Last Updated: February 24, 2022

# 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

1. An unknown number of standard 52-card decks are used.
2. 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

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