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Welcome to The Final Wager

“Keith Williams ruined everything.”

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With tiebreakers now in play…

…should I still wager to tie?

Jeopardy! tournament ties

You might be here to learn about Final Jeopardy! wagering. Even if not, the game theory behind it is useful in almost every area of life.

The USA-Germany World Cup game? Check.

The situation in Crimea? Yep.

Rock-paper-scissors? Duh.

I’m Keith Williams, the 2003 Jeopardy! College Champion. I created The Final Wager to make game theory accessible to people who are scared of math. In my Guide to Game Theory, I break down many of these ideas for you – with as little math as possible.

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What you’ll find here

In addition to teaching you how to wager in Final Jeopardy!, I offer a Guide to Game Theory, introducing you to many of the basic concepts of this versatile field.

You’ll also find an analysis of each night’s game, and other miscellaneous thoughts and advice on Jeopardy! play. I’d love to hear your feedback and suggestions! I invite you to follow me on Facebook and Twitter, and to send me an email.

The backstory

This project was born when my college friend Megan, slated to tape her appearance in a few weeks, called on me for advice. She recognized the importance of wagering in Final Jeopardy!, she said, but confided that the math scared her. Could I do something to help?

There’s plenty of head-spinning, high-level thinking out there, but until now, a guide for calculating wagers did not exist. Wagering 101, if you will. So I set out to fill that void. It helped that I was already sick of bad strategy.

I added a second challenge: making it accessible to people who want to use no more than addition and subtraction. It took a lot of thinking and a lot of paper, but I finally got it. The result was a four-part written tutorial. Now, here, it’s a video series.

Whether you’re a passionate fan, a future contestant, a game-theory buff, or just looking for a way to kill time, I hope you find it useful – and enjoyable.


P.S. For those of you wondering how Megan did, she made the correct wager (plus a dollar) – which Alex then derided as “interesting”.

About Keith

Keith Williams 1999 Vermont Geography BeeI represented Middlebury College in the 2003 Jeopardy! College Championship. I’ve been a fan of the show since I was old enough to talk. Probably the biggest disappointment of finishing 3rd in the Vermont Geography Bee in 8th grade was the loss of my chance to meet Alex.

I’m particularly fascinated by the way Final Jeopardy! wagering can make or break a player. Hence, this project, in an attempt to help people who need it.

In addition to breaking down Jeopardy! wagers, I’m a freelance journalist (you can find my clips here). I also run competitively. I live in Brooklyn. Find out more about my various exploits, or send me an email. Or both.

  1. Curious as to your thoughts on a possible added benefit to wagering for a tie in Final Jeopardy….if you do end up tied, you’ll know one opponent for the next game rather than facing two unknowns. Perhaps you see something about the opponent or their strategy that suggest you’d rather face them than an unknown, or perhaps you’d rather not face them again so you do not wager for the tie?

    • Keith Williams permalink

      I know from experience that you can “sense” an opponent’s strength throughout the course of the game, but one game is a too-small sample size to know for sure.

      Certainly, I focus on maximizing the probability of returning the next day over any consideration of whom you’ll be playing. I feel the latter is a bit like a receiver looking downfield before he’s caught the ball.

      • eric permalink

        There is also the idea of keeping another player at bay. Once a player commented that he was “scared to death” to face a player waiting in the wings (they all meet in the morning). A tie might keep that player waiting for one more game.
        I can say that I wouldn’t offer one to a 13 time returning champion, though. Ok, maybe: if she was really hot.

  2. Steve Herr permalink

    What about wagering just to win more money? Wouldn’t that come into play?

    • Keith Williams permalink

      It can if you have a big lead, but the best way to win more money is to return the next day.

      • eric permalink

        Perhaps, but what if you’re in a runaway, and you really like the category! You’re already assured of a return, and you could, perhaps significantly, increase your winnings.

  3. Peter permalink

    Your analysis seems to assume that your opponent knows that you are going to wager for a tie. I don’t believe that his information can be conveyed in a one shot game. It may still be sensible to wager for the tie if you are signalling your strategy to future opponents (should you win/tie this game). So I think for this strategy to be effective you have to be thinking beyond your current game. I also wonder if people wager for the tie hoping for reciprocation in subsequent games should the situations be reversed.

    • Keith Williams permalink

      Hi Peter – that’s a great point. It’s hard to convey your desire to wager for the tie in your first game, and even then your future opponents have to be paying attention.

      The most recent example I can think of: Ben Ingram’s opponent wagered for the tie in Ben’s third game (, but when Ben had the lead in the rematch (, he tacked on the extra dollar! His opponent wagered everything, hoping the favor might be returned.

      • KBlaney permalink

        You are assuming that there is no communication between the players. The cheat here, based on the context of the game, is that you could simply state your intention to wager for a tie since your opponent knowing this information doesn’t really hurt you. (Granted, I’ve never been on Jeopardy and you have, so I don’t know if there is a good way to express that intention. Perhaps during a commercial break you could say, “So I read on this wagering theory blog…”?)

  4. In the video you referred to the trailer betting it all as “irrational”. This strategy is anything but irrational if the leader might play for the tie.

    • Keith Williams permalink

      Very true, Jonathan. But unless you have evidence the leader will, in fact, wager for the tie, you’re better off assuming he won’t.

  5. Garrett Simpson permalink

    I was a two-day champion in 1989 and it was a great experience. I won $45,000.00 over two days. I was all-in every chance I got.

  6. If you knew for certain that your first-place opponent was playing for the tie, wouldn’t the optimal strategy be to bet it all if you were in second? That way, you win when both of you get it right. Playing it your way, you win when both of you get it wrong, but if we are smart I would think both of use getting it right is a more likely outcome. I do however agree that if you know your opponent will bet the extra $1, you need to follow your strategy.

    • Keith Williams permalink

      Depends on a few things, Josh. How confident are you that: 1) the leader will go for the tie? 2) the leader will answer correctly? 3) YOU will answer correctly (since you’ll lose if you’re wrong)?

      Imagine Arthur, in second place in a close game, faces a Final Jeopardy! with “SPORTS” as the category, and knows the leader’s going for the tie. I doubt Arthur’s putting it all on the line.

      • I too doubt Arthur bets it all given “SPORTS” is the category. But, isn’t that simply because the probability of both being wrong exceeds the probability of both being right, and for almost all categories the opposite will be the case (after all, “the leader always wagers to win”).

  7. Marc permalink

    I have heard some of the repeat Jeopardy winners indicate that the returning winner has a significant added benefit having played already and learning the “rhythm” of pushing the button. Does that create a reason not to play for the tie? If you play for the tie, and there is a tie, then that means that you will have an opponent for the next game that has gone through that “learning curve” as compared to having two new opponents, neither of whom have that benefit.

    • Hi Marc – yes, it’s a valid point. My analysis is based on a single goal: advancing to the next game. In terms of game theory, withholding that extra dollar is “weakly dominant” over wagering to win outright, which is why I say it’s the right play.

  8. What do you think about the newest Jeopardy phenomenon – Arthur?

  9. Hey Keith,
    You may be interested to learn that my roommate in grad school, John Ryan was on Jeopardy in 1987 and did quite well. He made it to the Tournament of Champions that years. We talked about game theory at length before he went on, and strategies for final jeopardy. enjoyed browsing your site.

    • Welcome, CF! Thanks for stopping by. I remember watching John in the UTOC – he played a few weeks after I did. What exactly did the two of you discuss?

  10. Wait WHAT? So confused by this. I need it even plainer. Gotta settle a dispute between me and my gf!

  11. Matt permalink

    Hey Keith,

    Great site! Question for you related to Arthur vs Semret last night. On Twitter (yes I’m a huge nerd), Semret said “I was positive Arthur would bet $401, so I could only win if he missed it. If that’s true, no upside to betting it all.” Wondering about your thoughts on this. As I think about it:

    1) If you know with 100% certainty that Arthur is betting $401 (which you don’t), then I understand that Semret can only win if Arthur gets it wrong. But in this case, Semret can only win if he himself answers correctly, so why not bet it all to maximize upside?

    2) Because you don’t know with certainty that Arthur will be $401, and because he might in fact wager $400 for the tie, wouldn’t Semret be better off betting it all?

    In this case, I don’t see a good reason for Semret to do anything other than wager it all. What am I missing?


    • Matt permalink

      One additional point re #1 – because you assume that Arthur is rational and won’t do something crazy like wager 20k, you know you can only win if you get it right. If you bet it all and end up with $0, you may end up in 3rd instead of 2nd place, but the downside of this seems very small relative to the upside of betting it all for the potential of a tie.

      • Matt permalink

        OK I lied, one more question / comment.

        I think the totals were as follows (I don’t recall the woman’s name or exact amt but it was close to the below:

        Arthur – $21,400
        Semret – $11,400
        #3 – $7,500

        Assuming that Semret answers correctly, Arthur can only win if he also answers correctly. If I’m correct that the optimal wager for Semret is to bet all $11,400, Semret will finish with $21,400. Now assume that #3 wagers $7,500 (which may not be optimal, but she’s out of the running anyway) and gets it right and ends with $15,000. Since Arthur needs to answer correctly to win, wouldn’t his optimal wager be $6,400, so that he ties #3 if both she and Semret get it wrong and so that he maximizes his own upside if he himself gets it right? Basically, is there any practical difference between wagering $400 and $6,400?

        OK, will stop rapid fire commenting now. Looking forward to your thoughts!

  12. Not You permalink

    Is Alex not really all that sharp or is it just me thinking that?

    How many of his speaking mistakes are edited out after all and what they leave in sometimes is pretty weak if that’s his best performance.

    • I’ve watched around 30 shows in studio, and I think he’s re-recorded a clue twice. He’s a great host, although it’s easy to find flubs because there’s just so much material available!

  13. Xarrexar permalink

    Why not adopt a strategy for all three players to tie and continue on to the next game. In final Jeopardy, third place bets 0, first and second place intentionally get the question wrong and bet so as to tie with third place. The players could do this game after game, returning indefinitely. Is there some rule in place to prevent this?

    • It’s an interesting idea, Xarrexar, but there are a few arguments against this:

      1) it relies entirely on trusting your opponents to do the right thing. (Why wouldn’t first place just wager zero and keep his money?)
      2) there are strict rules against collusion.

  14. Xarrexar permalink

    1) Putting aside the reaction of the judges for a moment, there isn’t much danger that a player acting in his self-interest would betray. The greatest rewards are not in winning a single big sum but in winning game after game. A perpetual three-way tie delivers the best long term reward. Any player that betrays will sooner or later lose, and most likely sooner, so that “long term” doesn’t have to get very long before it outstrips any other strategy. The only reasons a rational player could have for betrayal is that he feels his opponent is not rational or is unaware of this strategy.

    2) I see no reason to believe that three players could not recognize the rewards in a perpetual three-way tie and adopt the strategy even without communication. However, even lacking evidence of collusion, the judges would be forced to act in the best interests of the show, breaking this legal strategy. That might go very badly for all involved. For this reason, I expect most players will not attempt this.

    Perhaps Jeopardy should change the rules around three-way ties to remove the incentives. They could rule a three-way tie as a three-way loss with no one returning. They could rule it a three-way win but for no money. They could rule that the tying player who was most recently in the lead is the winner. Regardless, it is an interesting situation to ponder.

  15. I am an aspiring Jeopardy contestant and so I find your blog super useful! I have been blogging to report on my journey to get onto jeopardy. Check out my blog:

  16. Hey Keith, nice site, great work.

    I saw that you were training for the marathon. Did you have the chance to run the Boston Marathon earlier this year?

    I heard that it was a great event with a lot of people participating, and that it was of historical significance, after what happened last year. I’m also glad that an american won, Meb I think was his name, right?

    I’m actually hoping, kind of training to run a marathon later this year in my hometown. It’ll be my first.

    And sorry, but if you don’t see my post on youtube, I was wondering whether you understood all of this wagering theory before going on Jeopardy or if you learned it after your appearance.


  17. Also Keith, I don’t know if I should ask this but I have to say I’m a little intimidated by the competition. And I haven’t even met the competition yet. LoL.

    I suppose that you being in the college tournament must have thought at some point that there are a lot of other very smart people here. How did you maintain your confidence in yourself and what you knew?

    I know that as knowledgeable as I am, there will always be someone, a lot of people probably who will know more than I do.

    And of course, watching Brad Rutter, Ken Jennings and Roger Craig can be quite humbling and rather intimidating.

    But doing some research I’ve seen that they, well at least Ken and Brad have “quizbowl” or trivia backgrounds. I never did anything like that. All I do is watch the game diligently and actively, and hope to hold my own.

    Like Brad had once intimated, I’ve been quite a slacker.

    And finally, I’ve come to learn that most of the people on Jeopardy are really super smart nerds and geeks just waiting for their chance to cash in on their knowledge and have their 15 minutes of fame so to speak.

    For example, Larissa Kelly the wonderful contestant from a few years back. I was actually doing some research on her and found out some very interesting things. Along with being the second highest winning female player, only behind Julia Collins, she was on the “quizbowl” team or whatever it’s called for her high school. She also works as a writer and editor of trivia questions now, according to what she said on her BOTD midshow interview. And of course, she now holds a doctoral degree. On a side note I saw that she resides in Richmond, CA which interestingly and coincidentally happens to be where all my mail gets held up. I’ve been tracking some movies I ordered online and they all seem to get stuck at Richmond, CA for some reason. And now I know where it is. ;-)

    I’m just a simple guy, an eccentric and reclusive loaner who likes to watch Jeopardy. I can’t even claim to be the average Joe really. How can I possibly compete against people with their fancy degrees, scholarly dispositions, elite learning and such? I never completed college myself.

    Hope you don’t mind my posting this here, let me know if you have a problem. I just thought it would be more appropriate(and private) here, rather than on Youtube. I would guess your site is more of a place for general Jeopardy questions, rather than your “Final Wager” video posts.

    Anyway, thanks. And enjoy your evening.

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