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How Game Theory can help you win Jeopardy and lose friends

If you are ever fortunate enough to find yourself on the television game show, Jeopardy!, you may want to keep in mind the most interesting “winning” strategy of 11-time winner, Arthur Chu. Ironically, the strategy Arthur used to win the game involved playing to tie rather than win. Using his acquired knowledge of game theory, Arthur hedged his bet in Final Jeopardy in an unusual attempt to tie with the second place contestant should they both answer correctly. The context of Arthur’s bet is very important as he was in first place with $18,200 going into the final round leading the second place competitor with $13,400 and the third place competitor with $8,400. The intuitive bet for the first place contestant is usually to double their earnings by wagering all their money, however, Arthur bet only $8,600. His bet would leave him tied for first place if he and the second place competitor, who he knew would bet her entire earnings, answered correctly. These wagers would leave them both at $26,800, allowing them both to return for the next week’s game. If the contestants were faced with an impossibly difficult final clue and were to all answer incorrectly, he would be left with $9,600, with the closest contestant having only $8,400 (if the third place contestant were to bet nothing), and the formerly second place contestant having $0. For those of you who might wonder “Why not just bet $8,601 and go for a narrow win?,” Arthur presumably reasoned that tying was the Nash Equilibrium, and if he were to get the question wrong, he would have another dollar to lead the third place contestant if he were to bet less than his entire balance (winning/losing by $1 is not unheard of in Jeopardy).

Astonishingly, Arthur and the second place contestant both answered correctly while the third place contestant answered incorrectly. This led to an unbelievable naming of co-champions, as they were both able to advance the next round. This mutually beneficial outcome illustrates the Nash Equilibrium as both contestants chose the optimal wager considering each other’s possible bets. Without considering the second place contestant’s possible bet, Arthur’s optimal wager would be all of his money in order to double his earnings for the day. To relate it to “The Prisoner’s Dilemma,” their choices were the equivalent of both confessing, although the ideal outcome for Arthur (doubling his money without considering the other contestants’ bets) was the equivalent of denying.

Arthur’s brilliant implementation of game theory has earned him some enemies among disgruntled Jeopardy lovers, so be warned that using this strategy may burn some bridges! In addition to his final wager, Arthur consulted his knowledge of game theory throughout the game by hopping around the board searching for daily doubles and denying his competitors the opportunity to answer the questions and gain an advantage. If you would like to know more about his strategy, the article below describes his other techniques that contributed to his 11-game win streak.


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