Comparing Probabilities: Rock, Paper, Scissors, and Coin Toss

The two most popular decision-making processes are tossing a coin and playing rock, paper, scissors. In the activity described in this article, students find the theoretical probabilities of winning a coin toss and a round of the rock, paper, scissors game. They next devise strategies to win and test them out. Students then compare the theoretical probabilities they found with the experimental probabilities. The mathematical topics covered in this activity include calculating basic probability; understanding that for independent events A and B, P(A and B) = P(A) × P(B); recognizing a geometric series and applying the appropriate formula to find what it converges to; and understanding the meaning of descriptive statistics. Students were able to prove that although theoretically both games are fair in that they both give each of the two players a 50 percent chance of winning, several strategies can be employed to make each game unfair.