HIGH CARD FLUSH – STRATEGY Charles Mousseau has calculated a simple strategy, which says to raise with any T-8-6 flush or higher. The strategy is easy to remember and has a house edge of only 0.06% higher than the optimal strategy.
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- Recently, the game has become all that people want to play on casino floors and online. The game has similar rules to 3 card poker and the Caribbean stud poker. To fold or raise in the game follows the same rules as these games. The only catch comes to the hand rankings. For the high card flush, all that you need is to make the best out of the.
- Aug 28, 2019 High Card Flush is a poker variation that first started circulating across the USA casinos several years ago (around 2011), increasing in popularity after being introduced at the M Resort in Las Vegas.
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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. After that slow beginning the game caught on and today has lots of placements.
The game follows a fold or raise 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
- High Card Flush is played with a standard 52-card deck of playing cards.
- To begin play, each player makes the mandatory Ante wager, and if desired, the optional Bonus wager.
- The player and dealer each receive seven cards face down.
- 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.
- Each player then decides upon one of the following options:
- Fold, and surrender the Ante.
- Raise, placing a second bet equal to at least the Ante. The maximum amount of the Raise wager depends on the rank of the player?s hand:
- With a two-, three- or four-card flush, the maximum Raise wager is equal to the Ante wager.
- With a five-card flush, the maximum Raise wager is double the Ante wager.
- With a six- or seven-card flush, the maximum Raise wager is triple the Ante wager.
- Once all players have decided, the dealer turns over his seven cards and evaluates his hand in a similar fashion as described above.
- If the dealer does not have at least a three-card flush, nine-high, all remaining players have their Antes paid, and the Raise bets are pushed.
- 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 Raise wagers paid at even money.
- All players with a lower-ranking hand lose, and have their Ante and Raise wagers collected.
- Players with the exact same ranking hand as the dealer push both their Ante and Raise wagers.
- 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 raise on T-8-6 or higher. The player should always make the largest allowed Raise bet. This strategy has a house edge of 0.06% higher than optimal strategy.
That means to raise any four-card or higher flush, and any three-card flush of rank T-8-6 or greater. For example, you would raise 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 raises 3x, dealer qualifies, player wins | 4 | 0.001604 | 0.006416 |
Player raises 2x, dealer qualifies, player wins | 3 | 0.021374 | 0.064121 |
Player raises 1x, dealer qualifies, player wins | 2 | 0.258352 | 0.516703 |
Player raises 1x, dealer does not qualify | 1 | 0.160076 | 0.160076 |
Player raises 2x, dealer does not qualify | 1 | 0.006590 | 0.006590 |
Player raises 3x, dealer does not qualify | 1 | 0.000444 | 0.000444 |
Player raises 1x, dealer qualifies, player pushes | 0 | 0.000839 | 0.000000 |
Player raises 2x, dealer qualifies, player pushes | 0 | 0.000001 | 0.000000 |
Player raises 3x, dealer qualifies, player pushes | 0 | 0.000000 | 0.000000 |
Player folds | -1 | 0.320589 | -0.320589 |
Player raises 1x, dealer qualifies, player loses | -2 | 0.229568 | -0.459136 |
Player raises 2x, dealer qualifies, player loses | -3 | 0.000559 | -0.001678 |
Player raises 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%.
High Card Flush Advanced Strategy
Wizard of Odds contributor Gordon Michaels has published a High Card Flush Advanced Strategy. His strategy considers the suit distribution of the penalty cards with T-3-2 to T-9-8. The bottom line is a house edge of 2.6855%. Please click the link for the specifics.
Optimal Strategy
An optimal strategy has yet to be put in writing. However, we can narrow it down, as follows.
- Make maximum raise 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 raises 3x, dealer qualifies, player wins | 4 | 0.001618 | 0.006473 |
Player raises 2x, dealer qualifies, player wins | 3 | 0.021472 | 0.064417 |
Player raises 1x, dealer qualifies, player wins | 2 | 0.258181 | 0.516361 |
Player raises 1x, dealer does not qualify | 1 | 0.160038 | 0.160038 |
Player raises 2x, dealer does not qualify | 1 | 0.006617 | 0.006617 |
Player raises 3x, dealer does not qualify | 1 | 0.000448 | 0.000448 |
Player raises 1x, dealer qualifies, player pushes | 0 | 0.000840 | 0.000000 |
Player raises 2x, dealer qualifies, player pushes | 0 | 0.000001 | 0.000000 |
Player raises 3x, dealer qualifies, player pushes | 0 | 0.000000 | 0.000000 |
Player folds | -1 | 0.321365 | -0.321365 |
Player raises 1x, dealer qualifies, player loses | -2 | 0.228857 | -0.457715 |
Player raises 2x, dealer qualifies, player loses | -3 | 0.000560 | -0.001679 |
Player raises 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 raise 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 heard of two pay tables for the Flush bet. The following three tables show the details.
Pay Table 1
Cards | Pays | 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 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 | 1,592 | 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 |
Acknowledgements
- Thanks for Charles Mousseau for providing the math for this game, except on the Straight Flush side bet. Charles' web site is tgscience.com.
- Gordon Michaels for his High Card Flush Advanced Strategy.
Written by: Michael Shackleford
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Introduction
The casino game High Card Flush has been growing in popularity. The only published strategy for High Card Flush has been the Charles Mousseau Strategy, which is to make a maximum Raise bet on any four-card or higher flush, and to Raise any three-card flush of rank T-8-6 or greater, otherwise FOLD. That strategy for three card flushes was developed without regard to cards that are not part of the flush.
Below is a slightly more powerful strategy that does take into account the off-suit cards in a hand with a three-card flush.
Three-Card Flush Strategy
The strategy for a three-card flush depends first upon the ranks of the cards in the flush:
- J32 to AKQ — always raise
- T32 to T98 — it depends upon the off-suit cards
- 432 to 987 — always fold.
So, the off-suit cards need only be considered when you play a 10-high three-card flush, which will occur with a frequency of about 5.3% of all your hands.
Let’s look at the EV of 2 hands with the same T86 flush but with very different off-suit cards:
- Th-8h-6h + Js-Ad-Qd-Jc — EV = -0.86655 — CALL
- Th-8h-6h + 7d-4d-2d-9c — EV = -1.06993 — FOLD
The differences in the ranks of the off-suit cards, and, less importantly, their difference in suit distribution are the reason these T-8-6 flushes have such different expected values. In order to better decisions when playing a 10-high three-card flush, this strategy requires that you count the number of high cards in your hand and, sometimes, check your suit distribution.
The presence of high cards in your four off-suit cards increase the power of your 10-high three-card flush because they reduce the probability that the dealer will beat your hand with a higher ranking three- card flush. Similarly, cards lower than a 10, 2-9, in your off-suit cards, weaken your 10-high flush because they reduce the probability that the dealer will have a low-ranking three-card flush that you can beat.
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The optimal CALL/FOLD decision on your 10-high three-card flush will also occasionally depend on your suit distribution. Here is the nomenclature for suit distributions that is used here.
High Flush Poker Game
- 3211 — a three card flush, with 2 cards in a second suit and one card in each of the other two suits
- 3220 — a three card flush, with 2 cards in each of two different suits and with no cards in the fourth suit
- 3310 — a hand with two three card flushes in different suits and one card in one of the other two suits. With this hand, of course, the higher-ranking flush is always played.
The 3211 distribution will occur the most frequently, and the 3310 distribution the least frequently.
Basic Strategy for a 10-high three-card flush
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CALL with any 10-high three card flush (T32 to T98) in which all four offsuit cards are in the range T-A.
Otherwise, the table below provides the minimum three-card flush hand for which you should make a CALL bet as a function of the suit distribution and the number of off-suit high cards, J-A, in your hand. With lower-ranking flushes than those shown in the table, you should FOLD.
Minimum Three-Card Flush to Make a CALL Bet
How To Play High Flush Poker
Offsuit Cards J-A | 3211 distribution | 3220 distribution | 3310 distribution |
---|---|---|---|
0 | J32 | J32 | J32 |
1 | T87 | T93 | T94 |
2 | T75 | T82 | NA |
3 | T54 | T62 | NA |
Here is how to implement the strategy when you have a 10-high 3-card flush:
- First, check to see if all four of your off-suit cards are in the range 10-A. If they are then CALL, if not go to step 2.
- Count the number of cards in your hand that are in the range J-A, if it is zero then FOLD. If the number of high cards, J-A, are in the range 1-3, go to step 3.
- Check your suit distribution and check whether your flush is at least as high as the appropriate entry in the table above.
Examples
Example: Ts-3s-2s +Ac-Qc-Jh-Td
This is a relatively weak T32 flush but it has four off-suit cards in the range T-A, so the best action is CALL. The EV of the CALL bet is -0.98119, which is better than FOLD = -1.0.
Example: Th-9h-3h + 8c-8d-4c-3d
This hand, which has a T93 flush, does not have 4 off-suit cards that are 10 or higher, indeed it has no cards that are J or higher. The best action is FOLD. The CALL EV = -1.05224
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Example: Th-9h-3h + Kc-8d-4c-3s
This hand does not have 4 off-suit cards that are 10 or higher, however it has one card (the king of clubs) that is J or higher. It is a T93 flush and has the suit distribution 3211, i.e., 3 hearts, 2 clubs, 1 spade and 1 diamond. The T93 flush is higher than T87 in the above table and the best action is to raise. The EV by raising is -0.99302.
Note that if the suit distribution had been 3310, then the table above indicates that the T93 flush with one card J-A should be folded. For a 3310 suit distribution, the Raise EV = -1.01846.
Example: Th-7h-4h + Ks-4s-Ac-Jc
This hand does not have 4 off-suit cards that are 10 or higher, however it has three cards, that are J or higher. Regardless of the suit distribution a T74 flush with 3 high (>T) offsuit cards is high enough to raise. With the 3220 suit distribution shown here, the raise EV = - 0.93468.
House Edge
A simulation of High Card Flush using 200 500 million trials produced these values of house edge:
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- Mousseau strategy: House Edge = 2.74446%
- This strategy: House Edge = 2.6855%
So, this strategy produces an additional increment of expected value to the player of almost 0.059%. There are a few rare hands for which this strategy is not mathematically perfect, but overall it should be very close to an optimal strategy.
Acknowledgement
Thanks to James for performing these house edge calculations.
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About the Author
Gordon Michaels is a research scientist who has been Chief Technology Officer of Oak Ridge National Laboratory and Senior Scientist in the U.S. Department of Energy's Office of Intelligence. He was a card counter at Blackjack in the 1980s, and has since developed novel mathematical tools for analyzing casino games. He is sought out by 'advantage players' from around the world for his help with advanced topics in gaming mathematics. He goes by Gordonm888 on the Wizard of Vegas forums.
Written by: Gordon Michaels