# Discount Gambling

## Flush Rush @ The D Casino, Las Vegas

Posted in Uncategorized by stephenhow on May 3, 2014

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.

Ante Pay Table
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.

Optimal Play Outcomes (Liberal Rules)
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%.

Optimal Play Outcomes (Strict Rules)
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
All-Or-Nothing Side Bet
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.)

### 5 Responses

1. Mike said, on May 4, 2014 at 5:22 pm

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.

2. Dan said, on May 4, 2014 at 7:59 pm

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.

3. Adam R Cohen said, on May 5, 2014 at 1:03 pm

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

4. ugly999999 said, on July 1, 2014 at 12:53 pm

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?

5. Julio said, on July 30, 2014 at 3:54 pm

This has been removed from The D. It was replaced by War Blackjack.