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Craps is an exciting yet fickle game. It’s often featured in television and movie scenes, with occasional hooting and hollering around the craps table. So why all the excitement? And what’s the deal with 7?

Calculating the probability of winning is cumbersome — the casino relies on the complexity of the calculation to hide their edge. However, what makes it cumbersome is a slightly complicated sample space and conditional probabilities! In this lesson, students learn about the game of craps as the avenue for some sophisticated theoretical probability calculations, and they learn why, in the long run, the house always wins.

Students will

  • Generate experimental data for a simplified version of craps
  • Determine the sample space for the sum of two dice, and compare experimental and theoretical probabilities
  • Generate experimental data for the full game of craps
  • Calculate the theoretical probability of winning a game of craps

Before you begin

Students will be expected to know that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs, and be able to represent the sample space for compound events using a table. They should know that the probability of a chance event can be approximated by observing the long-run relative frequencies of experimental results. Finally, they should be familiar with multiplying probabilities of independent events to determine the probability that both will occur, and adding the probabilities of mutually exclusive events to find the probability that one or the other will occur.

Common Core Standards

Content Standards
Mathematical Practices

Additional Materials

  • Dice (2 per student or per small group)