Last Updated: June 21, 2019

# Side Bet City

## Introduction

Side Bet City is a table game by Evolution Gaming, a provider of live dealer games for Internet casinos. The game is pretty simple, the dealer deals out three cards, then another two to make a five-card hand, and then two more to make a seven-card hand. The player may bet on the poker value of any of the three hands or all three to lose. Except for the addition of the No Win bet, the game is much like 3-5-7 Poker with different pay tables.

## Rules

1. The game is played with a single 52-card deck.
2. All hands are scored according to conventional poker rules, which I assume the reader is familiar with.
3. There are four bets available, as follows:
• 3 Card Hand
• 5 Card Hand
• 7 Card Hand
• No Win
4. The outcome of bets on the 3 Card Hand shall be determined by the poker value of the first three cards dealt and the pay table below.
5. The outcome of bets on the 5 Card Hand shall be determined by the poker value of the first five cards dealt and the pay table below.
6. The outcome of bets on the 7 Card Hand shall be determined by the poker value of all seven cards dealt and the pay table below.
7. The "No Win" bet shall win and pay 0.7 to one if all three hands lose.

The following tables show what each hand pays on the 3-, 5-, and 7-Card Hand bets. Wins are on a "for one" basis.

### 3 Card Hand Pay Table

Hand Pays
Royal flush 100
Straight flush 40
Three of a kind 35
Straight 5
Flush 4
Pair 1

### 5 Card Hand Pay Table

Hand Pays
Royal flush 1000
Straight flush 250
Four of a kind 100
Full house 50
Flush 40
Straight 25
Three of a kind 7
Two pair 4
Pair (jacks or better) 1

### 7 Card Hand Pay Table

Hand Pays
Royal flush 500
Straight flush 100
Four of a kind 50
Full house 7
Flush 5
Straight 4
Three of a kind 3

## Analysis

The following table shows my analysis of the 3 Card Hand bet. The lower right cell shows a house edge of 3.31%.

### 3 Card Hand

Hand Pays Combinations Probability Return
Royal flush 100 4 0.000181 0.018100
Straight flush 40 44 0.001991 0.079638
Three of a kind 35 52 0.002353 0.082353
Straight 5 720 0.032579 0.162896
Flush 4 1,096 0.049593 0.198371
Pair 1 3,744 0.169412 0.169412
All other -1 16,440 0.743891 -0.743891
Total 22,100 1.000000 -0.033122

The following table shows my analysis of the 5 Card Hand bet. The lower right cell shows a house edge of 4.79%.

### 5 Card Hand

Hand Pays Combinations Probability Return
Royal flush 1000 4 0.000002 0.001539
Straight flush 250 36 0.000014 0.003463
Four of a kind 100 624 0.000240 0.024010
Full house 50 3,744 0.001441 0.072029
Flush 40 5,108 0.001965 0.078616
Straight 25 10,200 0.003925 0.098116
Three of a kind 7 54,912 0.021128 0.147899
Two pair 123,552 0.047539 0.190156
Pair (jacks or better) 1 337,920 0.130021 0.130021
All other -1 2,062,860 0.793725 -0.793725
Total 0 2,598,960 1.000000 -0.047876

The following table shows my analysis of the 7 Card Hand bet. The lower right cell shows a house edge of 5.66%.

### 7 Card Hand

Hand Pays Combinations Probability Return
Royal flush 500 4,324 0.000032 0.016160
Straight flush 100 37,260 0.000279 0.027851
Four of a kind 50 224,848 0.001681 0.084034
Full house 7 3,473,184 0.025961 0.181727
Flush 5 4,047,644 0.030255 0.151275
Straight 4 6,180,020 0.046194 0.184775
Three of a kind 3 6,461,620 0.048299 0.144896
All other -1 113,355,660 0.847300 -0.847300
Total 133,784,560 1.000000 -0.056582

The following table shows my analysis of the No Win bet. The lower right cell shows a house edge of 3.71%.

### All Lose

Hand Pays Combinations Probability Return
No wins 0.7 15,913,035,072 0.566406 0.396484
At least one win -1 12,181,722,528 0.433594 -0.433594
Total 28,094,757,600 1.000000 -0.037110

## Methodology

Finding a mathematical solution was too messy, I wrote a simple looping program. Here is the logic of it:

1. Loop through all 22,100 ways to choose 3 cards out of 52.
2. If the three-card hand is a winner, add combin(49,2)*combin(47,2)=1,271,256 to the losing combinations. If a loser, then go to step 3.
3. Loop through all 1,176 ways to choose 2 cards out of the 49 cards left in the deck, to combine with the three-card hand to make a five-card hand.
4. If the five-card hand is a winner, add combin(47,2)=1081 to the losing combinations. If a loser, then go to step 5.
5. Loop through all 1,081 ways to choose 2 cards out of the 47 cards left in the deck, to combine with the five-card hand to make a seven-card hand.
6. If the seven-card hand is a winner, add one to the losing combinations. If a loser, then add one to the winning combinations.