# Replay -- Craps Side Bet

## Introduction

Replay is a craps side bet I spotted at the Boulder Station on September 16, 2010. It pays if the shooter makes the same point at least three times before sevening out.

## Rules

The bet starts with a new shooter and ends with a seven-out. The following table shows the pay table. Wins are on a "to one" basis.

### Replay Pay Table

Event Pays
Point of 4 or 10 achieved four or more times 1000
Point of 5 or 9 achieved four or more times 500
Point of 4 or 10 achieved three times 120
Point of 6 or 8 achieved four or more times 100
Point of 5 or 9 achieved three times 95
Point of 6 or 8 achieved three times 70

## Analysis

The following table shows my analysis of the Replay bet. The lower right corner shows a house edge of 24.81%.

### Replay Return Table

Event Pays Probability Return
Point of 4 or 10 achieved four or more times 1000 0.00003691863657 0.03691863656821
Point of 5 or 9 achieved four or more times 500 0.00020671490002 0.10335745001061
Point of 4 or 10 achieved three times 120 0.00052298052124 0.06275766254895
Point of 6 or 8 achieved four or more times 100 0.00069820960363 0.06982096036327
Point of 5 or 9 achieved three times 95 0.00179993294223 0.17099362951155
Point of 6 or 8 achieved three times 70 0.00429327448455 0.30052921391822
Loser -1 0.99244196891176 -0.99244196891176
Total   1.00000000000000 -0.24806441599095

## Methodology

Integral calculus was used to analyze this bet, thus the results accurate to as many decimal places stated. A random simulation was also done to confirm the results, which matched to within 0.03% of return.

I have a ten-page PDF document that details my analysis of the Replay bet.