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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, then 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%.
Large bettors should be wary of maximum payouts. If your ante bet is more than 1/500 of the maximum payout, then you will get shortchanged on a royal flush. For every 100 the effective payout on a royal goes down, the house edge will go up by 0.308%. In other words, the increase in the house edge will be [500-(MP/500)]*0.0000308, where MP is the maximum payout.
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.
There is a good page on the next two decision points at discountgambling.net.
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.
I have an uncomfirmed report that the Buffalo Thunder casino in Sante Fe, New Mexico, has a $1 progressive side bet for Ultimate Texas Hold 'Em. If the player flops a royal flush then he wins the jackpot. If the player gets a royal flush, using at least one hole card, then he wins 5% of the jackpot. The following table shows the return for a hypothetical jackpot of $100,000. All pays are on a "for one" basis, meaning the player never gets his original bet back, even if he wins.
| Buffalo Thunder Progressive — $100,000 Jackpot | ||||
| Event | Pays | Permutations | Probability | Return |
| Player flops royal | 100000 | 1037760 | 0.000002 | 0.153908 |
| Royal partially on board | 5000 | 19717440 | 0.000029 | 0.146212 |
| Royal entirely on board | 3000 | 1037760 | 0.000002 | 0.004617 |
| Straight flush | 250 | 187790400 | 0.000279 | 0.069627 |
| Four of a kind | 100 | 1133233920 | 0.001681 | 0.168067 |
| Full house | 10 | 17504847360 | 0.025961 | 0.25961 |
| All other | 0 | 655426517760 | 0.972047 | 0 |
| Total | 674274182400 | 1 | 0.802042 | |
The return for at any given time is 50.19% plus 3.00% for each $10,000 in the meter. For exactly zero house edge, the meter would need to be $165,959.74. I'm told the meter is seeded at $5,000, and 27% of money bet goes towards the meter. Fixed wins are not deducted from the meter. That would make the overall return 77.96%.
I have a report that the Firekeeper's casino in Michigan has a $1 progressive jackpot based on the flop and the player's two hole cards. I do not know the jackpot seed or contribution rate. The following table shows the return based on a hypothetical $100,000 jackpot. All wins are on a "for one" basis, meaning the player doesn't get his bet back if he wins.
| Michigan Progressive — $100,000 Jackpot | ||||
| Event | Pays | Combinations | Probability | Return |
| Royal flush | 100000 | 4 | 0.000002 | 0.153908 |
| Straight flush | 10000 | 36 | 0.000014 | 0.138517 |
| Four of a kind | 300 | 624 | 0.00024 | 0.072029 |
| Full house | 50 | 3744 | 0.001441 | 0.072029 |
| Flush | 40 | 5108 | 0.001965 | 0.078616 |
| Straight | 30 | 10200 | 0.003925 | 0.117739 |
| Three of a kind | 9 | 54912 | 0.021128 | 0.190156 |
| All other | 0 | 2524332 | 0.971285 | 0 |
| Total | 2598960 | 1 | 0.822994 | |
The lower right cell shows that for a jackpot of exactly $100,000 the return would be 82.30%. For any given jackpot amount, the return is 53.057% + 2.924% for every $10,000 in the jackpot meter. The breakeven point, where there would be zero house edge is at a mater of $160530.53.
Here's a link to Shufflemaster's Ultimate Texas Hold'em page.
discountgambling.net has an outstanding analysis of this game, including strategy for the second and third decision poitns.
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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