Last Updated: February 24, 2021

# Flushed

## Introduction

Flushed began a field trial at the Stratosphere on February 2, 2021. The idea is that the dealer will deal cards from a 52-card deck until he obtains a flush. The player may bet on the color, suit, and poker value of this flush as well as how many cards it will take.

## Rules

The following rules are based on the rack card for the game, as opposed to how they actually dealt the game, I would say incorrectly, at the time of my visit on February 5, 2021.

1. A single 52-card deck is used and shuffled before every round.
2. Players place their bets (listed below).
3. The dealer shall deal one card at a time.
4. As each card is dealt, the dealer will place it on a 4x4 grid according to it's suit and the count of the number of cards dealt in that suit.
5. The dealer will stop dealing under either of the following conditions:
• Any given suit reaches five cards, indicating a flush.
• Sixteen cards are dealt and no flush has been reached.
6. If a flushed is reached, then the dealer shall pay winning bets according to the suit of the flush, poker value of that flush, and the number of cards dealt.
7. If the dealer reaches 16 cards without a flush, then all bets shall lose except the bet on 17 cards. Note that in this situation, the 17th card must form a flush as all four suits already have a count of four.

The following table shows the available "inside bets," based on the total number of cards dealt. Pays are on a "to one" basis.

### Inside Bets Pay Table

Cards Pays
5 400
6 100
7 40
8 20
9 12
10 9
11 7
12 5
13 5
14 5
15 7
16 12
17 35

The following table shows the available "outside bets," which are miscellaneous bets based on the number of cards dealt and the actual flush formed. Pays are on a "to one" basis.

### Outside Bets Pay Table

Bet Pays
Color 1
Suit 3
Odd {a} 1
Even {b} 1
Ace-high flush 1.5
Straight flush {c} 100
Royal flush 1000
Total of 5 to 10 3
Total of 11 to 13 1.2
Total of 14 to 16 2

Notes
{a}: The odd bet loses on a total of 17 cards
{b}: The even bet pays 1 to 2 on a total of 10 cards
{c}: Straight flush bet wins on a royal flush.

Following are pictures of both sides of the rack card. Click on either image for a larger version.

## Analysis

The following table shows the probability of winning and house edge of all inside bets.

### Inside Bets Analysis

Number of Cards Pays Prob. Win House Edge
5 400 0.20% 20.57%
6 100 0.82% 17.00%
7 40 2.04% 16.50%
8 20 3.91% 17.94%
9 12 6.39% 16.88%
10 9 9.31% 6.95%
11 7 12.23% 2.16%
12 5 14.54% 12.78%
13 5 15.49% 7.07%
14 5 14.45% 13.30%
15 7 11.30% 9.61%
16 12 6.81% 11.48%
17 35 2.52% 9.21%

The following table shows the probability of winning and house edge of all outside bets, except the even bet.

### Outside Bets Analysis

Bet Pays Prob. Win House Edge
Color 1 48.74% 2.52%
Suit 3 24.37% 2.52%
Odd 1 47.65% 4.71%
Ace-high flush 1.5 38.31% 4.23%
Straight flush 100 0.78% 21.52%
Royal flush 1000 0.08% 22.22%
Total of 5 to 10 3 22.66% 9.35%
Total of 11 to 13 1.2 42.26% 7.04%
Total of 14 to 16 2 32.56% 2.32%

Following is my return table for the even bet, which has three possible outcomes. The bottom right cell shows a house edge of 4.99%.

### Even Bet Analysis

Event Pays Probability Return
Even & not 10 1.0 0.405262 0.405262
10 0.5 0.093050 0.046525
Odd -1.0 0.501687 -0.501687
Total   1.000000 -0.049900

The mean number of cards to get to a flush is 12.3598.

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