# Throwing a Pair of Dice

Contents

## Introduction

When throwing a pair of dice, it is important to remember that the two dice are independent of each other.
is a different result than , even though they both add up to 7. There are a total of 36 different possible outcomes.

## Playing Craps

### Come Out Roll: 7 or 11 Wins; 2, 3, or 12 Loses

When playing craps, a 7 or 11 on the first roll wins and a 2, 3, or 12 loses. On the first roll, there are 8 ways to win, 4 ways to lose, and 24 ways to do neither.

Your chances of winning on the first roll are 8 : 4 : 24 (2 : 1 : 6) — 22.22% win, 11.11% lose, and 66.67% neither.

### Point 4: 4 Wins; 7 Loses

Your chances of winning are: 3 : 6 (1 : 2) or 33.33% win and 66.67% lose. Your chances of winning on the next roll are 3 : 6 : 27 (1 : 2 : 9) — 8.33% win, 16.67% lose, and 75.00% neither.

### Point 5: 5 Wins; 7 Loses

Your chances of winning are: 4 : 6 (2 : 3) or 40.00% win and 60.00% lose. Your chances of winning on the next roll are 4 : 6 : 26 (2 : 3 : 13) — 11.11% win, 16.67% lose, and 72.22% neither.

### Point 6: 6 Wins; 7 Loses

Your chances of winning are: 5 : 6 or 45.45% win and 54.55% lose. Your chances of winning on the next roll are 5 : 6 : 25 — 13.89% win, 16.67% lose, and 69.44% neither.

### Point 8: 8 Wins; 7 Loses

Your chances of winning are: 5 : 6 or 45.45% win and 54.55% lose. Your chances of winning on the next roll are 5 : 6 : 25 — 13.89% win, 16.67% lose, and 69.44% neither.

### Point 9: 9 Wins; 7 Loses

Your chances of winning are: 4 : 6 (2 : 3) or 40.00% win and 60.00% lose. Your chances of winning on the next roll are 4 : 6 : 26 (2 : 3 : 13) — 11.11% win, 16.67% lose, and 72.22% neither.

### Point 10: 10 Wins; 7 Loses

Your chances of winning are: 3 : 6 (1 : 2) or 33.33% win and 66.67% lose. Your chances of winning on the next roll are 3 : 6 : 27 (1 : 2 : 9) — 8.33% win, 16.67% lose, and 75.00% neither.

## Percent Chance of Winning

A table showing the percentages if you have n ways to win.

n % n % n % n %
1 2.78% 10 27.78% 19 52.78% 28 77.78%
2 5.56% 11 30.56% 20 55.56% 29 80.56%
3 8.33% 12 33.33% 21 58.33% 30 83.33%
4 11.11% 13 36.11% 22 61.11% 31 86.11%
5 13.89% 14 38.89% 23 63.89% 32 88.89%
6 16.67% 15 41.67% 24 66.67% 33 91.67%
7 19.44% 16 44.44% 25 69.44% 34 94.44%
8 22.22% 17 47.22% 26 72.22% 35 97.22%
9 25.00% 18 50.00% 27 75.00% 36 100.00%