Previous | ToC | Next Labs: Probability & Statistics. Part 1. Math Alive

## Playing Craps

Here we present the rules for playing the game of craps in our simulation below.

When a player rolls the dice for the first time, any combination of the two dice that adds up to 7 or 11 is a winner. Any dice total that equals 2, 3, or 12 is an immediate loser and is called craps. If the first roll is not an immediate winner or a loser, the total of the dice becomes known as the point. For all successive rolls, the player will win a game if the point is rolled again. However, if a 7 is rolled before the point is rolled, the player craps out.

Below you can play craps. It will count for you the total number of wins and losses. If you want to restart the count, click on the "Start Over" button.

The Game of Craps

Let us try to calculate the probability of winning. We can use the probabilities we calculated on the previous page. The probability of winning on the first roll is the probability of rolling 7 or 11, which is 1/6 plus 1/18, which equals to 2/9. Suppose we roll 4 on the first roll (the probability of rolling 4 is 1/12). On each successive roll the probability of rolling 7 is 1/6 and the probability of rolling 4 is 1/12. That is, on each successive roll the probability of losing is twice that of winning. That means, that on several rolls we are twice as probable to lose as to win. That is, the probability of winning after we rolled 4, is 1/3. Hence, the probability of rolling 4 and winning is 1/12 times 1/3, that is 1/36. Continuing in the same manner we can count the overall probability of winning. Can you do that?