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### 7.16. Case Study: A Game of Chance

One of the most popular games of chance is a dice game known as “craps.” The rules of the game are straightforward:

A player rolls two dice. Each die has six faces. Each face contains 1, 2, 3, 4, 5 or 6 spots. After the dice have come to rest, the sum of the spots on the two upward faces is calculated. If the sum is 7 or 11 on the first throw, the player wins. If the sum is 2, 3 or 12 on the first throw (called “craps”), the player loses (i.e., the “house” wins). If the sum is 4, 5, 6, 8, 9 or 10 on the first throw, that sum becomes the player’s “point.” To win, players must continue rolling the dice until they “make their point” (i.e., roll their point value). The player loses by rolling a 7 before making ...

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