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High Card Flush
Introduction
High Card Flush was introduced at Harrah's Laughlin during the summer of 2011. It made another appearance at the M Resort in Las Vegas in February 2013. After a slow start, the game gained popularity and is now widely featured.
This game utilizes a fold or raise format, similar to Caribbean Stud Poker and Three Card Poker. Its unique aspect lies in the hand rankings, which prioritize forming the highest possible flush from a total of seven cards.
Rules
- High Card Flush is played with a traditional deck of 52 playing cards.
- At the beginning of the game, every player must place an Ante bet, and they may also choose to make optional bets for flushes, straight flushes, and a Bonus Jackpot.
- Each player and the dealer receive seven cards dealt face down.
- The hands are ranked based on the following criteria:
- The primary criterion for ranking hands is the maximum number of cards within a single suit, known as the 'maximum flush.' For example, a hand featuring a maximum four-card flush surpasses any hand with a maximum three-card flush but is beaten by a hand with a maximum five-card flush.
- The second criterion adheres to traditional poker rankings for flushes; that is, a hand with a four-card flush K-Q-J-T is superior to one with K-Q-J-9, yet inferior to a hand with A-4-3-2.
- Each player must then select one of the following options:
- Fold, and surrender the Ante.
- Increase the wager by placing a second bet that is at least equal to the Ante. The maximum raise amount depends on the ranking of the player's hand:
- For a flush consisting of two to four cards, the maximum Raise is equivalent to the Ante bet.
- If the player has a five-card flush, they can raise up to double their Ante.
- A six- or seven-card flush allows for a maximum Raise wager that is three times the Ante.
- Once all players have made their decisions, the dealer reveals his seven cards and determines his hand using the same ranking system.
- If the dealer has less than a three-card flush, nine-high, the remaining players receive their Ante back, and no Raise bets are settled.
- If the dealer possesses at least a three-card flush, nine-high, his hand is then measured against each player’s:
- Players whose hands rank higher will win and receive their Ante and Raise bets back at face value.
- Players whose hands rank lower will lose, and their Ante and Raise bets will be collected.
- If any player holds a hand that matches the dealer's ranking exactly, those players will push their Ante and Raise bets.
- Finally, any player who placed a Bonus wager will have their hand evaluated against the Bonus payout table, and payments will be made or collected accordingly.
Mousseau Strategy
Charles Mousseau concluded that, disregarding cards outside the highest flush, a nearly optimal strategy involves raising with hands of T-8-6 or better. Players should consistently make the maximum allowed Raise bet, which results in a 0.06% higher house edge than the ideal strategy.
This means raising on any four-card flush or any three-card flush ranked T-8-6 or better. For instance, you would raise with J-3-2 but fold T-7-5.
The upcoming table displays the probabilities and returns for each event based on Mousseau's strategy, showing a house edge of 2.71% in the bottom right cell.
Mousseau Strategy Return Table
| Event | Pays | Probability | Return |
|---|---|---|---|
| If the player raises 3x and the dealer qualifies, the player wins. | 4 | 0.001604 | 0.006416 |
| If the player raises 2x and the dealer qualifies, the player wins. | 3 | 0.021374 | 0.064121 |
| If the player raises 1x and the dealer qualifies, the player wins. | 2 | 0.258352 | 0.516703 |
| If the player raises 1x and the dealer does not qualify, then... | 1 | 0.160076 | 0.160076 |
| If the player raises 2x and the dealer does not qualify, then... | 1 | 0.006590 | 0.006590 |
| If the player raises 3x and the dealer does not qualify, then... | 1 | 0.000444 | 0.000444 |
| If the player raises 1x, the dealer qualifies, and the player pushes. | 0 | 0.000839 | 0.000000 |
| If the player raises 2x, the dealer qualifies, and the player pushes. | 0 | 0.000001 | 0.000000 |
| If the player raises 3x, the dealer qualifies, and the player pushes. | 0 | 0.000000 | 0.000000 |
| Player folds | -1 | 0.320589 | -0.320589 |
| If the player raises 1x, the dealer qualifies, and the player loses. | -2 | 0.229568 | -0.459136 |
| If the player raises 2x, the dealer qualifies, and the player loses. | -3 | 0.000559 | -0.001678 |
| If the player raises 3x, the dealer qualifies, and the player loses. | -4 | 0.000003 | -0.000013 |
| Totals | 1.000000 | -0.027065 |
According to the Mousseau strategy, the average final wager is calculated at 1.712 units. Therefore, element of risk is 2.706%/1.712 = 1.581%.
High Card Flush Advanced Strategy
Gordon Michaels, a contributor for Wizard of Odds, has shared High Card Flush Advanced Strategy . His strategy takes into account the distribution of suits among penalty cards from T-3-2 to T-9-8. The result is a house edge of 2.6855%. Click the link for detailed information.
Optimal Strategy
A perfectly optimal strategy has not yet been formally documented. However, we can outline some guidelines:
- Always place the maximum raise when holding J-9-6 or better.
- Fold 9-7-4 or lower.
- You\"re on your own with 9-7-5 to J-9-5.
The subsequent table indicates that under an unknown optimal strategy, the house edge is 2.64%.
Optimal Strategy Return Table
| Event | Pays | Probability | Return |
|---|---|---|---|
| If the player raises 3x and the dealer qualifies, the player wins. | 4 | 0.001618 | 0.006473 |
| If the player raises 2x and the dealer qualifies, the player wins. | 3 | 0.021472 | 0.064417 |
| If the player raises 1x and the dealer qualifies, the player wins. | 2 | 0.258181 | 0.516361 |
| If the player raises 1x and the dealer does not qualify, then... | 1 | 0.160038 | 0.160038 |
| If the player raises 2x and the dealer does not qualify, then... | 1 | 0.006617 | 0.006617 |
| If the player raises 3x and the dealer does not qualify, then... | 1 | 0.000448 | 0.000448 |
| If the player raises 1x, the dealer qualifies, and the player pushes. | 0 | 0.000840 | 0.000000 |
| If the player raises 2x, the dealer qualifies, and the player pushes. | 0 | 0.000001 | 0.000000 |
| If the player raises 3x, the dealer qualifies, and the player pushes. | 0 | 0.000000 | 0.000000 |
| Player folds | -1 | 0.321365 | -0.321365 |
| If the player raises 1x, the dealer qualifies, and the player loses. | -2 | 0.228857 | -0.457715 |
| If the player raises 2x, the dealer qualifies, and the player loses. | -3 | 0.000560 | -0.001679 |
| If the player raises 3x, the dealer qualifies, and the player loses. | -4 | 0.000003 | -0.000013 |
| Totals | 1.000000 | -0.026418 |
Under the Mousseau strategy, the average final wager stands at 1.711 units. Therefore, element of risk is 2.642%/1.711 = 1.544%.
Miscellaneous statistics:
- Overall, players adopting the optimal strategy will raise approximately 67.86% of the time.
- Dealers will qualify with a hand about 75.36% of the time.
- There will be a tie between the player and dealer 0.08% of the time.
- The standard deviation is 1.63.
Flush Bet
I've come across two different pay tables for the Flush bet. The following three tables detail the variations.
Pay Table 1
| 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 |
Pay Table 2
| Cards | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 7 | 300 | 6,864 | 0.000051 | 0.015392 |
| 6 | 75 | 267,696 | 0.002001 | 0.150071 |
| 5 | 5 | 3,814,668 | 0.028514 | 0.142568 |
| 4 | 2 | 26,137,540 | 0.195370 | 0.390741 |
| 3 or less | -1 | 103,557,792 | 0.774064 | -0.774064 |
| Total | 133,784,560 | 1.000000 | -0.075292 |
Straight Flush Bet
The Straight Flush side bet rewards based on the longest straight flush a player can construct. I've only seen this at Planet Hollywood, and the house edge in this instance is 13.11%.
Straight Flush Side Wager
| Cards | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 7 | 8000 | 32 | 0.000000 | 0.001914 |
| 6 | 1000 | 1,592 | 0.000012 | 0.011900 |
| 5 | 100 | 39,960 | 0.000299 | 0.029869 |
| 4 | 60 | 676,196 | 0.005054 | 0.303262 |
| 3 | 7 | 8,642,932 | 0.064603 | 0.452224 |
| 2 or less | -1 | 124,423,848 | 0.930031 | -0.930031 |
| Total | 133,784,560 | 1.000000 | -0.130864 |
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Bonus Jackpot
The subsequent table summarizes my assessment of the $1 progressive side bet Bonus Jackpot.Bonus Jackpot
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 7-card straight flush | 100% Jackpot | 32 | 0.000000 | ? |
| 6-card straight flush, ace-high | 100% Jackpot | 180 | 0.000001 | ? |
| For a 6-card straight flush, king-high or lower, | 10% Jackpot | 1,412 | 0.000011 | ? |
| 5-card straight flush | 300 | 39,960 | 0.000299 | 0.089607 |
| 4-card straight flush | 50 | 676,196 | 0.005054 | 0.252718 |
| 3-card straight flush | 3 | 8,642,932 | 0.064603 | 0.193810 |
| All other | 0 | 124,423,848 | 0.930031 | 0.000000 |
| Total | 133,784,560 | 1.000000 | 0.536135 |
The lower right section of the previous table indicates that fixed wins return 53.61% to the player. Each increase of $1,000 in the jackpot meter raises this return by 1.69%. The side bet achieves break-even at $175,702.05, and at a reset value of $5,000, the return is 54.93%.
Acknowledgements
- Gratitude to Charles Mousseau for providing the mathematical analysis for this game, excluding the Straight Flush side bet. You can visit Charles' website, tgscience.com .
- Gordon Michaels for his High Card Flush Advanced Strategy .