Mathematics and The Price Is Right

I just read a very entertaining article on the use of game theory for improving contestants’ odds of winning the various games on the long-running television game show “The Price Is Right.” Quoting from the article:

On a crisp November day eight years ago, I took the only sick day of my four years of high school. I was laid up with an awful fever, and annoyed that I was missing geometry class, which at the time was the highlight of my day. I flipped on the television in the hope of finding some distraction from my woes, but what I found only made me more upset: A contestant named Margie who was in the process of completely bungling her six chances of making it out of Contestants’ Row on The Price is Right.

Many contestants fail to win anything on The Price is Right, of course. But as I watched the venerable game show that morning, it quickly became clear to me that most contestants haven’t thought through the structure of the game they’re so excited to be playing. It didn’t bother me that Margie didn’t know how much a stainless steel oven range costs; that’s a relatively obscure fact. It bothered me, as a budding mathematician, that she failed to use basic game theory to help her advance. If she’d applied a few principles of game theory—the science of decision-making used by economists and generals—she could have planted a big kiss on Bob Barker’s cheek, and maybe have gone home with … a new car! Instead, she went home empty-handed…

To help future contestants avoid Margie’s fate, I decided to make a handy cheat sheet explaining how to win The Price Is Right—not just the Contestants’ Row segment, but all of its many pricing games. This guide, which conveniently fits on the front and back of an 8.5-by-11-inch piece of paper, does not rely on the prices of items.