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High Card Flush Advanced Strategy
Introduction
The casino game High Card Flush The interest in this game has been on the rise. Up until now, the only known method for High Card Flush is the Charles Mousseau Strategy, which suggests placing a maximum Raise bet when holding four cards or more of the same suit, and opting to Raise with any three-card flush that includes ranks from T-8-6 or higher; otherwise, the correct move is to FOLD. This particular guideline for three-card flushes was created without considering the off-suit cards.
Presented here is a more robust strategy that assesses the relevance of off-suit cards in a hand featuring a three-card flush.
Three-Card Flush Strategy
The approach to playing a three-card flush is initially guided by the ranks of the cards that form the flush:
- J32 to AKQ — always raise
- T32 to T98 — The off-suit cards play a crucial role in this strategy.
- 432 to 987 — always fold.
Consequently, off-suit cards should only come into play when handling a 10-high three-card flush, which appears around 5.3% of the time in your hands.
Let’s examine the expected value (EV) of two hands containing the same T86 flush but differing in their 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 discrepancies in the ranks of the off-suit cards, along with their varying suit distributions, account for the significant variations in the expected values of these T-8-6 flushes. To refine your decisions when playing a 10-high three-card flush, it's important to evaluate the number of high cards in your hand and, in some cases, to analyze your suit distribution.
High cards among your four off-suit cards enhance the strength of your 10-high three-card flush because they decrease the chances of the dealer out-ranking you with a higher three-card flush. Conversely, any lower-ranking cards, like the 2-9 in your off-suit cards, reduce the effectiveness of your 10-high flush by lowering the odds of the dealer achieving a low-ranking flush that you can beat.
The ideal CALL or FOLD choice with respect to your 10-high three-card flush can also hinge on your suit distribution. Here’s the terminology that will be used for suit distributions.
- 3211 — indicates a configuration where there are three cards of one suit, two cards of a different suit, and one card each from the remaining suit types.
- 3220 — represents a situation where there are two cards from each of two suits and none from the fourth suit.
- 3310 — describes a hand possessing two three-card flushes across different suits alongside one card from either of the other two suits. It is important to play the higher-valued flush when such hands occur.
The 3211 distribution appears most often, while the 3310 distribution is the least common.
Fundamental Strategy for a 10-high three-card flush
PLACE A CALL BET with any configuration of a 10-high three-card flush (ranging from T32 to T98) if all four off-suit cards are valued between T and A.
In other scenarios, refer to the table below that outlines the minimum three-card flush required for making a CALL bet based on your suit distribution and the number of high off-suit cards (J-A) in your hand. If your flush is below the ranks indicated in the table, the advisable strategy is to FOLD.
Minimum Requirements for a Three-Card Flush to Initiate a CALL Bet
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’s how you can activate this strategy when holding a 10-high three-card flush:
- First, verify if all four of your off-suit cards are within the range of 10 to A. If they all are, you should CALL; if not, proceed to step 2.
- Next, count how many cards in your hand are in the range from J to A. If you find none, then your best option is to FOLD. If there are between one and three high cards within that range, move on to step 3.
- Assess your suit distribution and determine whether your flush meets or exceeds the suitable rank identified in the table above.
Examples
Example: Ts-3s-2s +Ac-Qc-Jh-Td
This hand holds a relatively timid T32 flush, yet it includes four off-suit cards ranging from T to A, thus the optimal choice is to CALL. The expected value of calling stands at -0.98119, which is preferable over the FOLD option with an EV of -1.0.
Example: Th-9h-3h + 8c-8d-4c-3d
Meanwhile, this hand bears a T93 flush but lacks four off-suit cards valued at 10 or above, and it appears there's not a single card rated J or higher. The optimal response here is to FOLD, as the EV of calling would be -1.05224.
Example: Th-9h-3h + Kc-8d-4c-3s
In this situation, even though four off-suit cards below 10 are absent, there exists one high card (the king of clubs) that meets or exceeds J. The hand features a T93 flush with a suit distribution of 3211, meaning there are three hearts, two clubs, one spade, and one diamond. Given that the T93 flush ranks higher than T87 on the previous table, the advisable action is to raise. The EV for raising stands at -0.99302.
Be aware that if the suit distribution had been 3310, the prior table suggests folding the T93 flush despite the presence of one J-A card. For a suit distribution of 3310, raising would yield an EV of -1.01846.
Example: Th-7h-4h + Ks-4s-Ac-Jc
Although this hand lacks four off-suit cards valued at 10 or above, it features three cards that are rated J or higher. Regardless of suit distribution, a T74 flush containing three high off-suit cards has sufficient strength to justify raising. Illustrated with the 3220 suit distribution, the raise's EV tallies at -0.93468.
House Edge
A simulation involving 200 million trials of High Card Flush yielded certain values on the house edge:
- Mousseau strategy: House Edge = 2.74446%
- This strategy: House Edge = 2.6855%
Thus, this strategy provides an additional boost in expected value to the player amounting to nearly 0.059%. While there are a few unusual hands for which this strategy isn't entirely mathematically sound, it generally approximates an optimal approach.
Acknowledgement
Special thanks to James for conducting the calculations on house edge.
About the Author
Gordon Michaels is a research scientist who has served as the Chief Technology Officer at Oak Ridge National Laboratory and as a Senior Scientist in the U.S. Department of Energy's Office of Intelligence. He gained notoriety as a card counter in Blackjack during the 1980s and has since developed innovative mathematical methods to analyze casino games. He is frequently sought after by 'advantage players' globally for insightful guidance on advanced gaming mathematics. He is commonly referred to as Gordonm888 on the Wizard of Vegas forums .