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Last Updated: August 15, 2016

Chase the Flush

Introduction



Chase the Flush is a poker-based game with the goal of having a higher flush than the dealer. It follows a similar bet structure as Ultimate Texas Hold 'Em with the flush scoring of High Card Flush. I first noticed it at the Luxor in Las Vegas on August 11, 2016. It can also be found at the Fantasy Springs near Palm Springs. The game is marketed by AGS.

Rules



Following are the rules for Chase the Flush. If two rules seem to contradict, then the one listed first should be adjudicated first.

  1. The game is played with a single 52-card deck.
  2. Play begins with the player making equal bets on the Ante and the X-Tra Bonus. The player may also make an optional Same Suit Bonus side bet.
  3. The player and the dealer receive three hole cards each.
  4. After examining his cards, the player may check or bet 3x the Ante on the All In bet.
  5. The dealer then places the first two community cards face up on the layout.
  6. If the player did not already make an All In bet, then he may check or bet 2x the Ante on the All In bet.
  7. The dealer then places the final two community cards face-up on the layout.
  8. If the player did not already make an All In bet, then he must bet 1x the Ante on the All In bet or fold.
  9. The dealer then reveals his three hole cards and determines his best flush hand.
  10. The dealer needs a nine-high three-card flush in order to qualify.
  11. If the dealer does not qualify, then the Ante bet pushes.
  12. The player and dealer hands shall then be compared, the higher hand wins. The first consideration is that the longest flush wins. If there is a tie for the number of cards, then the individual cards will be compared, as in conventional poker.
  13. If the player has the higher hand, then the Ante* and All In bets shall pay even money and the X-Tra Bonus bet according to the pay table below.
  14. If the player and dealer tie, then the Ante*, All In, and X-Tra Bonus bets shall all push.
  15. If the dealer has the higher hand, then the Ante*, All In, and X-Tra Bonus bets shall all lose.
  16. The Same Suit bet shall pay according to the player's hand only and the pay table below.


*: Please note that for purposes of adjudicating the Ante wager, rule 11 supersedes this rule. In other words, if the dealer does not qualify, then the Ante will be returned before any comparison of the player and dealer hands.

X-Tra Bonus Pay Table

Event Pays
7-card flush 250 to 1
6-card flush 50 to 1
5-card flush 5 to 1
4-card flush 1 to 1
All other Push


Same Suit Pay Table

Event Pays
7-card straight flush 2000 to 1
6-card straight flush 2000 to 1
7-card flush 300 to 1
5-card straight flush 100 to 1
6-card flush 50 to 1
4-card straight flush 20 to 1
5-card flush 10 to 1
4-card flush 1 to 1


Strategy



So far nobody has tested any kind of quantifiable strategy to the best of my knowledge. Until that time, the following table of the probability of each player action may be of some help.

Player Action

Raise Probability
3 23.84%
2 24.90%
1 35.17%
Fold 16.09%
Total 100.00%


I suggest the following vague strategy, which I admit has not been tested but is based on the table above.

  • At the first decision point raise with any three suited or Q-9 suited or better with two suited. If close to Q-9, consider the singleton, the higher in rank the better.
  • At the second decision point, raise with any three suited cards.
  • The third decision point is tough. 68.6% of the time you will raise at this point. If forced, I would raise with any three suited or two strong suited pairs.


Analysis



The following table shows the probability and contribution to the return of all possible outcomes of the Ante, All In, and X-Tra Bonus wagers, assuming optimal player strategy. It is organized from left to right according to the player's raise first, whether the dealer qualifies, the number of cards in the player's longest flush, the outcome against the dealer, the net win, number of combinations, probability, and contribution to the return.

Base Game Analysis

Event Pays Combinations Probability Return
3 Yes 7 Win 254 20,439,619,200 0.000051 0.013023
3 Yes 6 Win 24 534,992,418,432 0.001342 0.032207
3 Yes 5 Win 9 4,296,578,849,136 0.010777 0.096997
3 Yes 4 Win 5 16,130,726,914,176 0.040462 0.202309
3 Yes 3 Win 4 16,796,416,174,704 0.042132 0.168527
3 Yes Any Loss -5 30,809,847,740,400 0.077283 -0.386413
3 Yes Any Tie 0 2,751,669,318,312 0.006902 0.000000
3 No 6 Win 23 24,404,889,600 0.000061 0.001408
3 No 5 Win 8 1,075,217,004,000 0.002697 0.021576
3 No 4 Win 4 6,377,470,048,800 0.015997 0.063988
3 No 3 Win 3 12,970,988,479,440 0.032536 0.097608
3 No 2 Win 3 1,600,580,385,168 0.004015 0.012045
3 No Any Loss -4 1,162,087,560,552 0.002915 -0.011660
3 No Any Tie 0 478,678,665,600 0.001201 0.000000
2 Yes 6 Win 23 227,291,635,008 0.000570 0.013113
2 Yes 5 Win 8 4,704,150,904,080 0.011800 0.094398
2 Yes 4 Win 4 21,499,155,021,948 0.053928 0.215712
2 Yes 3 Win 3 14,714,103,160,440 0.036908 0.110725
2 Yes Any Loss -4 32,751,544,964,688 0.082153 -0.328613
2 Yes Any Tie 0 622,124,227,116 0.001561 0.000000
2 No 5 Win 7 187,837,403,616 0.000471 0.003298
2 No 4 Win 3 6,488,002,635,144 0.016274 0.048823
2 No 3 Win 2 16,304,458,158,816 0.040898 0.081795
2 No 2 Win 2 987,169,878,672 0.002476 0.004952
2 No 2 Loss -3 710,513,189,700 0.001782 -0.005347
2 No 2 Tie 0 79,383,252,492 0.000199 0.000000
1 Yes 5 Win 7 393,192,506,064 0.000986 0.006904
1 Yes 4 Win 3 10,828,061,228,676 0.027161 0.081482
1 Yes 3 Win 2 20,718,789,206,988 0.051970 0.103941
1 Yes Any Loss -3 68,485,489,408,332 0.171787 -0.515362
1 Yes Any Tie 0 7,086,006,696,552 0.017774 0.000000
1 No 5 Win 6 5,385,180,384 0.000014 0.000081
1 No 4 Win 2 1,985,444,394,456 0.004980 0.009960
1 No 3 Win 1 26,514,857,520,000 0.066509 0.066509
1 No 2 Win 1 1,746,004,992,372 0.004380 0.004380
1 No Any Loss -2 2,094,365,166,192 0.005253 -0.010507
1 No Any Tie 0 362,165,402,664 0.000908 0.000000
Fold -2 64,139,016,142,080 0.160885 -0.321769
Total 398,664,610,344,000 1.000000 -0.023907

The bottom right corner shows that the ratio of the expected total loss to the Ante bet is 2.39%. Since the player must bet at least two units, I would define the house edge as the expected total units lost to the initial bet, which would 0.023907/2 = 1.20%.

For comparing one game to another, I like to use the Element of Risk, which is the ratio of the expected loss to the average amount bet. The average bet in Chase the Flush is 3.564878 units. Thus, the Element of Risk is 0.023907/3.564878 = 0.67%, which makes it a very competitive bet.

Same Suit Analysis



The following tables shows the probability and contribution to the return of all possible outcomes of the Same Suit bet. The bottom right cell shows a house edge of 5.67%.

Same Suit Analysis

Event Pays Combinations Probability Return
7-card straight flush 2,000 32 0.000000 0.000478
6-card straight flush 2,000 1,592 0.000012 0.023799
7-card flush 300 6,644 0.000050 0.014899
5-card straight flush 100 39,312 0.000294 0.029385
6-card flush 50 256,620 0.001918 0.095908
4-card straight flush 20 636,272 0.004756 0.095119
5-card flush 10 3,550,872 0.026542 0.265417
4-card flush 1 25,735,424 0.192365 0.192365
Loss -1 103,557,792 0.774064 -0.774064
Total 133,784,560 1.000000 -0.056694



  • AGS — Marketing materials by the game owner.
  • Wizard of Vegas — Discussion about Chase the Flush in my forum.


Acknowledgements



I would like to thank the game owner, AGS, for providing to me the math report by Stephen How of Discount Gambling. This saved me a lot of time analyzing the base game myself and I always trust Stephen's work. The analysis on the Same Suit bet I did myself and it agrees with How's report.


Written by: Michael Shackleford

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