$4000 Wagering Tutorial
by Ben Ingram, Jeopardy! superchamp, 2014 Tournament of Champions winner, bridge enthusiast and wagering expert
Know what I find strange? Watch Jeopardy! on a regular basis, and I promise you most of the contestants will make poor wagers when Final Jeopardy! rolls around. Why? Because everything ever written about Final Jeopardy! wagering theory is 100% wrong. Now, I know it's the Internet, and most of what you read on the Internet is wrong anyway. Believe me, I'm a strong believer in freedom of speech and net neutrality and all that. But I just hate seeing all these players put in all that effort in preparing, only to get up there on stage, overthink, use "math" and "science" and "game theory", or whatever, and all for waste. It's not their fault, so don't throw things at your TV screen. It's just that it's hard for anyone to separate the wheat from the chaff these days.
Until now. We figured it was time to come up with something better. So we went to work. We spared no expense. We put in the long hours. We used algorithms. The result is our gift to the Jeopardy! contestants of the future: the definitive tutorial on Final Jeopardy! wagering theory. We hope you'll find it useful, because it is.
Two-player situations
The best way to learn is by example, so let us begin with some simple two-player cases.
Fred16,001 |
Lamont10,000 |
Fred should wager $4000. This will guarantee a win even if Lamont bets it all and gets it right.
Lamont should wager $4000. This way, if Fred misses, Lamont can win through the back door.
Grady15,000 |
Bubba12,000 |
According to Snipes's rule, Grady should wager $4000.
Bubba should bet $4000. This is the only wager that satisfies the Bose-Einstein criterion.
Esther28,800 |
Julio26,000 |
This is a retrograde payoff case of the semi-static Herschel matrix, which calls for a $4000 wager.
Julio is presented with a symmetric Gorbachev dilemma, which means he has a choice. If he likes the category, he should wager $4000. If not, or if he thinks Esther likes the category, he should wager $4000.
Leroy17,200 |
Skillet17,000 |
This is a special case of the Catcher-Hilbert theorem known as the "Chico and the Man" situation. Leroy, who is "the Man", should wager $4000.
Skillet ought to wager $4000, but if Skillet figures Leroy knows Skillet is versed in Binev kernels, he should not wager $4000 but instead has to bet $4000.
Melvin3,800 |
Otis2,900 |
Neither player has enough to wager $4000. Both should wager $4000.
Three-player situations
Now let's extend what we've learned to three players.
Roger22,000 |
Dwayne18,800 |
Rerun12,400 |
Roger has to bet $4000. This satisfies the Homer-Bierstadt corollary of Lemke's inequality.
Dwayne, according to Clapinger's lemma, should bet $4000 unless he can find a better alternative. There is none, so he should bet $4000.
Rerun is in a "Hello Jeopardy!" situation because any wager other than $4000 is a wrong number.
Wilona24,000 |
Michael11,000 |
JJ4,000 |
Wilona should bet nothing in this situation except $4000.
Michael's optimal wager is $4000, but that's hard to figure out on the stage when you are terrified beyond the capacity for rational thought. So as a shortcut Michael should use Spengler's rule and instead wager $4000.
JJ should wager $4000 unless the category is Things That Rhyme With Dy-No-Mite. In that case he should wager everything he has.
Finally, here is a special case to remember from the semifinals of the 1991 Jefferson Day tournament:
George15,200 |
Louise14,000 |
Bentley18,000 |
Bentley should wager $4000. This is called a Pete Carroll because it's a bad decision.
George should make what is known as Pascal's Wager here, which is $4000.
Louise may as well wager $4000 because she can't win anyway due to outchange.
There you have it; the most in-depth and easy-to-learn Final Jeopardy! wagering tutorial known to humanity. Accept no imitations. Study and learn this material, and I guarantee if you make it onto the show, there will be a result.