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9 Card Fortune Flush
Introduction
9 Card Fortune Flush, the latest table game based on flushes, is evidently trying to ride the coattails of High Card Flush. However, unlike the other flush-based games out there, in 9 Card Fortune Flush you don't need to beat a dealer hand. You just choose a color and a type of bet and hope to get a long flush in the chosen color.
I first saw the game on August 19, 2016, at Ballys where it was on field trial.
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Rules
- The game is played with a single 52-card deck.
- Play begins with the player making a 9 Cards bet on either red or black. The player may not bet both colors. This is the only mandatory bet.
- The player may also make side bets on the First 3, Player's 6, and 9 Card Bonus. On each the player must bet the same color as he did on the 9 Cards bet.
- After bets have been placed, the dealer will give the player three cards.
- The player must then make a Play bet, equal to the 9 Cards bet, or fold.
- The dealer will then deal the player six more cards, for a total of nine.
- The player should turn face up his longest flush in his chosen color and discard the rest.
- The dealer will pay each bet according to the pay tables below.
The following is the pay table for both the 9 Cards and Play bets, which are based on all nine cards.
9 Cards
| Longest Flush |
Pays |
|---|---|
| 4+ | 1 to 1 |
| 3 | Push |
The following is the pay table for the First 3 bet, which is based on the player's first three cards.
First 3
| Longest Flush |
Pays |
|---|---|
| 3 | 5 to 1 |
| 2 | 2 to 1 |
The following is the pay table for the Player's 6 bet, which is based on the six cards dealt after the initial three.
Player's 6
| Longest Flush |
Pays |
|---|---|
| 4+ | 3 to 1 |
| 3 | 2 to 1 |
The following is the pay table for the 9 Card Bonus, which is based on all nine cards.
9 Card Bonus
| Longest Flush |
Pays |
|---|---|
| 9 | 5000 to 1 |
| 8 | 1000 to 1 |
| 7 | 100 to 1 |
| 6 | 20 to 1 |
| 5 | 10 to 1 |
Here are scans of both sides of the rule card. Click either image for a larger version. The rules state the first three cards are "community cards," but when I played at Ballys every player got his own cards.
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Strategy
The only strategic decision is whether to make the Play bet or fold. The odds favor making the Play bet with at least one card in the chosen color. Fold if all three cards are the opposite color only.
Analysis
The following table shows the possible outcomes of the 9 Cards bet, assuming the optimal strategy above. The lower right cell shows a house edge of 2.17%.
9 Cards
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 4-card flush or longer | 2 | 85,937,451,600 | 0.278077 | 0.556153 |
| 3-card flush | 0 | 115,636,938,560 | 0.374178 | 0.000000 |
| Fold | -1 | 36,357,921,600 | 0.117647 | -0.117647 |
| 2-card flush or shorter | -2 | 71,110,021,840 | 0.230098 | -0.460196 |
| Total | 309,042,333,600 | 1.000000 | -0.021690 |
The player will raise 88.24% of the time, for an average final bet of 1.8824 units. That makes the Element of Risk, defined as the ratio of the expected loss to average total bet, as 2.17%/1.8824 = 1.15%.
The following table shows the possible outcomes of the First 3 bet. The lower right cell shows a house edge of 1.88%.
First 3
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 3 | 5 | 572 | 0.025882 | 0.129412 |
| 2 | 2 | 6,084 | 0.275294 | 0.550588 |
| Other | -1 | 15,444 | 0.698824 | -0.698824 |
| Total | 22,100 | 1.000000 | -0.018824 |
The following table shows the possible outcomes of the Player's 6 bet. The lower right cell shows a house edge of 1.31%.
Player's 6
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 4+ | 3 | 1,163,448 | 0.057148 | 0.171444 |
| 3 | 2 | 5,145,712 | 0.252755 | 0.505509 |
| Other | -1 | 14,049,360 | 0.690097 | -0.690097 |
| Total | 20,358,520 | 1.000000 | -0.013144 |
The following table shows the possible outcomes of the 9 Card Bonus bet, assuming the optimal strategy above. The lower right cell shows a house edge of 8.89%.
9 Card Bonus
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 9 | 5000 | 1,430 | 0.000000 | 0.001943 |
| 8 | 1000 | 100,386 | 0.000027 | 0.027286 |
| 7 | 100 | 2,543,112 | 0.000691 | 0.069124 |
| 6 | 20 | 31,365,048 | 0.008525 | 0.170505 |
| 5 | 10 | 211,714,074 | 0.057545 | 0.575455 |
| Other | -1 | 3,433,351,350 | 0.933210 | -0.933210 |
| Total | 3,679,075,400 | 1.000000 | -0.088898 |
External Links
Wizard of Vegas — Discussion about 9 Card Fortune Flush.