Spinner Games

Introduction

Suppose you run a spinner game at a school fair, with a small entry fee and a prize for landing on the winning segment. This exploration asks you to design that game, calculate its expected value, and decide what fee and prize structure keeps it profitable for you while still enticing players to pay. Extension: design your own spinner, then collect data to estimate its probabilities experimentally rather than calculating them from the geometry.

Guiding Questions

• Design a spinner game with money payoffs. What makes a game fair?
• Calculate the expected value of your game and adjust it to favour the house slightly.
• Run the game many times. How quickly does the average settle towards the expectation?
• Design a game that looks generous but isn't. What disguises the true expected value?