | 0.0817 | -0.209388 |
| 7/K unsuited | 1 | 0 | 0 | 0 | 0.081354 |
| 7/A unsuited | 1 | 0 | 0 | 0 | 0.465996 |
| 8/9 unsuited | 0 | 0.344286 | 0.289869 | 0.365845 | -0.236111 |
| 8/10 unsuited | 0 | 0.37148 | 0.366061 | 0.26246 | -0.193462 |
| 8/J unsuited | 0 | 0.370816 | 0.474244 | 0.154939 | -0.154944 |
| 8/Q unsuited | 1 | 0 | 0 | 0 | -0.069429 |
| 8/K unsuited | 1 | 0 | 0 | 0 | 0.166259 |
| 8/A unsuited | 1 | 0 | 0 | 0 | 0.575314 |
| 9/10 unsuited | 0 | 0.405153 | 0.334936 | 0.259911 | -0.07946 |
| 9/J unsuited | 0 | 0.42 | 0.427722 | 0.152278 | -0.038548 |
| 9/Q unsuited | 1 | 0 | 0 | 0 | 0.132505 |
| 9/K unsuited | 1 | 0 | 0 | 0 | 0.371024 |
| 9/A unsuited | 1 | 0 | 0 | 0 | 0.667695 |
| 10/J unsuited | 1 | 0 | 0 | 0 | 0.174024 |
| 10/Q unsuited | 1 | 0 | 0 | 0 | 0.369495 |
| 10/K unsuited | 1 | 0 | 0 | 0 | 0.607484 |
| 10/A unsuited | 1 | 0 | 0 | 0 | 0.906071 |
| J/Q unsuited | 1 | 0 | 0 | 0 | 0.455681 |
| J/K unsuited | 1 | 0 | 0 | 0 | 0.691991 |
| J/A unsuited | 1 | 0 | 0 | 0 | 0.991767 |
| Q/K unsuited | 1 | 0 | 0 | 0 | 0.782942 |
| Q/A unsuited | 1 | 0 | 0 | 0 | 1.080609 |
| K/A unsuited | 1 | 0 | 0 | 0 | 1.171914 |
| 2/3 suited | 0 | 0.306071 | 0.271131 | 0.422798 | -0.649268 |
| 2/4 suited | 0 | 0.313265 | 0.268168 | 0.418567 | -0.599061 |
| 2/5 suited | 0 | 0.317857 | 0.268349 | 0.413794 | -0.552398 |
| 2/6 suited | 0 | 0.315867 | 0.260915 | 0.423218 | -0.609673 |
| 2/7 suited | 0 | 0.3125 | 0.25629 | 0.43121 | -0.650352 |
| 2/8 suited | 0 | 0.31801 | 0.260772 | 0.421218 | -0.588712 |
| 2/9 suited | 0 | 0.33301 | 0.294364 | 0.372625 | -0.527903 |
| 2/10 suited | 0 | 0.363316 | 0.365854 | 0.27083 | -0.429841 |
| 2/J suited | 0 | 0.395306 | 0.42622 | 0.178474 | -0.33622 |
| 2/Q suited | 0 | 0.422194 | 0.444596 | 0.133211 | -0.22044 |
| 2/K suited | 1 | 0 | 0 | 0 | -0.074507 |
| 2/A suited | 1 | 0 | 0 | 0 | 0.399855 |
| 3/4 suited | 0 | 0.326582 | 0.269192 | 0.404226 | -0.472659 |
| 3/5 suited | 0 | 0.327041 | 0.272155 | 0.400804 | -0.423657 |
| 3/6 suited | 0 | 0.324745 | 0.264753 | 0.410502 | -0.479822 |
| 3/7 suited | 0 | 0.325969 | 0.256953 | 0.417078 | -0.52088 |
| 3/8 suited | 0 | 0.321837 | 0.257764 | 0.420399 | -0.557778 |
| 3/9 suited | 0 | 0.343112 | 0.290837 | 0.366051 | -0.482501 |
| 3/10 suited | 0 | 0.374031 | 0.361153 | 0.264816 | -0.38425 |
| 3/J suited | 0 | 0.401582 | 0.43196 | 0.166458 | -0.289096 |
| 3/Q suited | 0 | 0.427092 | 0.454265 | 0.118643 | -0.172115 |
| 3/K suited | 1 | 0 | 0 | 0 | 0.022 |
| 3/A suited | 1 | 0 | 0 | 0 | 0.496714 |
| 4/5 suited | 0 | 0.337908 | 0.275477 | 0.386615 | -0.298984 |
| 4/6 suited | 0 | 0.33699 | 0.266402 | 0.396608 | -0.351849 |
| 4/7 suited | 0 | 0.334388 | 0.2618 | 0.403812 | -0.392104 |
| 4/8 suited | 0 | 0.332398 | 0.261349 | 0.406253 | -0.429525 |
| 4/9 suited | 0 | 0.35398 | 0.283815 | 0.362206 | -0.452472 |
| 4/10 suited | 0 | 0.392857 | 0.351632 | 0.255511 | -0.339384 |
| 4/J suited | 0 | 0.413673 | 0.432751 | 0.153576 | -0.242526 |
| 4/Q suited | 0 | 0.436429 | 0.460315 | 0.103256 | -0.124449 |
| 4/K suited | 1 | 0 | 0 | 0 | 0.117016 |
| 4/A suited | 1 | 0 | 0 | 0 | 0.590105 |
| 5/6 suited | 0 | 0.348316 | 0.268747 | 0.382936 | -0.226888 |
| 5/7 suited | 0 | 0.34449 | 0.264516 | 0.390994 | -0.264165 |
| 5/8 suited | 0 | 0.344949 | 0.262638 | 0.392413 | -0.30074 |
| 5/9 suited | 0 | 0.381378 | 0.275176 | 0.343446 | -0.323487 |
| 5/10 suited | 0 | 0.409388 | 0.339889 | 0.250723 | -0.308004 |
| 5/J suited | 0 | 0.423316 | 0.431525 | 0.145159 | -0.194062 |
| 5/Q suited | 0 | 0.442245 | 0.471463 | 0.086292 | -0.07447 |
| 5/K suited | 1 | 0 | 0 | 0 | 0.219148 |
| 5/A suited | 1 | 0 | 0 | 0 | 0.690217 |
| 6/7 suited | 0 | 0.35551 | 0.262945 | 0.381544 | -0.140962 |
| 6/8 suited | 0 | 0.360102 | 0.257902 | 0.381996 | -0.174977 |
| 6/9 suited | 0 | 0.390561 | 0.273507 | 0.335932 | -0.196585 |
| 6/10 suited | 0 | 0.419184 | 0.339803 | 0.241014 | -0.18096 |
| 6/J suited | 0 | 0.429286 | 0.424012 | 0.146703 | -0.163644 |
| 6/Q suited | 1 | 0 | 0 | 0 | -0.006074 |
| 6/K suited | 1 | 0 | 0 | 0 | 0.309149 |
| 6/A suited | 1 | 0 | 0 | 0 | 0.649275 |
| 7/8 suited | 0 | 0.374796 | 0.254913 | 0.370291 | -0.052754 |
| 7/9 suited | 0 | 0.398367 | 0.273578 | 0.328054 | -0.071685 |
| 7/10 suited | 0 | 0.424694 | 0.340031 | 0.235275 | -0.053435 |
| 7/J suited | 0 | 0.432806 | 0.425739 | 0.141455 | -0.034445 |
| 7/Q suited | 1 | 0 | 0 | 0 | 0.062776 |
| 7/K suited | 1 | 0 | 0 | 0 | 0.403899 |
| 7/A suited | 1 | 0 | 0 | 0 | 0.767431 |
| 8/9 suited | 0 | 0.414286 | 0.26514 | 0.320574 | 0.051069 |
| 8/10 suited | 0 | 0.445663 | 0.324835 | 0.229502 | 0.075411 |
| 8/J suited | 1 | 0 | 0 | 0 | 0.107386 |
| 8/Q suited | 1 | 0 | 0 | 0 | 0.278932 |
| 8/K suited | 1 | 0 | 0 | 0 | 0.481611 |
| 8/A suited | 1 | 0 | 0 | 0 | 0.86889 |
| 9/10 suited | 0 | 0.477194 | 0.296558 | 0.226249 | 0.205485 |
| 9/J suited | 1 | 0 | 0 | 0 | 0.317837 |
| 9/Q suited | 1 | 0 | 0 | 0 | 0.489199 |
| 9/K suited | 1 | 0 | 0 | 0 | 0.694571 |
| 9/A suited | 1 | 0 | 0 | 0 | 0.953564 |
| 10/J suited | 1 | 0 | 0 | 0 | 0.778841 |
| 10/Q suited | 1 | 0 | 0 | 0 | 0.943595 |
| 10/K suited | 1 | 0 | 0 | 0 | 1.148469 |
| 10/A suited | 1 | 0 | 0 | 0 | 1.409312 |
| J/Q suited | 1 | 0 | 0 | 0 | 1.024156 |
| J/K suited | 1 | 0 | 0 | 0 | 1.2275 |
| J/A suited | 1 | 0 | 0 | 0 | 1.489507 |
| Q/K suited | 1 | 0 | 0 | 0 | 1.31262 |
| Q/A suited | 1 | 0 | 0 | 0 | 1.572705 |
| K/A suited | 1 | 0 | 0 | 0 | 1.658326 |
| 2/2 pair | 0 | 0.144388 | 0.792662 | 0.06295 | -0.179478 |
| 3/3 pair | 1 | 0 | 0 | 0 | 0.088456 |
| 4/4 pair | 1 | 0 | 0 | 0 | 0.46157 |
| 5/5 pair | 1 | 0 | 0 | 0 | 0.831643 |
| 6/6 pair | 1 | 0 | 0 | 0 | 1.159873 |
| 7/7 pair | 1 | 0 | 0 | 0 | 1.486948 |
| 8/8 pair | 1 | 0 | 0 | 0 | 1.811461 |
| 9/9 pair | 1 | 0 | 0 | 0 | 2.132513 |
| 10/10 pair | 1 | 0 | 0 | 0 | 2.480803 |
| J/J pair | 1 | 0 | 0 | 0 | 2.749739 |
| Q/Q pair | 1 | 0 | 0 | 0 | 3.018649 |
| K/K pair | 1 | 0 | 0 | 0 | 3.289359 |
| A/A pair | 1 | 0 | 0 | 0 | 3.601073 |
I never quantified a strategy to this game, because my computer figured out the optimal strategy on a hand by hand basis. However, the table above shows that that a large raise should be made on the following hands.
Shufflemaster literature mentions the following four possible pay tables on the Trips bet.
| Trips Bet - Pay Table 1 | ||||
| Player Hand | Combinations | Pays | Probability | Return |
| Royal flush | 4324 | 50 | 0.000032 | 0.001616 |
| Straight flush | 37260 | 40 | 0.000279 | 0.01114 |
| Four of a kind | 224848 | 30 | 0.001681 | 0.05042 |
| Full house | 3473184 | 9 | 0.025961 | 0.233649 |
| Flush | 4047644 | 7 | 0.030255 | 0.211785 |
| Straight | 6180020 | 4 | 0.046194 | 0.184775 |
| Three of a kind | 6461620 | 3 | 0.048299 | 0.144896 |
| All other | 113355660 | -1 | 0.8473 | -0.8473 |
| Total | 133784560 | 1 | -0.009018 | |
| Trips Bet - Pay Table 2 | ||||
| Player Hand | Combinations | Pays | Probability | Return |
| Royal flush | 4324 | 50 | 0.000032 | 0.001616 |
| Straight flush | 37260 | 40 | 0.000279 | 0.01114 |
| Four of a kind | 224848 | 30 | 0.001681 | 0.05042 |
| Full house | 3473184 | 8 | 0.025961 | 0.207688 |
| Flush | 4047644 | 6 | 0.030255 | 0.18153 |
| Straight | 6180020 | 5 | 0.046194 | 0.230969 |
| Three of a kind | 6461620 | 3 | 0.048299 | 0.144896 |
| All other | 113355660 | -1 | 0.8473 | -0.8473 |
| Total | 133784560 | 1 | -0.01904 | |
| Trips Bet - Pay Table 3 | ||||
| Player Hand | Combinations | Pays | Probability | Return |
| Royal flush | 4324 | 50 | 0.000032 | 0.001616 |
| Straight flush | 37260 | 40 | 0.000279 | 0.01114 |
| Four of a kind | 224848 | 30 | 0.001681 | 0.05042 |
| Full house | 3473184 | 8 | 0.025961 | 0.207688 |
| Flush | 4047644 | 7 | 0.030255 | 0.211785 |
| Straight | 6180020 | 4 | 0.046194 | 0.184775 |
| Three of a kind | 6461620 | 3 | 0.048299 | 0.144896 |
| All other | 113355660 | -1 | 0.8473 | -0.8473 |
| Total | 133784560 | 1 | -0.034979 | |
| Trips Bet - Pay Table 4 | ||||
| Player Hand | Combinations | Pays | Probability | Return |
| Royal flush | 4324 | 50 | 0.000032 | 0.001616 |
| Straight flush | 37260 | 40 | 0.000279 | 0.01114 |
| Four of a kind | 224848 | 20 | 0.001681 | 0.033613 |
| Full house | 3473184 | 7 | 0.025961 | 0.181727 |
| Flush | 4047644 | 6 | 0.030255 | 0.18153 |
| Straight | 6180020 | 5 | 0.046194 | 0.230969 |
| Three of a kind | 6461620 | 3 | 0.048299 | 0.144896 |
| All other | 113355660 | -1 | 0.8473 | -0.8473 |
| Total | 133784560 | 1 | -0.061808 | |
I'm told that the most common pay table for the Trips bet is Pay Table 2, at a 1.9% house edge.
Here's a link to Shufflemaster's Ultimate Texas Hold'em page.
This was a difficult game to analyze and required 40 days of computer time to cycle through all the combinations. As with most other poker based games my analysis was combinatorial in C++, looping through all possible combinations of cards by brute force.
Shufflemaster literature states the element of risk to 0.8%. This figure is based on the analysis of Elliot Frome. As shown above my element of risk is slightly lower at 0.526%. So I respectfully disagree with Mr. Frome.
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