Recreational Math

Card and Dice Games

What are the odds when playing craps?

Craps is probably the most popular game of chance in the world; it is also illegal to play in many places. But it has a long history: It was played in ancient Greece and Rome and was even a mainstay of some old 1930s and ‘40s movies. Craps can be played using a wall and a pair of dice. It is a popular casino game in places such as Las Vegas—and even on the Internet—with betting on craps involving a complex equation.

Its popularity no doubt comes from its simplicity. In craps, a player throws two dice; their number (roll) is the total of the dots on the top faces of the dice. If the initial roll is a 7 or 11 (called a natural), the player wins. If the number 2, 3, or 12 comes up—called craps—the player loses, but keeps the dice. If the sum of the dice adds up to the number 4, 5, 6, 8, 9, or 10, that number becomes the thrower’s “point.” The player then continues to shoot until he or she throws the point number again, in which case the gambler wins and retains the dice. But if the player shoots a sum of 7 before he or she can roll the point value, he or she loses and gives the dice to the next player.

Craps is truly a game of chance, with the probability mathematics of craps fairly straightforward. For example, take the probability of winning on a roll-by-roll basis, in which P(p = n) is the probability of rolling a point n. The resulting numbers show that the probability of winning is 244/495, or the shooter wins about 49.2929 percent of the time.


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