Like retired dweebs everywhere I watch Jeopardy on TV and am enjoying the run of the current champion, James Holzhauer, a professional sports bettor from Las Vegas who has won a total of $1,225,987 in his sixteeen consecutive victories. James's dominance makes me wonder whether the bell-curve distribution applies to Jeopardy contestants. Before him, the record take from a single game was $77,000. James has gone over $100,000 several times now. His average amount won per game is within a few hundred dollars of the previous single-game record.
There are it seems to me only a few elements to Jeopardy stardom. The most obvious is having a head full of knowledge on diverse topics. Another is physical reflexes. From what I understand, after the question is asked there is a short period of time in which you cannot "ring in." Moreover, if you do ring in early, you are locked out for another flash of time--long enough so that one of your opponents will likely beat you to the draw. Of course, if you're too slow you'll lose out, too. So there is an art and rhythm to working the signaling device, and if you're not good at that you'll never win: the other contestants have heads full of knowledge, too, else they wouldn't be on Jeopardy.
But these elements are on the bell-curve continuum. James is way out to the right on both, and this can plausibly account for 16 wins in a row, but not for the way in which he laps the field in race after race. The credit for that, I think, must go to superior strategy. James's Jeopardy run has elicited a lot of commentary, much of it relating to his aggressive betting, which is the hallmark of his in-game strategy, but I think there is a psychological aspect to it that I haven't seen anyone discuss. Since I don't want to get into the details of Jeopardy rules, how you win and all that, consider the following simpler game that mimics a common Jeopardy dilemma--it's no doubt the source for the name, Jeopardy:
Suppose you're given a chance to win money by answering a lot of questions. If you choose to answer, and you're correct, you win $500, but you have to pay $500 if you're wrong. So you answer the question if you can, and pass if you don't know. There are a lot of questions. You're doing really well and have given enough correct answers to earn $20,000. Now suddenly for one question the game changes. Before hearing the question, you have to bet any amount, up to the whole $20,000 you've won, that you can answer it correctly. After you make your wager, the question is read, and if you answer correctly you add whatever you bet to your 20k. Naturally you lose the same amount if you answer incorrectly. No passing allowed on this question. If you don't know, and you bet a lot, you're going to lose a lot. Of course there is a high potential upside, too. How much should you bet?
It obviously depends on how likely you are to answer correctly. But let's say that so far you've known about two-thirds of the answers, and you trust that the game is honest--the question will be about as hard as all the others that you could pass on if you wanted. In that case, shouldn't you bet the whole $20,000, assuming your goal is to win as much money as possible? It's a matter of "expected return." If you have a two-thirds chance of answering correctly, and you play three times, betting everything each time, you'd win $40,000 twice and nothing once for a total of $80,000. Divide by three games to get an expected return per game of $26,667. If you bet anything less than the whole $20,000, your expected return is less. For example, if you are really conservative, and bet nothing, your expected (and actual) return is just $20,000. So long as you have a better than even chance of answering correctly, bet everything to maximize your expected return.
If you were playing this game in "real life," personal considerations might require a more conservative approach. If, for example, you start the game with only the shirt on your back and an $18,000 debt to a loan shark, due and payable in a week, you should probably bet $2,000 at the most, even if you're pretty sure you'll know the answer. But the details of how the Jeopardy game work cut in another direction. It's more like three people are playing the above game simultaneously, and only the one who accrues the most money gets to keep the money--the other two get comparatively worthless consolation prizes. In such a game, betting very aggressively is the best strategy, assuming you know most of the answers--and I assume the vetting process for potential contestants guarantees that they all will know most of the answers.
And here's the thing: James is a very aggressive bettor, but a lot of contestants aren't. I think that for most of us regulars there is something psychologically or emotionally repellent about the prospect of losing in one trial everything we'd accumulated over time by getting a lot of things right. What a blow that would be! We just can't bring ourselves to risk it, even if, in our head, we know it's the right thing to do. It's possible to dive deeper into the psychology of Jeopardy. Speaking for myself, I am the kind of person who'd really hate to lose everything I'd painstakingly acquired. I also am the kind of person who'd figure out that, to win, I really should take big risks. So I would force myself to do what I am uncomfortable with doing, and the result of that is I'd probably be less apt to answer the question correctly. My brain might freeze on a question about the Minnesota Twins! I think it's interesting that James's day job is Las Vegas sports bettor, a line of work that I assume involves pretty routinely a mix of big wins and big losses. Pursuing the optimal strategy doesn't phase him in the least.
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