Last Updated: Oct. 22, 2014

High Card Flush

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Introduction



High Card Flush made its debut at Harrah's Laughlin in summer 2011. In February 2013 it found another placement at the M in Las Vegas. The game follows a fold or call structure, like Caribbean Stud Poker and Three Card Poker. Where it differs is in the hand ranking, which is all about making the highest possible flush out of seven cards.

Rules



  1. High Card Flush is played with a standard 52-card deck of playing cards.
  2. To begin play, each player makes the mandatory Ante wager, and if desired, the optional Bonus wager.
  3. The player and dealer each receive seven cards face down.
  4. Hands are evaluated in the following fashion:
    • The first ranking criteria is the greatest number of cards in any one suit. This is referred to as the "maximum flush." For instance, any hand with a maximum four-card flush beats any hand with a maximum three-card flush, but loses to any hand with a maximum five-card flush.
    • The second ranking criteria is the standard poker-rankings for flushes; that is, a hand with a maximum four-card flush of K-Q-J-T would beat a hand with a maximum four-card flush of K-Q-J-9, but lose to a hand with a maximum four-card flush of A-4-3-2.
  5. Each player then decides upon one of the following options:
    • Fold, and surrender the Ante.
    • Call, placing a second bet equal to at least the Ante. The maximum amount of the Call wager depends on the rank of the player?s hand:
      • With a two-, three- or four-card flush, the maximum Call wager is equal to the Ante wager.
      • With a five-card flush, the maximum Call wager is double the Ante wager.
      • With a six- or seven-card flush, the maximum Call wager is triple the Ante wager.
  6. Once all players have decided, the dealer turns over his seven cards and evaluates his hand in a similar fashion as described above.
  7. If the dealer does not have at least a three-card flush, nine-high, all remaining players have their Antes paid, and the Call bets are pushed.
  8. If the dealer has at least a three-card flush, nine-high, his hand is compared to each other player:
    • All players with a higher-ranking hand win, and have their Ante and Call wagers paid at even money.
    • All players with a lower-ranking hand lose, and have their Ante and Call wagers collected.
    • Players with the exact same ranking hand as the dealer push both their Ante and Call wagers.
  9. Finally, any player who made the Bonus wager has his hand evaluated against the Bonus paytable, and the Bonus wager is either paid or collected as necessary.

Mousseau Strategy



Charles Mousseau determined that without regard to cards not part of the highest flush, a close to perfect strategy is to call on T-8-6 or higher. The player should always make the largest allowed Call bet. This strategy has a house edge of 0.06% higher than optimal strategy.

That means to call any four-card or higher flush, and any three-card flush of rank T-8-6 or greater. For example, you would call J-3-2, but fold T-7-5.

The following table shows the probability and return for each possible event under the Mousseau strategy. The lower right cell shows a house edge of 2.71%.

Mousseau Strategy Return Table

Event Pays Probability Return
Player calls 3x, dealer qualifies, player wins 4 0.001604 0.006416
Player calls 2x, dealer qualifies, player wins 3 0.021374 0.064121
Player calls 1x, dealer qualifies, player wins 2 0.258352 0.516703
Player calls 1x, dealer does not qualify 1 0.160076 0.160076
Player calls 2x, dealer does not qualify 1 0.006590 0.006590
Player calls 3x, dealer does not qualify 1 0.000444 0.000444
Player calls 1x, dealer qualifies, player pushes 0 0.000839 0.000000
Player calls 2x, dealer qualifies, player pushes 0 0.000001 0.000000
Player calls 3x, dealer qualifies, player pushes 0 0.000000 0.000000
Player folds -1 0.320589 -0.320589
Player calls 1x, dealer qualifies, player loses -2 0.229568 -0.459136
Player calls 2x, dealer qualifies, player loses -3 0.000559 -0.001678
Player calls 3x, dealer qualifies, player loses -4 0.000003 -0.000013
Totals 1.000000 -0.027065

Under the Mousseau strategy, the average final wager is 1.712 units. Thus, the element of risk is 2.706%/1.712 = 1.581%.

Optimal Strategy



An optimal strategy has yet to be put in writing. However, we can narrow it down, as follows.

  • Make maximum Call bet with J-9-6 or higher.
  • Fold 9-7-4 or lower.
  • You're on your own with 9-7-5 to J-9-5.

The following table shows that under the unknown optimal strategy the house edge is 2.64%.

Optimal Strategy Return Table

Event Pays Probability Return
Player calls 3x, dealer qualifies, player wins 4 0.001618 0.006473
Player calls 2x, dealer qualifies, player wins 3 0.021472 0.064417
Player calls 1x, dealer qualifies, player wins 2 0.258181 0.516361
Player calls 1x, dealer does not qualify 1 0.160038 0.160038
Player calls 2x, dealer does not qualify 1 0.006617 0.006617
Player calls 3x, dealer does not qualify 1 0.000448 0.000448
Player calls 1x, dealer qualifies, player pushes 0 0.000840 0.000000
Player calls 2x, dealer qualifies, player pushes 0 0.000001 0.000000
Player calls 3x, dealer qualifies, player pushes 0 0.000000 0.000000
Player folds -1 0.321365 -0.321365
Player calls 1x, dealer qualifies, player loses -2 0.228857 -0.457715
Player calls 2x, dealer qualifies, player loses -3 0.000560 -0.001679
Player calls 3x, dealer qualifies, player loses -4 0.000003 -0.000013
Totals 1.000000 -0.026418

Under the Mousseau strategy, the average final wager is 1.711 units. Thus, the element of risk is 2.642%/1.711 = 1.544%.

Miscellaneous statistics:

  • All told, when the player plays optimally, the player will call 67.86% of the time.
  • The dealer will have a qualifying hand 75.36% of the time.
  • The player and dealer will tie 0.08% of the time.

Flush Bet



I have seen two pay tables for the Flush bet. The following two tables show the details.

Flush Side Wager — Harrah's Laughlin

Cards Pays Probability Return
7 200 0.000051 0.010198
6 50 0.002004 0.100183
5 6 0.028510 0.142551
4 1 0.195315 0.195315
3, 8-high or less 0 0.061903 0.000000
2 0 0.184443 0.000000
3, 9-high or more -1 0.527774 -0.527774
Total 1.000000 -0.079526

Flush Side Wager — Planet Hollywood

Cards Pays Combinations Probability Return
7 300 6,864 0.000051 0.015392
6 100 267,696 0.002001 0.200095
5 10 3,814,668 0.028514 0.285135
4 1 26,137,540 0.195370 0.195370
3 or less -1 103,557,792 0.774064 -0.774064
Total 133,784,560 1.000000 -0.078072

Straight Flush Bet

The Straight Flush side bet pays according to the longest straight flush the player can make. I observed it only at the Planet Hollywood. The lower right cell shows a house edge of 13.11%.

Straight Flush Side Wager

Cards Pays Combinations Probability Return
7 8000 32 0.000000 0.001914
6 1000 1,568 0.000012 0.011720
5 100 39,924 0.000298 0.029842
4 60 676,148 0.005054 0.303240
3 7 8,642,916 0.064603 0.452223
2 or less -1 124,423,972 0.930032 -0.930032
Total 133,784,560 1.000000 -0.131093

Acknowledgements

Thanks for Charles Mousseau for providing the math for this game. If you're in need of a gaming mathematician, Charles' web site is tgscience.com.

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