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Flush
Introduction
I first noticed the Flush side bet at the Four Queens on February 22, 2022 at the Four Queens in Las Vegas. It is the same as the Flush Plus bet in the game 3 Card Super Shot. The game was closed at the time I saw it, so I don't know the number of decks it used. Based on the low house edge for four or more decks, it probably was on a one-deck or two-deck game.
Rules
- An unknown number of standard 52-card decks are used.
- Wins are based on the poker value of the player's initial two cards and the dealer's up card, according to the pay table below. Wins are on a "to one" basis.
Flush Pay Table
| Event | Pays |
|---|---|
| Straight flush | 30 |
| 3 of a kind | 20 |
| Straight | 10 |
| Flush | 7 |
One Deck Analysis
The following table shows my analysis of the Flush bet with one deck. The lower right cell shows a house edge of 12.81%.
Flush Return Table — One Deck
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Straight flush | 30 | 48 | 0.002172 | 0.065158 |
| 3 of a kind | 20 | 52 | 0.002353 | 0.047059 |
| Straight | 10 | 720 | 0.032579 | 0.325792 |
| Flush | 7 | 1,096 | 0.049593 | 0.347149 |
| All other | -1 | 20,184 | 0.913303 | -0.913303 |
| Total | 22,100 | 1.000000 | -0.128145 |
Two Deck Analysis
The following table shows my analysis of the Flush bet with two decks. The lower right cell shows a house edge of 6.27%.
Flush Return Table — Two Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Straight flush | 30 | 384 | 0.002109 | 0.063261 |
| 3 of a kind | 20 | 728 | 0.003998 | 0.079954 |
| Straight | 10 | 5,760 | 0.031630 | 0.316303 |
| Flush | 7 | 10,016 | 0.055002 | 0.385011 |
| All other | -1 | 165,216 | 0.907262 | -0.907262 |
| Total | 182,104 | 1.000000 | -0.062733 |
Four Deck Analysis
The following table shows my analysis of the Flush bet with two decks. The lower right cell shows a house edge of 2.86%.
Flush Return Table — Four Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Straight flush | 30 | 3,072 | 0.002078 | 0.062344 |
| 3 of a kind | 20 | 7,280 | 0.004925 | 0.098494 |
| Straight | 10 | 46,080 | 0.031172 | 0.311719 |
| Flush | 7 | 85,120 | 0.057581 | 0.403070 |
| All other | -1 | 1,336,704 | 0.904244 | -0.904244 |
| Total | 1,478,256 | 1.000000 | -0.028618 |
Six Deck Analysis
The following table shows my analysis of the Flush bet with six decks. The lower right cell shows a house edge of 1.70%.
Flush Return Table — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Straight flush | 30 | 10,368 | 0.002068 | 0.062043 |
| 3 of a kind | 20 | 26,312 | 0.005248 | 0.104968 |
| Straight | 10 | 155,520 | 0.031021 | 0.310214 |
| Flush | 7 | 292,896 | 0.058424 | 0.408965 |
| All other | -1 | 4,528,224 | 0.903239 | -0.903239 |
| Total | 5,013,320 | 1.000000 | -0.017049 |