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September 17, 2013

How to wager in Final Jeopardy!: Part One

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Before you begin the tutorial, be sure to check out my video on common Final Jeopardy! misconceptions.

There are few things you control in the game of Jeopardy!. In fact, wagering strategy might be the only thing.

The best way to approach any complicated situation is to break it down into smaller parts. In Part One of my tutorial, you’ll learn the basics of Final Jeopardy! wagering strategy: how to calculate when only two players are involved.

We’ll also introduce the overarching concept of the game, which is tying for first is as good as winning outright. You get to keep your money and come back the next day.

What might surprise you is that the category is usually a moot point. What you want to focus on is called game theory.

Game theory is not about putting all of your chips on black and hoping the ball falls your way; it’s about maximizing your probability of winning across all possible outcomes. Sure, you could wager everything; if you get it right, great! If you get it wrong, boo! But in the first case you still might lose, and in the latter case you definitely won’t win.

I’ll walk you through a scenario in which the leader, Tim, has 14,200; the second-place, player, Liz, has 11,000. Disregarding the third player for now, what should each wager?

Each player’s proper wager is predicated on three simple rules.

Rule #1: The leader always wagers to win

You’re obviously very smart if you’re on Jeopardy!. So if you’re in the lead going into Final Jeopardy!, you should bet on yourself to win. This means you’ll wager so that if you’re right, you’ll win no matter what the other player wagers.

To calculate this, double the other player’s score, and subtract your score. If Liz wagers everything and gives a correct response, she’ll have 22,000. Tim needs to have at least that to win the game – a minimum wager of 7,800.

Tim will need to wager at least 7,800 to guarantee he returns the next day if he’s right.

Rule #2: The trailer positions himself to win if the leader gets it wrong

If you’re trailing, you’ll probably lose no matter what if the leader gets it right. You should focus instead on what he’ll have should he answer incorrectly, and aim to have at least that total.

If Tim is wrong and wagers at least 7,800 (from Rule #1), he’ll have at most 6,400. Liz will need to have at least this total to return the next day. Her current total, 11,000, minus 6,400 is 4,600. So Liz can wager at most 4,600.

Rule #3: If safe, each player covers a zero wager by the other

Sometimes players will wager zero. Usually they will do this when they’re trailing in a close game, but sometimes even the leader will do it. You want to account for this situation, if possible – but as this is less important than either of the first two rules, you should only do so if the wager jibes.

Note: only one player, at most, will have the ability to rationally use a wager from Rule #3.

Let’s start with Tim. If Liz wagers zero, she’ll have 11,000. So that he doesn’t fall below 11,000 if he gets it wrong, he can wager no more than 3,200. But since he already has to wager at least 7,800 from Rule #1, we’ll ignore this.

For Liz: If Tim wagers zero, he’ll have 14,200. To match this total, Liz will need to wager at least 3,200. This works with her maximum wager of 4,600 from Rule #2. So against Tim, Liz needs to wager at least 3,200, but no more than 4,600.

In Part Two we’ll go through a few special scenarios: in which one or both players is forced to make a specific wager.

Since you’ve made it this far, how about liking The Final Wager on Facebook?

Skip to Part: One | Two | Three | Four

  1. Jess permalink

    It amazes me how retarded Jeopardy contestants are when it comes to wagering. Almost every time, the person in 2nd place wagers everything, which is a terrible strategy. How do people go on Jeopardy without thinking this through ahead of time?

    • As someone who was on the show during Keith’s year, I can assure you that the craziness of being filmed and actually being on Jeopardy gets to you.

      You know how some folks are bad test takers (despite having mastered the knowledge being tested) merely because an exam puts pressure on them? Imagine having multiple cameras on you, you’re on set knowing this will be nationally broadcast (and you’ve already let your friends and family know you’ve been selected), and this is one of your life’s goals.

      Not the most opportune time for optimal, mathematical thinking.

  2. Why do contestants wager anything at all,when they do not know the answer???
    Then they loose anything they had earned !

What do you think?