Debates like these have apparently been raging on the Sony Pictures Jeopardy! board for years, although skimming over them it seems like the tone is slightly more pleasant over there (not that it's bad ITT).

Most of the time, the player in first (let's call him 1) bets enough to cover an all in bet by the player in second (let's call him 2). But should he? If player 3 is close enough to be a factor, 2 will often not bet all in but go small enough to protect against an all in from 3.

Here is a link to games satisfying the conditions of "Shore's Conjecture" which I won't go into rigorous detail about, but the gist of the conjecture is that if 2 has 3 locked out going into Final Jeopardy, 2 will bet "small" and keep 3 locked out, hoping 1 bets "big" (which usually happens).

The link has a review of seasons 20-25 of Jeopardy! showing that in games meeting those conditions, 2 in fact did bet "small" 93 out of 154 times (60.4%).

A guy's been keeping track of games satisfying the Shore conditions for seasons 20-25 and Shore (aka "small") betting has come out ahead of shutout betting 28-21, with 105 draws. That is, the Shore bet would have won 28 times when the shutout would have lost, the shutout bet would have won 21 times when the Shore bet would have lost, and 105 times it didn't make a difference.

As many have said, for most player 1s, betting small would have to be substantially better than shutout betting to offset the psychological trauma of being in first place, getting Final Jeopardy correct, and still losing.

Just thought I'd throw out some empirical data, I'm fully aware it doesn't take into account all the variables.

Fleeborh,
I think that shows pretty clearly that betting big is better, since you don't win that much more often, but when you win you win much more money.

Well...I don't think it clearly shows that betting big is always better, it depends on the conditions. Although for most conditions I am in agreement with you.

guy i knew in college actually did this (bet less than double 2nd), both got it right and he lost. it is the first thing that gets brought up anytime anyone i know sees him, and it is the first thing that people remember about him when he comes up in conversation, and is obviously a source of huge embarrassment.

Right. I see the conversation something like this:

"Dude, what were you thinking?"

"Well you see, I was actually slightly correct based on game theory and an assumption that 2nd would play rationally vs. 3rd. So in reality, assuming 2nd was not a moron was my only mistake."

"Whatever dude, you got the question right and LOST. That was HILARIOUS. Hey George come here, this is the guy I was telling you about..."


You guys can argue whatever you want. I guarantee for me it would be a no-brainer, no way I get the question right and still have a chance to lose.

BTW I plugged these numbers into the calculator posted itt earlier and here's what it says:

Player C: Try wagering $2,399, which is as much as you can put up against Player B without being usurped by a doubled score on the part of Player A.
Player B: Wager $10,201 to cover Player C. If you feel like using Shoretegy, try wagering $601.
Player A: There's no way you can cover a rational wager by Player C, but if Player C decides for some reason to wager everything, you can eke out a win on a Triple Stumper if you wager no more than $1,200.

Which is pretty damned close to what I said in the OP. Obviously these aren't equiliibrium strategies but they shouldn't be, because that's not how real people behave on television 99% of the time. You should tailor your betting to how people are likely to behave in the situation, not trying to emulate an unexploitable equilibrium strategy.

http://www.math.ucla.edu/~tom/papers/lastround.pdf

what's the difference between this and "whatever dude, you called with pocket aces AND LOST. hey george, here's the guy i was telling you about that blew it at the world series of poker!

Sounds like this isn't a "Final Jeopardy strategy" argument as it is a "my friends are idiots and jackasses" argument.

Wow. I think some of you guys might be great at games and strategy, but really bad at extrapolating what the future would hold for you if you didn't bet enough to cover in final Jeopardy and lost. Not just for your friends, or randoms who barely know you, but questioning yourself. Just bet enough to cover and save yourself the hassle.

Not even close to the same analogy. No one makes fun of you for calling with pocket aces and losing. This is more like folding trips to a huge river bet when you know 90% of your opponents range has you beat, and everyone sees on TV he has the 10% side. Which could kind of suck but only semi-knowledgeable poker players would give you **** about it. Good players would understand it and people who don't know poker wouldn't have an opinion. Everyone thinks they know enough to have an opinion about final jeopardy betting.

And the biggest thing is can you live with yourself? I can live with myself knowing I folded trips correctly. But expecting 2nd to play rational in final jeopardy, when they have probably the most confusing set of options of the three players, and the angst of getting that wrong - forget it. I'm just going to make 100% sure I win it if I get the question right.

I'm thinking Alex Trebek rapes my dog at that point. Is that a good extrapolation? EDIT: You are including getting made fun of as a major factor in your equity calculation. I think you can forgive the rest of the thread for thinking that's laughable.

It is obviously a fairly complicated question, and without reads I don't think there's a clear set answer about how two big stacks should play it. Stuff like Fleebrog is linking to with data about how people typically play is certainly helpful, and knowledge about what the category is helps, but I can certainly see scenarios where #2 betting small is worthy.

MORE EDIT: Also, good to see Jesus Ferguson's dad is on this stuff.

The one thing I've learned from this thread is that a Jeopardy tournament with nothing but OOT players might not be great from a getting the questions right standpoint but would have some sick 13th level wagering in the final round. I probably really, really suck at game theory, but why can't we just assume very standard play by 2nd and 3rd place players when choosing our final amount to wager (assuming we're leading obv). It's not like they're going to have JT3 stats on us so we have to worry about balancing our range.

Oh, and years ago I saw a final Jeopardy where 3rd was correct and doubled up, just barely edging ahead of 2nd, 2nd was correct and bet just enough to beat a double up by 3rd and 1st got the question wrong, but bet $0 FTW. I was floored. It was awesome.

A lot of the game theory stuff in here relies on the chance of getting a question right as consistent across the players. You can estimate your chances a little off the category, ditto for your opposition if you've got a read, and right and wrong answers will clump together based on how difficult the question is.

Grunching.

How? Neither of them knew the answer, and P2 left himself ahead of both of them.

Strategy would have to be mixed, I think.

EDIT: I haven't looked through the rest of this post, but I assume someone answered this.

I don't see why "based on game theory" would be the response. It would be something like "If I bet small then I knew I would win if he either got it wrong or bet small and I thought at least one of those happening was more likely than me getting the question right".

This feels like an evolution debate where the creationists claim that those on our side simply believe in "science" instead of religion. In that case, those arguing for evolution wouldn't, or at least shouldn't, just say "the scientific community says so" but make the case for why they do as well as arguing for the scientific method if necessary.

If I make a guess at how likely the guy is to wager big or small as well as get it right in either scenario then I can work out the EV equations and decide which is best. I don't see how it's different than something like folding or shoving early in a poker hand. Sometimes you're going to look bad, but if you made the right decision then it's not hard to justify yourself. Sometimes your read of your opponent is wrong and he calls you with a hand you thought he'd fold, but you don't have all the info so that's how it goes. Same applies to Jeopardy IMO.

I'm really looking forward to Jeopardy tonight.

If you go to the Jeopardy messge board, you can read some trip reports by contestants. One of the things players can do in the green room while waiting to play is to try to figure out if their opponents are the kind of people who would use game theory in their wagering. That would be the biggest factor for me in choosing between a shut-out bet and betting small.

Good post, and glad to see I wasn't the only other annoyed person. Excited for tonight, let's see if the champ can not make the same mistake if in a similar situation

I'm digging this chick in the middle, she's got like a Rachel Ray thing going on but younger and hotter.

Wow, super tough spots tonight.

Final totals are: 17,400; 9400; and 12400.

I wouldn't really blame anyone for betting anything here but I will basically guarantee that P1 bets $7401 or more to cover P3's double, and this is really the only assumption I was ever making.

BTW, it is after 730 but I haven't seen the wagers yet.

my thoughts,

p1 has to bet 7400+ to guarantee win if correct fj answer
p2 has to bet 600 to guarantee win if she right, others miss
p3 has to bet 6400+ to guarantee win if correct and p1 is wrong


btw, fj was super easy, p1 and p3 got it right, chick missed it

Why not just ship it in if she has to get it right to win anyway?

THIS

Until jeopardy players as a class start showing the ability to actually wager with more than 0 level thinking, you have to bet based on 2nd betting the whole thing--so 3rd bets 0 or a small amount, for example.

Assuming they are also using some rational wagering system is like assuming that your local donkament fish bet sizing means the same thing as if Chris Ferguson was across the table.