As I post this message on Saturday, January 8, 2022, Amy Scheider has just passed the $1 million mark in Jeopardy! winnings. Since, like many Spirited Reasoners, I’m an avid Jeopardy! fan, I thought it might be fun to revisit our strategy of wagering in Final Jeopardy!

As you know, contestants end the Jeopardy! and Double Jeopardy! rounds having amassed a sum of money usually ranging from around $1,000 (for the person in third place) up to as much as $20,000 or $30,000 for the leader. In the Final Jeopardy! round, each contestant is allowed to wager all or any portion of their “bank accounts” on getting a correct response to one last question. What makes this round so interesting is that the contestants are first shown the category of the Final Jeopardy! answer (e. g., European History, Biology, Sports, etc.), then must seal their wagers, and only then are they shown the actual “answer” for which they must write the correct “question.”

The contestant with the highest total going into the Final Jeopardy! round—currently almost always Amy Schneider—has the most straightforward betting strategy. She must ensure that neither of the other two contestants can beat her by wagering all their money on the final question. To do that, she must engage in a thought process that goes something like this:

• Am I far enough ahead so that the other challengers can’t beat me even by wagering all their money? If so, then I’d be safe in making a high-ish wager; i. e., one just large enough to earn me lots of money if my response is correct, yet not large enough to permit the possibility that another contestant could pass my total if I happen to get the question wrong. Amy Schneider has been in this position often enough, so that she has been able to make sizable bets in the Final Jeopardy! round, leaving her with monster payouts, because she almost always comes up with the correct response. Even in those few games where she was wrong, her bets were conservative enough to leave her with a comfortable winning margin.
• Would my closest competitor be able to surpass my current total by betting all their money and getting the final response right? If so, then the leader must calculate the smallest amount of money required to win if we both contestants come up with the correct response. For example, if Amy Schneider has $19,000 and her closest competitor has $10,000 going into Final Jeopardy!, she should wager $1,001 dollars, so that she will wind up with $20,001 with the correct response and $17,999 if her response is incorrect. Then, even if her opponent wagers everything, her opponent can wind up with no more than $20,000, leaving Amy in the lead if their responses are both correct. Why not bet more? Because there’s no guarantee that her opponent will wager everything. In that case, she might lose the game even if both come up with an incorrect response. For example, using the example above, suppose she were to get greedy and wager $10,000 while her second-place opponent wagered zero. Her opponent would defeat her by a score of $10,000 to $9,000 they both answered Final Jeopardy! incorrectly.
• Is this category so foreign to me that I am likely to give an incorrect response? If so, all other strategy goes out the window and a zero bet would be in order.

Note that the contestant with the second-highest total only has a chance to win in the (b) or (c) cases listed above. This contestant should generally always wager everything, hoping to get the question right while the first-place contestant writes down an incorrect response. (Even a maximum bet and a correct response won’t win the game for this contestant if the first-place finisher follows the (b) strategy and writes down the correct response.) There’s no reason to wager less than everything unless this second-place contestant is worried about the prospect of finishing third rather than second. (Recall that, according to Jeopardy! rules, the second-place finisher is awarded only $2,000, regardless of the amount shown in their “account” window at the end of the game. The third-place finisher is awarded only $1,000.)

The poor contestant in third place should take a hard look at the totals going into the Final Jeopardy! round. If the third-place total is close enough to the other two totals, then the correct strategy, oddly enough, is to bet zero. This strategy gives the third-place contestant two chances to win, as follows: (1) the case in which everyone gets the Final Jeopardy! response wrong, and the two highest contestants make large wagers; or (2) the case in which third-place finisher is the only contestant to write down the correct response (while the other two lose their large wagers). It’s the first of these that most third-place contestants forget. Instead, they typically make large wagers based on the mistaken notion that the only way they can win is to bet everything. The key here is for the third-place contestant to make a calculated guess as to whether the scores require the first two contestants to wager big. If so, the best strategy is to make a wager based on the hope that no one writes down the correct final response.

In the case where the third-place contestant is too far behind the first-place contestant to have a chance of winning, the better strategy might to place a wager aimed at beating only the second-place contestant. Then, upon returning home, this contestant can at least claim bragging rights over one player (plus an extra $1,000, for what it’s worth.)