Bidding Optimally on The Price Is Right

What is the best strategy in the bidding game on The Price Is Right? over the last twenty-four years, the television game show The Price Is Right has begun with the announcer asking four contestants to come on down to Contestants' Row. At that point, a prize is displayed; and the players are asked one after another to guess its retail price. The bids are positive whole-dollar amounts and may not equal a previous bid. The player whose bid is closest to the actual price of the prize, without going over, wins the prize and - more importantly - goes on stage possibly to win additional prizes. If all of the players overbid, then they are given chances to lower their bids. A player who bids the exact price wins $100 bonus.This game is repeated, with the three unsuccessful contestants, plus a new member from the audience who takes the place of winner of the previous round (and bids first). Six bidding games in all are completed during each one-hour show.

We analyze this bidding game using a mathematical model faithful to the actual television game show. Then we derive optimal strategies for any number of players. Finally, we analyze a related multiplayer card game, giving the optimal strategy for any number of players 1 ≤ n ≤ 52.

We hope that this study of a popular television game show and related games will serve in the classroom as an entertaining yet useful introduction to applied probability.

Table of Contents:

INTRODUCTION

THE CONTINUOUS GAME

OPTIMAL STRATEGIES

THE DISCRETE GAME

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR