COME ON DOWN ... THE PRIZE IS RIGHT IN YOUR CLASSROOM

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Mar 2004 by Butterworth, William T, Coe, Paul R

ABSTRACT: The Price is Right ( TPIR) is a rich source of examples of applied probability, combinatorics, and game theory. While some of the games played on stage by individual contestants stress a knowledge of pricing, many are also heavily based on probability. TPIR stage games are a treasury of interesting modules that can be effective learning tools in a wide range of classrooms, from Liberal Arts and Mathematics Education classes to Discrete Mathematics and Upper-level Probability classes. We will show how students explore important mathematics and improve their problem-solving skills by analyzing some of these games. Because these examples are drawn from a familiar source, they provide special motivation for study, and often reduce math anxiety. After a general discussion of how these games can be adapted for classroom use, we will explore two different pricing games, PLINKO and Money Game, each of which has its own mathematical and pedagogical value.

KEYWORDS: Probability, conditional probability, combinatorics, recreational mathematics, popular culture, The Price is Right.

INTRODUCTION

One of the most popular game shows in the history of television, The Price is Right (TPIR), is also one of the most useful in the classroom for the study of mathematics in popular culture. The tremendous variety in the complexity of its games contributes to its effectiveness in illustrating mathematical concepts of probability, combinatorics, game theory and strategy, while its popularity among students brings fun and excitement to the mathematics classroom. In this paper we will discuss how and why TPJA has been used for mathematical study in some of our courses, and give samples of how we present TPIR modules in our classrooms.

THE PRICE IS RIGHT FORMAT

The Price is Right [10], an hour-long game show hosted by Bob Barker on CBS for over 30 years, consists of four main features, each with its own mathematical content ripe for discussion:

* Contestant Selection and Bidding

This segment involves selection and competition to qualify for stage games. Contestants selected for Contestants' Row all guess (bid) the price of a special prize. The contestant whose bid is closest to the actual retail price of the prize, without going over, wins that prize and advances to the stage for an individual pricing game. In this segment the announcer makes the famous call to "Come on down... you're the next contestant on The Price is Right."

* The Pricing Games (a. k. a. Stage Games)

Six contestants compete individually in games that combine knowledge of prices, luck and strategy.

* The Showcase Showdown (a. k. a. Big Wheel)

Twice during each show three contestants vie to qualify for the Showcase at the end of the show. The winner is the contestant who is closest to $1.00, without going over, in one spin or a combination of two spins on a wheel marked with the nickel values 0.05, 0.10, ..., 1.00. Extra money can be won in bonus spins if exactly $1.00 is obtained.

* The Showcase

The two winning Showcasecontestants vie for prizes. The contestant who bids closest to the actual retail price of a prize package, without going over, wins that prize package. These packages are often worth tens of thousands of dollars.

While each of these segments has been treated in the literature ([2]-[4], [6], [7], [8], [11]) and could be used successfully in a classroom setting, we will restrict our remarks to pricing games since we have used them almost exclusively in our classes. In this paper we will discuss the general use of pricing games in our classes, the benefits of this use, pitfalls to avoid, and student reactions to our efforts.

PRICING GAMES

As noted above, the pricing games, or stage games, on TPIR are a rich source of games with a tremendous variety of flavor and complexity. There are more than 70 stage games available to producers at any given time, although there is a core of 30 or so that are played regularly. Sometimes tens of thousands of dollars can be won in these games, so they are interesting to contestants, audience members and viewers alike as they witness small fortunes being won (and sometimes lost again). Students are drawn to analyze these games because they are interested in their outcomes, and are prone to ask themselves questions such as: How would I, or how should I, have played that gamel

There is also great variation in difficulty of individual games, which involve, to varying degrees, elements of luck, skill, knowledge of prices, and strategy. The following is a non-exhaustive list of games that are classified according to the complexity of their mathematical analysis for use in the classroom:

For further details on these and other games, see the TPIR game archive at http://www.cbs.com/daytime/price/games/cliff_hanger.shtml.>USING TPIR IN THE CLASSROOM

Many of these pricing games have been effectively used as instruments of mathematical discussion and analysis in two types of courses:

* Liberal Arts /Math Survey/Mathematics Education

* Upper-level Probability or Combinatorics