Flush Rush @ The D Casino, Las Vegas
A reader told me about a new ShuffleMaster game at The D Casino, where you try to make a 4- to 7- card flush, starting with 4 hole cards, and paying to see 5th/6th and 7th Streets on a community board. The betting structure is similar to Mississippi Stud, where you post an Ante, then make a 1x Play decision to see 6th Street, and a final 1x Play decision to see 7th Street. The game pays odds on the Ante if you make a 4-card flush or better, and even-money on the 1x Play bets. Otherwise, if you fold or don’t make a hand, you lose your bets.
Length | Flush | Straight Flush |
---|---|---|
7 | 300-to-1 | 1000-to-1 |
6 | 20-to-1 | 500-to-1 |
5 | 9-to-1 | 100-to-1 |
4 | 5-to-1 | 15-to-1 |
I believe The D will award the highest possible payout for a given hand. So, if you make a 5-card flush that contains a 4-card straight flush, they’ll pay you 15-to-1 (instead of 9-to-1). With this liberal rules interpretation, the house edge is 3.75%. The total possible outcomes for an optimal player are listed below.
Outcome | Combinations | Frequency | Net | Return |
---|---|---|---|---|
7-card Straight Flush | 3,360 | 2.3919E-07 | 1002 | 0.000240 |
6-card Straight Flush | 167,160 | 1.1900E-05 | 502 | 0.005974 |
7-card Flush | 697,620 | 4.9662E-05 | 302 | 0.014998 |
5-card Straight Flush | 4,127,760 | 0.000294 | 102 | 0.029972 |
6-card Flush | 26,945,100 | 0.001918 | 22 | 0.042119 |
4-card Straight Flush | 65,648,544 | 0.004673 | 17 | 0.079447 |
5-card Flush | 372,841,560 | 0.026542 | 11 | 0.291959 |
4-card Flush | 2,627,978,496 | 0.187080 | 7 | 1.309557 |
Nothing | 5,035,629,456 | 0.358475 | -3 | -1.075424 |
Fold before river | 4,431,366,576 | 0.315459 | -2 | -0.630917 |
Fold before flop | 1,481,973,168 | 0.105498 | -1 | -0.105498 |
Total | 14,047,378,800 | 1.000000 | -0.037493 |
If the rules are interpreted strictly, and you must make a straight flush with all your cards of the same suit, then the house edge is 5.41%.
Outcome | Combinations | Frequency | Net | Return |
---|---|---|---|---|
7-card Straight Flush | 3,360 | 2.3919E-07 | 1002 | 0.000240 |
7-card Flush | 717,360 | 5.1067E-05 | 302 | 0.015422 |
6-card Straight Flush | 147,420 | 1.0494E-05 | 502 | 0.005268 |
6-card Flush | 27,960,660 | 0.001990 | 22 | 0.043790 |
5-card Straight Flush | 3,112,200 | 0.000222 | 102 | 0.022598 |
5-card Flush | 397,427,940 | 0.028292 | 11 | 0.311212 |
4-card Straight Flush | 41,062,164 | 0.002923 | 17 | 0.049693 |
4-card Flush | 2,627,978,496 | 0.187080 | 7 | 1.309557 |
Nothing | 5,035,629,456 | 0.358475 | -3 | -1.075424 |
Fold before river | 4,431,366,576 | 0.315459 | -2 | -0.630917 |
Fold before flop | 1,481,973,168 | 0.105498 | -1 | -0.105498 |
Total | 14,047,378,800 | 1.000000 | -0.054059 |
Outcome | Combinations | Frequency | Net | Return |
---|---|---|---|---|
All hole cards same suit | 2,860 | 0.010564 | 30 | 0.316927 |
All hole cards different suits | 28,561 | 0.105498 | 5 | 0.527491 |
Others | 239,304 | 0.883938 | -1 | -0.883938 |
Total | 270,725 | 1.000000 | -0.039520 |
Of course, the only reason why I analyzed the game was to Monte Carlo the 6-way collusion edge. The return is about +4.07% for 6 players sharing perfect info under strict rule interpretation, and +5.67% under the liberal rules. That’s not much, considering it’s pretty hard to convey suit information between confederates. It’s probably not worth anyone’s trouble to attack the game. I didn’t bother working out a practical strategy.
(FYI, I’m spending a lot more time outside of the casino these days. Before, I used to practically live in the casino. About 9 months ago, I changed obsessions. You can read about my current mania on my other blog.)
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