Overly long, boring post about Jeopardy wagering strategy
Various online media outlets have been reporting on yesterday's "Jeopardy!" game, which ended with all three contestants winning $16,000. This is the first time this has happened in the show's 23 seasons, and according to a game theorist at Washington University in St. Louis who was contacted by the show, the odds of a three-way tie are one in 25 million. I like Wash U (because my brother went there and it has a funny name), but this number is ridiculously low, especially when one considers how the tie came about. (The returning champion was leading with $13,400, and the others tied for second place with $8,000. The champion thought it would be neat to have a three-way tie, and bet enough that if all three players got it right and the other two bet everything, such a tie would result. So really such a tie is possible whenever the two trailing players are tied going into Final Jeopardy and the leader has less than twice their score, and the leader is in a somewhat unusual mood, tie-wise. And one could argue that there are sometimes strategic reasons for the leader to bet for a tie, as it occasionally happens that the trailing players make strategic bets with the goal of just barely beating the leader if he makes the conventional "shutout bet" and gets it wrong.)
(Qualification: The second game of the current syndicated version of Jeopardy resulted ended in a three-way loss, when all of the players ended with 0. In this case, they were all considered losers, and there were three new players the following day. This was a result of poor wagering strategy by the leader, who needlessly bet all of his money on the Final Jeopardy clue.)
(Tom Walsh, the first Jeopardy player to win seven regular games, had a habit of always playing for a tie in Final Jeopardy. It was pointed out at the time that this can be an advantage, as the second-place player, if he suspects Walsh will bet for a tie (having seen his previous games), has an incentive to bet everything, knowing that if he gets the question right, he will be guaranteed a win or tie. This way, the leader still gets a win (possibly a co-win) if he gets Final Jeopardy right, while also eliminating the second-place player from contention should that player get it wrong. Had the second-place player expected the leader to bet for an outright win, he might change his strategy to making a bet that would give him a chance of winning if both he and the leader got the question wrong.)
(As if this post were not long and boring enough, there was an instance in 2000 of a three-way tie going into Final Jeopardy, with all three players having $5,200. Two of the players bet everything, but the third, much to Alex's disappointment, held back $200 and bet $5,000. Interestingly, this player found a Daily Double on the penultimate clue of the game, trailing the two others by $1,100 with a $1,000 clue remaining. She bet $1,100 and got it right, thus tying the other two players, and the tie stood when the final clue was not answered by any of the players. In retrospect, this was a rather poorly chosen wager. With a game that close that late, the player should be concentrating on being in the lead going into Final Jeopardy. With an $1,100 wager, she eliminated herself from any possibility of being in the lead if she got the question wrong, but still was only tied with one question to go if she got it right. A slightly larger wager, say $1,200, would still have eliminated her from the possibility of leading going into Final Jeopardy if she were wrong, but would have given her the lead outright with one question to go if she were right, thus giving her the optimal position given the fact that the final question of the round was unanswered. But it's hard to really fault her, since there isn't exactly time to think carefully about Daily Double wagers.)
(Random addendum: When we play "Math Jeopardy" in class at CTY, the kids almost never wager strategically. They just pick a number and bet that.)
If you read all the way to the end of this post, you should win some compensation. Maybe a lollipop, since I occasionally have more of those than I care to consume.
(Qualification: The second game of the current syndicated version of Jeopardy resulted ended in a three-way loss, when all of the players ended with 0. In this case, they were all considered losers, and there were three new players the following day. This was a result of poor wagering strategy by the leader, who needlessly bet all of his money on the Final Jeopardy clue.)
(Tom Walsh, the first Jeopardy player to win seven regular games, had a habit of always playing for a tie in Final Jeopardy. It was pointed out at the time that this can be an advantage, as the second-place player, if he suspects Walsh will bet for a tie (having seen his previous games), has an incentive to bet everything, knowing that if he gets the question right, he will be guaranteed a win or tie. This way, the leader still gets a win (possibly a co-win) if he gets Final Jeopardy right, while also eliminating the second-place player from contention should that player get it wrong. Had the second-place player expected the leader to bet for an outright win, he might change his strategy to making a bet that would give him a chance of winning if both he and the leader got the question wrong.)
(As if this post were not long and boring enough, there was an instance in 2000 of a three-way tie going into Final Jeopardy, with all three players having $5,200. Two of the players bet everything, but the third, much to Alex's disappointment, held back $200 and bet $5,000. Interestingly, this player found a Daily Double on the penultimate clue of the game, trailing the two others by $1,100 with a $1,000 clue remaining. She bet $1,100 and got it right, thus tying the other two players, and the tie stood when the final clue was not answered by any of the players. In retrospect, this was a rather poorly chosen wager. With a game that close that late, the player should be concentrating on being in the lead going into Final Jeopardy. With an $1,100 wager, she eliminated herself from any possibility of being in the lead if she got the question wrong, but still was only tied with one question to go if she got it right. A slightly larger wager, say $1,200, would still have eliminated her from the possibility of leading going into Final Jeopardy if she were wrong, but would have given her the lead outright with one question to go if she were right, thus giving her the optimal position given the fact that the final question of the round was unanswered. But it's hard to really fault her, since there isn't exactly time to think carefully about Daily Double wagers.)
(Random addendum: When we play "Math Jeopardy" in class at CTY, the kids almost never wager strategically. They just pick a number and bet that.)
If you read all the way to the end of this post, you should win some compensation. Maybe a lollipop, since I occasionally have more of those than I care to consume.