# Ride the Line

## Introduction

Ride the Line is a fairly simple side bet that pays based on the total number of pass line wins a shooter achieves before a seven-out.

At the time of this writing (June 9, 2017), it can be found in four properties in Colorado.

## Rules

1. The side bet is for use in the game of craps, which I assume the reader is already familiar with.
2. The bet may be placed before a new shooter makes his first throw.
3. The bet shall win according to the number of pass line wins the shooter achieves before rolling a seven-out. A win may be achieved by either a (1) 7 or 11 on the come out roll, or (2) achieving a point and rolling it again before a seven.
4. When the shooter does roll a seven out, Ride the Line wagers shall be paid according to the total number of pass line wins and the particular pay table the casino uses. There are seven pay tables available, as shown below.

The following table shows the various pay tables available for Ride the Line. Wins shown are on a "to one" basis. A 0 represents a push and a -1 represents a loss.

### Ride the Line Pay Table

Wins Pay Table 1 Pay Table 2 Pay Table 3 Pay Table 4 Pay Table 5 Pay Table 6 Pay Table 7
11+ 50 75 100 150 50 100 150
10 25 40 40 30 40 30 40
9 20 30 30 20 30 25 25
8 15 20 20 15 20 20 15
7 8 12 10 10 10 12 10
6 6 6 6 4 8 7 7
5 4 4 3 3 5 5 4
4 2 2 2 2 2 3 2
3 1 1 1 1 1 0 0
2 0 -1 -1 -1 -1 -1 -1
1 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 -1 -1 -1

## Analysis

The following table shows the probability of 0 to 11 pass line wins before a seven out. The win for 11 includes more than 11 wins.

### Ride the Line Pay Probabilities

Wins Probability
0 0.445454545
1 0.247024793
2 0.136986476
3 0.075965228
4 0.042126172
5 0.023360877
6 0.012954668
7 0.007183952
8 0.003983828
9 0.002209214
10 0.001225109
11 0.001525136

The following table shows the contribution to the return for all possible outcomes of all possible pay tables. The bottom line shows the expected return to the player. As you can see, the house edge ranges from 8.52% under pay table 6 to 10.60% for pay table 4.

### Ride the Line Return Table

Wins Pay Table 1 Pay Table 2 Pay Table 3 Pay Table 4 Pay Table 5 Pay Table 6 Pay Table 7
0 -0.445455 -0.445455 -0.445455 -0.445455 -0.445455 -0.445455 -0.445455
1 -0.247025 -0.247025 -0.247025 -0.247025 -0.247025 -0.247025 -0.247025
2 0.000000 -0.136986 -0.136986 -0.136986 -0.136986 -0.136986 -0.136986
3 0.075965 0.075965 0.075965 0.075965 0.075965 0.000000 0.000000
4 0.084252 0.084252 0.084252 0.084252 0.084252 0.126379 0.084252
5 0.093444 0.093444 0.070083 0.070083 0.116804 0.116804 0.093444
6 0.077728 0.077728 0.077728 0.051819 0.103637 0.090683 0.090683
7 0.057472 0.086207 0.071840 0.071840 0.071840 0.086207 0.071840
8 0.059757 0.079677 0.079677 0.059757 0.079677 0.079677 0.059757
9 0.044184 0.066276 0.066276 0.044184 0.066276 0.055230 0.055230
10 0.030628 0.049004 0.049004 0.036753 0.049004 0.036753 0.049004
11+ 0.076257 0.114385 0.152514 0.228770 0.076257 0.152514 0.228770
Total -0.092792 -0.102527 -0.102127 -0.106042 -0.105753 -0.085219 -0.096485