Project: Determine the Best Strategy for a Game of Chance

For this project, we suggest that you analyze a game of chance known as Pig, but you are free to analyze any game of chance that you wish. The goal of the project is to use mathematics to determine the strategy that will give you the highest score in the game in the long run, and to communicate your strategy in a way that others will understand.

The game of Pig is simple. On your turn, you roll a die. If your score is 2-6, you collect that many points and have the choice of whether or not to roll again. You collect points with every roll until you either decide to end your turn OR you roll a 1. If you decide to end your turn before rolling a 1, your score is the sum of all the rolls during your turn. If you roll a 1, your turn automatically ends and your score for the turn is 0.

When you play Pig, you and your friends can decide at what point you will stop and declare a winner. Will you play for a certain length of time, like 30 minutes, and whoever has the most points at the end wins? Will you play for a certain number of turns, like 25 each, and whoever has the most points wins? Will you play to a certain number of points, like 100, and whoever gets there first wins? Is there another way you can determine the winner?

The activities in the next sections will explain the mathematics necessary to calculate which strategy will get you the best score in Pig in the long run. Your goal is to use math to calculate the theoretical best strategy, then put it to the test by trying it out in the game, and finally, present an analysis of your results and recommendations for others. You may present the information in any way you choose - blog, video, simulation, or anything else you can imagine.

<And remember, Pig is just the example we chose. There are many games of chance that can be mathematically analyzed to determine a best strategy. We encourage you to branch out to a game of your choice and share your analysis!</p>

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