Good Thinking

Ideas that influence the way we think.

What's Wrong With Arthur Chu's Jeopardy Strategy

Chu's Jeopardy strategy is simply this: Win by making sure others can't play.

What's wrong with Arthur Chu's Jeopardy playing style? Quite simply this: It's not about winning because you know the most. It's about winning by making sure others can't play.

When people tune in to watch Jeopardy, they watch with an implicit assumption: That the winner is the most knowledgeable and the best strategist. But Arthur Chu's "game theory" playing style strips out the first of these. As he himself puts it:

…you can leverage your advantages in Jeopardy!, even if you’re not necessarily the person who knows the most trivia, or if you’re about evenly matched with your opponents, how can you increase your chance of winning. It turns out there’s a lot of things you can do that most people don’t do for whatever reason.

Some would bridle at the claim that Jeopardy is simply a trivia show along the lines of Family Feud or Hollywood Squares. The questions run the gamut from ancient history to pop culture. And some question categories require figuring out puns or turns of phrase that provide clues to the answer. But Chu's message is clear: You can be pretty ignorant of every category yet still win if you just ensure that no one else gets a chance to play.

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This is particularly true of the game-changing Daily Doubles. Chu's strategy is to find them as quickly as possible and play them or waste them—just make sure that the other two opponents don't get a chance at them.

After one of his games, Chu forced an unusual tiebreak when he didn't have to, allowing one of his fellow contestants to also go home with $26,800, instead of leaving the show for good with $2,000. But even this seemingly altruistic move was actually a manifestation of self-interest: By forcing the tie-break, he increased his own odds of returning the next day because he induced his opponent to bet everything. If he was right, he would advance, but if both he and his opponent were wrong, he'd advance anyway.

What people find obnoxious about this style of play is that it is entirely focused on winning by limiting one's opponent's opportunities to play, not on actually knowing anything. The NFL has gotten strict about limiting tactics aimed at injuring quarterbacks because, sure, you can win that way, but most people actually come to watch good football get played. Only dyed-in-the-wool fans and bettors are interested only who wins. In the NBA, the rules are structured so that it isn't possible to win just by continually fouling the best players. It used to be possible, but they changed the rules so that (a) you foul out, and (b) free throw percentage is much higher than field goal percentage, meaning that you are handing over an advantage to those you foul. People want to see the game played, and they want the winners to be good ball players as well as strategists.

But Chu doesn't see it that way. He says

…the producers weren't paying me to make the show pleasant to watch. If you were playing for fun, you could talk about poor sportsmanship, but within the rules, it's about winning. If you don't like it, change the rules.

Yes, indeed, wiser words were never spoken, and perhaps Jeopardy's producers should consider doing exactly that.

It would probably behoove those who consider Chu a genius and are enamored of his  playing style to learn a little more about game theory. Let's take a simple example such as Prisoner's Dilemma. In this simple game, if two parties cooperate, they get a modest payoff. If one defects, the defector gets a larger payoff and the cooperator gets a large penalty. If both defect, they both get modest penalties. For example, suppose you and a coworker jointly botched a report in a major way, and it ended up costing your employer $100,000. Your boss is in a rage, and plans to make the person who was responsible repay the company out their own pocket. He meets with each of you separately, and demands to know who botched the report. If you both blame each other, he will fine each of you $50,000. If only one blames the other, the person blamed will be fined $100,000 and the other will get off scot-free. If you both refuse to blame the other, then the boss will fine each of you $25,000 and will write the remaining $50,000 off.

You may be thinking that the best thing to do is for both of you to keep mum. That way you both lose some money, but no one gets stuck holding the bag. After all, you still have to work together after this mess is taken care of. But in economics, a rational agent is a self-interested agent: You seek to maximize your gain and minimize your losses. So the best (dominant) strategy in one-shot Prisoner Dilemma games like this is to defect. Take the money and run, leaving your partner (or your opponent) holding the bag.

But if you play this way, you had better hope you never meet up with the same players again. Here's why: If the players act like rational agents, and the other players are mindless automata, then it is possible to fix the game so that you continuously exploit them. But if the other players are capable of having a "theory of mind"—that is, they can figure out what you are likely to do—then Prisoner's Dilemma becomes equivalent to the Ultimatum Game, a game in which one person proposes how to split a sum of money and the other person gets to accept or refuse the proposal. If the offer is rejected, no one gets any money. The proposer can maximize his own outcome only by giving his partner more and there is no benefit to him in defecting. In fact, then they may choose to negotiate to each set the other’s score to the maximum cooperative value.

That is how purely rational agents behave, and it doesn't look too good for the pure defector. But the outcome looks even bleaker if we ask how people actually behave when playing these kinds of games. Countless studies in experimental economics and psychology have shown that people begin these games with a bias toward cooperation, and behave generously towards those who cooperate with them. Defection, however, is met with strong retaliation; cooperators will not engage in future transactions with defectors, and they will even pay a penalty in order to have the opportunity to punish defectors. They will even go so far as to incur a penalty on themselves to punish someone who defected on a someone else!

So perhaps, in the long run, defining winning simply as beating your opponents is not so smart after all.

For a plain English presentation of game theory strategies, see Chapter 2 of my book Good Thinking: Seven Powerful Ideas That Influence the Way We Think.

Copyright Dr. Denise Cummins February 25, 2014

Dr. Cummins is a research psychologist, a Fellow of the Association for Psychological Science, and the author of Good Thinking: Seven Powerful Ideas That Influence the Way We Think.

More information about me can be found on my homepage.

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Denise Dellarosa Cummins, Ph.D., is the author Good Thinking, The Historical Foundations of Cognitive Science, and Evolution of Mind.

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