A contestant on the popular television show Jeopardy! earned $131,127 in a single game, breaking the record for highest single-game winnings, according to the show’s website. Professional gambler James Holzhauer has amassed over a million dollars in 17 nights, with no sign of slowing down. Here’s how.
The Jeopardy! website features a page tracking ongoing champion James Holzhauer’s statistics so far. As of April 28, he holds the top seven spots for single-game winnings on the show and has earned an average of $75,035 per game—for a grand total of $1,275,587. Game theory is a popular subject of study that explains how odds, strategies, players, and more factor into the way we play games. Understanding the basics can help us make sense of Holzhauer’s runaway success.
Jeopardy Records and the Three Components of a Game
In a broad sense, any game has three main components: players, strategies, and payoffs. “The players are just the people playing the game; that’s easy enough,” said Dr. Scott P. Stevens, Professor of Computer Information Systems and Management Science at James Madison University. “Each player has available a set of strategies—what they’ll do, how they’ll respond—and when those strategies interact, each player ends up with a payoff which specifies how much they like the result.”
As Dr. Stevens said, we all know what the players of a game are. Moving on, when we think of strategies, we tend to think of a general plan or an unspecific set of rules that guides our decision-making. “In game theory, a strategy has to specify what decision you would make in every possible situation in which you could find yourself,” he said.
Payoffs are also more dynamic than at first glance. If we look at wagering for money, which would include game shows like Jeopardy!, the payoff isn’t simply the money you make. Dr. Stevens explains it with a hypothetical situation about the buying and selling of a vase. “I bought the vase for $8,” he said. “If I sell it to you for $10, but you think it’s worth $18, I’ve made $2 on the deal; you’ve made $8.” Game show contestants may win with high earnings or low, but many shows pay for the contestants to be flown to the studio and be put up in a hotel, followed by an appearance on national television. The fun and experience of being at the game show may be worth plenty to the contestant.
Jeopardy Winning Tricks – Auctioning a Hundred-Dollar Bill
One popular trick on Jeopardy! happens during Final Jeopardy. Contestants wage any amount of their winnings based on the subject of Final Jeopardy and their confidence in it. The “answer” is shown, contestants have a short time interval to write the correct question, and the wagers are revealed. Sometimes, two contestants will wager all of their money and lose it all. Next to them, the final contestant wagers all of their money except one dollar and they win with just a dollar’s earnings. In this instance, the winner didn’t beat the others with a large sum, but won simply by losing less than the others.
Dr. Stevens shows how this is applied to a war of attrition with a fascinating example. He said that Max Bazerman of Harvard Business School once spoke to an audience of 75 seasoned Wall Street workers and told them he would be auctioning off a crisp $100 bill, with a catch: The winner paid his or her bid and received the bill, while the second-highest bidder also paid his or her bid but received nothing in return.
The $100 bill went for $465. Why? Winning by losing less than the other player.
“Bidding got to $95, then $100,” Dr. Stevens said. “If it had stopped there, the $95 bidder would be out $95 with nothing to show for it in second place, but if they bid $105 and won, they would only be out $5, so they bid $105. But now the person who bid $100 was out $100, so they bid $110, and so on, and so on. Someone finally got the message at $465.”
According to Dr. Stevens, Bazerman claims to have run the $100 auction over 600 times and has never once seen the bidding stop at less than $100.
By carefully calculating how much risk he’s willing to take and the amount he’s willing to lose night by night, Holzhauer is being very careful with his money and earning a tremendous amount. Of course the knowledge of subjects is paramount, but in Jeopardy!, a little game theory goes a long way.
Dr. Scott P. Stevens contributed to this article. Dr. Stevens is Professor of Computer Information Systems and Management Science at James Madison University in Harrisonburg, Virginia. He holds a Ph.D. in Mathematics from The Pennsylvania State University, where he received B.S. degrees in both Mathematics and Physics and graduated first in his class in the College of Science.