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September 23, 2013

How to wager in Final Jeopardy!: Part Two

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In Part Two of my tutorial, we’ll look at some special scenarios involving two players.

We add a fourth rule (and a corollary) to our first three regarding wagering in Final Jeopardy!:

1. The leader always wagers to win
2. The trailer positions himself to win if the leader gets it wrong
3. If safe, each player covers a zero wager by the other
4. If your opponent is forced into a specific wager, hone yours

In Part One, I showed you that optimal game theory suggests the leader bet for a tie. In some circumstances, however, he HAS to bet for a tie. Let’s look at an example from last season.

Nichole is in the lead with 17,200, and Paula in second with 8,600.

Rule #1 is the leader always wagers to win. If Paula doubles her score, she’ll have 17,200. This is already Nichole’s total, so to guarantee a tie, she can wager no more than zero. You can’t wager less than zero, so because zero is the most Nichole can wager, it’s what she has to wager.

Rule #2 is the trailer positions himself to win if the leader gets it wrong. If Nichole gets it wrong, she’ll still have 17,200, so Paula needs to wager at least 8,600 to match this total. You can’t wager more than you have, so Paula has to wager 8,600.

This situation is special because the leader has exactly twice the trailer’s score – or the trailer has 1/2 the leader’s score. In this situation, both players must wager to tie.

This requirement to tie also occurs when the trailer has 2/3 or 3/4 of the leader’s score.

Example for the 2/3 scenario: Aaron has 21,600; Rosanne has 14,400.

For Rule #1, Aaron must wager at least 7,200 to cover Rosanne. But notice that if he’s wrong and Rosanne wagers zero, he will lose if he wagers more than 7,200. So he must wager 7,200.

Rosanne then has a choice. She can wager zero and hope Aaron gets it wrong; or she can wager everything and hope that she’s right. This is one of the few times when the category matters.

Example for the 3/4 scenario: Katie has 17,600; Joon has 13,200.

For Rule #1, Katie must wager at least 8,800.

For Rule #2, Joon can wager at most 4,400 to stay at or above Katie’s total.

For Rule #3, Joon should wager at least 4,400 to match a zero wager by Katie. But this means his minimum and maximum are both 4,400, making that his only acceptable wager. Katie responds with Rule #4 by capping her wager at 8,800.

But notice that both players now have other possibilities. If Katie thinks Joon will wager 4,400, she can wager 0 and guarantee herself a win. If Joon thinks Katie will wager 8,800, he can wager everything and hope to get it right.

Phew! But there’s one more point:

If you’re tied with another player, there are only two acceptable options: everything or nothing.

Feel free to leave questions in the comments below, and to like The Final Wager on Facebook.

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  1. Nope permalink

    Holy crap what is with the yellow text on white? You’re obviously a smart dude, so that is a real wtf for me.

  2. Nope permalink

    Ah I see something was up with how it was loading on my phone, yellow on blue is obviously much more readable.

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