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.)
Discount Gambling 
hmmm…this is interesting. I am hooked on High Card Flush, even though I am down BIG TIME playing the game…and that is even after a 6-card straight flush good for $10k! The payout seems better on High Card Flush, but then again, those payouts are on the bonus bets.
The player is awarded his best payout from the hand: a six-card flush with a 4-card straight flush pays 20:1 for the 6-card flush; a 5-card flush with a 4-card straight flush pays the 15:1 straight flush.
? Wouldn’t the optimal collusion yield 5.7%? the 4.07% player collusion edge was based on the original strict interpretation, I think.
Excellent job as usual Stephen. The basic strategy is really easy on this game:
Fold before flop: 1 of each suit
Bet river: any 3 or more suited cards
Stephen, great job again, we have missed you. I am glad you have moved on to healthier things. One question: if you have 2 clubs and one heart and one spade. How many clubs does there have to be left in the deck to bet?
This has been removed from The D. It was replaced by War Blackjack.