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# Spin City

## What’s the best way to play roulette?

What’s the best way to play roulette? As glamorized in casino ads around the world, the prospect of winning big on a spin of roulette can set hearts racing. And yet somehow the house always wins in the end!

In this lesson, students use probabilities and odds to analyze roulette payouts and debate the optimal strategy for winning the game (including not playing at all).

### REAL WORLD TAKEAWAYS

• In the long run, people should expect to lose money playing roulette, and casinos should expect to gain money.
• Though not everyone does, you can use probabilities and expected value to inform life choices.

### MATH OBJECTIVES

• Describe the probability of an event given a sample space
• Calculate expected value
• Reason with probabilities to inform real-world decisions

This complex task is best as a culminating unit activity after students have developed formal knowledge and conceptual understanding.
Algebra 1
Probability (Beg.)
Algebra 1
Probability (Beg.)
Content Standards S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). S.MD.5 (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. (a) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast- food restaurant. (b) Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Mathematical Practices MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure.