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Chase The Flush

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Strategy for “BET 1X or FOLD” Decision on the River When Your Longest Flush is a 2-Card Flush

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  1. Playing Flush and Straight Draws. Mathematics: Flushes & Straights: Simple Pot Odds: Implied Odds: Reverse Implied Odds Watch SplitSuit's video on Flushes and Flush Draws for 8 hand histories involving strategy on playing flushes in Texas Hold'em. You are on the flop with a pretty decent flush draw. You have two hearts in your hand and there are another two on the flop.
  2. Chase the Flush is an exciting new card game where players and the dealer compete head-to-head using three hole cards and four community cards to make their longest possible seven-card flush. Players win by having more cards in their flush than the dealer. Card rankings Ace (high) – 2 (low) are used to break ties if a player and the dealer.
suitedFlush
Situation You have checked to the river in Chase the Flush.. You arrive at the river with a hand that has no flushes longer than a 3-Flush - a “2-Flush Hand.” (Actually, by definition, such a hand must contain three 2-card flushes in three different suits and a 7th card in the fourth suit.) When should you BET 1X? and when should you FOLD?
There is no published strategy for this. This post provides a strategy that is almost computer-perfect.The
Factors to Consider
1. Does the Board have 2 suited cards, i.e., a 2-card flush on the board? If it does, then you must FOLD. This is an absolute rule, correct in 100% of situations. When the board has 2 cards in the same suit, the probability of the dealer having a 3-card (or longer) flush is simply too high to justify Betting 1X on the river.
Another way to say this is:

Chase The Flush Ags


When your longest flush is 2 cards on the river, never consider betting 1X unless your starting hand has 3 suits and the board has all 4 suits. Both your starting hand and the board must be rainbow, otherwise FOLD.
2. How many dealer “OUTS” are there such that the dealer can make a 2-card flush that is higher than your highest 2-card flush? I will give many examples of this definition of dealer OUTS below and show you how to apply it. The short rule is:
- Dealer OUTS = 0-8: always Bet 1X
-Dealer OUTS = 9-11: it depends upon the third factor below.
- Dealer OUTS = 12 or higher: always FOLD.
3. Given a board with 4 different suits, how many cards on the board are in the range 2-8, i.e., are <9?
This surprising factor arises from the Ante payout rules in which the Ante Bet always pushes if the dealer does not qualify and the player has not folded - and the dealer must have a 9-high 3-card flush or higher to qualify. With a rainbow board, each card on the board lower than a 9 means that if the dealer does make a 3-card flush in that suit then the probability of that 3-card flush ‘not qualifying’ is about 20%. Conversely, for each hand on the board that is 9 or higher, there is zero chance that a dealer 3-card flush in that suit will not qualify. So, when you have no flush longer than a 2-card flush on the river and the board is rainbow, every card on the board that is lower than a 9 increases the EV of Bet 1X by about 5-6%. In plain English, low cards on the board increases the EV of going to showdown.
So, given a rainbow board and a player hand with nothing longer than a 2-card flush, there are two things to count: (1) Dealer “OUTS” to make a higher 2 card flush than the player and (2) number of cards on the board in the range 2-8. The table below gives the exact rule on how to combine them.

Chase The Flush Poker


Criteria on When to BET 1X on the River with a rainbow board and a longest flush of only 2 cards.
Max Dealer ‘OUTS” *
8
9
10
11

*To make a higher 2-card flush than player.
Chase the flush odds Examples
I am providing 5 examples of how to count dealer “OUTS,” because it can be tricky and how to apply the rule I’ve presented above. Note that all graphics refer to suits simply as suit A, suit B, suit C or suit D
Example 1. Player: As 9h 4d, Board: Qs Kh Kd Ac
You have made a high 2-card flush, an AQ but the rest of the board is scary: A, K and K. The graphic below illustrates that there are 4 dealer “OUTS” to have a better 2-card flush than AQ and that you should Bet 1x on this river.
Example 2. Player: Ts Qh 4d, Board: As Kh 3d Ac
You highest 2-card flush is AT in spades. Counting dealer “OUTS” on this board is tricky. The graphic below shows that there are only 7 outs and that you should BET 1x.
Example 3. Player: Ts 6h 4d, Board: Ks Jh 3d Jc
Your highest 2-card flush is K-T of spades. The board is dangerous, because there are two other suits with cards higher than the Ten that you are contributing from your hand. The graphic below shows that there are 8 outs.
Example 4. Player: Qs Th 7d, Board: 7s 8h 8d 9c
Your highest 2-card flush is Q-7 of spades. This is not a very high 2-card flush and the graphic below shows that there are 11 dealer “OUTS” to make a 2-card flush that is higher than Q-7. However, the board also has three suits in which the only card is in the range 2-8. The correct decision is BET 1X. This example, hand is at the very outer limits of qualifying for a BET 1x. If there had only been 2 board cards in the range 2-8, then the correct decision would be FOLD.
Example 5. Player: 6s 5h 2d, Board: As 3h 3d 4c
Your starting hand is terrible: 6-5-2 rainbow. The board has given you an A-6 as your highest 2-card flush –not a hand that you can often BET 1X with. However, the other 3 cards on the board are all lower than than the 6 that your starting hand contributes to the A-6 flush. The graphic below shows that there are only 7 dealer “OUTS”, namely the 7-K of spades. The rules say to BET 1X.
Summary
When you are on the river with a 2-card flush hand, you should not base your BET vs. FOLD decision strategy simply on how high your highest 2-card flush is. I propose a BET vs. FOLD strategy in which you count (1) the Dealer OUTS to make a higher 2-card flush than yours and (2) the number of board cards in the range 2-8. Except for a small number of rare situations in which your hand has 2 or more cards in the range of 2-8 and the board has cards<9 in the same suits, this proposed strategy appears to always provide the computer-perfect optimal decisions.

Chase The Flush Play

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