You've already won a refrigerator that dispenses crushed ice through the door, but you know that if you can get to the Showcase Showdown you could win a Ford Explorer or a trip to sunny Cancun.
Your first spin of the wheel lands on 55, which is good because it beats the first contestant's 50.
Now, should you stick with 55 and hope it ends up being a high enough score to beat Contestant 3? Or do you spin again, hoping to add to your sum without going over 100? Remember, with a spin of 45 you'll have an even 100, which would not only guarantee you at least a tie, but pay $1,000 and give you a bonus spin -- which could yield another $5,000 or $10,000. On the other hand, if you go over 100, you're out.
Such are the dilemmas contestants on the TV game show The Price is Right face during a contest known as The Wheel. The high point-getters from two spin-offs of a numbered wheel the size of a tractor tire qualify for the show's final price-guessing game, the Showcase Showdown, where the really big-ticket items, like cruises and cars, can be won.
Using sophisticated mathematical modeling, a team of researchers that includes two Notre Dame finance faculty members has calculated the rational way to play The Wheel game. Technically termed a Unique Subgame Perfect Nash Equilibrium, their strategy weighs the odds of certain numbers coming up on the wheel against such potential rewards as the bonus prizes and average bounty available in the Showcase.
Here's what the equations dictate when it comes to deciding whether to risk a second spin:
Contestant 1 should utilize a second spin if the first spin yielded 65 or fewer points.
Contestant 2 should take a second spin if the first spin yielded 55 or fewer points, or if the first spin isn't enough to beat Contestant 1.
Contestant 3 should take a second spin if the score from the first spin is 50 points or fewer and results in a tie with one other contestant; if the score from the first spin is 65 points or less and results in a tie with two contestants; or if spin one isn't enough to beat the best score so far.
The guidelines come from a research experiment by two Notre Dame assistant professors of finance and business economics -- Rafael Tenorio and Robert Battalio -- a doctoral candidate in finance at Indiana University, and a member of the finance faculty of the graduate school of the London Business School. They developed the experiment as a means to gain insight into financial decision-making behavior.
Using game-show outcomes in serious research is nothing new. A study by one researcher looked at contestant wagers in the Final Jeopardy portion of Jeopardy!. Another study focused on bid-making strategies employed by Price is Right contestants in the auction games that determine who makes it up on stage.
In 1996 USA Today carried an article about a University of Dayton undergraduate who had written a paper on the optimal strategy for playing The Wheel. However, that analysis didn't take into account bonus prizes for spinning an even 100.
Tenorio, Battalio and their colleagues examined the results of Wheel games played during 141 actual episodes of The Price is Right. They found that decisions the contestants made usually, but not always, meshed with those their strategy dictated. But, surprisingly, the winning percentage of the contestants was virtually the same as it would have been if they'd followed the calculated guidelines 100 percent of the time.
The Notre Dame faculty discussed their Price is Right experiment this past January in New Orleans at the winter 1997 meetings of the Econometric Society.