If anyone else watched Jeopardy tonight then maybe they feel my pain on this one. The worst part is that if either of the 2 trailing players had bet the "right" amount they would have won, including the guy who went into Final Jeopardy with only about 1/3 as many chips as the other players.

Dollar amounts of players from right to left entering Final Jeopardy from left to right (I don't remember their names):

P1: $4800 P2: $13,800 P3: $12,000

Category/question is irrelevant but for the curious it was "Acting Families" and they were looking for the last name of a father and son who played 2 different real US Presidents, one on film and one on TV.



Now obviously neither P1 nor P3 can possibly win if P2 gets the answer right. He is forced to bet at least $10,201 to give him a total of $24,001 which is $1 more than double 2nd places $12K total.

With that in mind, the only way either of the other 2 have any shot whatsoever is if P2 gets it wrong, and since he has to bet at least $10,201 then he will have, at most, $3599 when that happens.

This means that P1 actually has a chance here provided P3 is stupid enough to be an amount that allows him to win. He's totally in it, he should bet $0 and his answer is irrelevant. Basically if P3 is not smart enough to make his victory impossible then she's probably dumb enough to make a huge bet and he'll win if they both miss it (which actually happens quite a lot in Final Jeopardy).

P3 however shouldn't bet any more than $2399 since that would allow P1 to pass her if he bet it all and got it right, which she can't allow to happen if she's thinking about it at all. So she can bet whatever she want's between $0-$2399 and if the leader (P2) misses the question she is GUARANTEED to win as he MUST bet $10,201 minimum.

Well, here's how it actually went down:

They all got it WRONG. Here is what they bet and what they wound up.

P1: $4,799 >>> $1
P2: $13,000 >>> $800
P3: $11,900 >>> $100


They totally handed it to P2 by making horrible wagers. Had either of them made rational bets they would have won easily. Notice how P3 sort of understands that leaving herself with something if she gets it wrong is good but ultimately decides on $100 for some reason that I'm sure made sense to her at the time. I expect this kind of **** on The Price is Right, but Jeopardy contestants should really know better.

yeah this was pretty awful, nice writeup of it though. making it more egregious was P1's horrid bet of $4000 in double jeopardy on a daily double.

When I was watching this episode I was getting really angry at the terrible betting and hoped OOT would have a thread about it. Oh, redemption.

The middle guy was actually kinda dumb. His answer of Czechoslovakia for the nation Germany invaded with Operation Barbossa during WW2 was just a terrible, terrible guess. I'm fine with not knowing the actual answer, but guessing Poland or France or something is way more EV+ because CZECHOSLOVAKIA WAS NOT INVADED IN WW2. It was annexed prior to the outbreak of hostilities.

I never watch this show but stumbled upon it today (testing new OTA system) and thought the exact same you did. Glad to know it wasn't me being out of the loop.

btw i am not sure your breakdown is correct. basically you assume that P2 must bet 10k+, but then you say that p3 knows this and won't try to bet it all. some people in P2's position bet very conservatively (some guy won twice doing this last week). so i don't think assuming P2 betting 10k+ is necessarily founded.

There are categories were I would bet everything even if I was guaranteed a win by betting zero.

omg, who doesn't know this, seriously

Worse than the ******s on Wheel of Fortune that buy 4 vowels, then solve?

This is what I was thinking. He's assuming that player 2 "knows" player 3 will bet it all, but that player 3 should only bet $2,399.... because player 2 HAS to bet $10,201.

???

OP, your analysis ignores several important variables and you seem to be suggesting that there is an objectively "correct" bet size for each player that can be determined by an outside observer. You ignore the effect of (a) each contestant's knowledge of the Final Jeopardy category and their estimate of the probability of answering the question correctly, (b) the contestants' estimates of the probability of their opponents answering the question correctly and (c) any knowledge the contestants may have of their opponents' betting tendencies. When no one player is up by more than double, there is no objectively correct betting range that does not take into account the aforementioned variables. An obvious example is if the category is something that a given player knows he knows absolutely nothing about, then his correct bet size is 0.

Well basically you can't let somone beat you by simply betting it all as the leader, I really don't think any leader ever bets less than the amount that will give them $1 more than double 2nd place.

If you assume that all players are aware of and will be applying game theory (which would be a dangerous and foolish assumption to make as this episode demonstrates) then you may come to different conclusions, though I'm not sure the leader should ever allow himself a chance of losing if he gets it right. But mostly its just because 1st place guy wouldn't want to look stupid on TV by not betting enough to guarantee himself a win if he answers correctly.

I think its a really safe assumption that P2 bets >$10,200 here TBH, and he can't assume anything about how the other players will bet and he doesn't have to. Also, P3 is really just using the same logic as P2 here but applying the "$1 more than double" rule to P1 and realizing that P2 will bet an amount that will bring his total below her's should P2 whiff.

If P2 knows that P3 knows what he should bet and P3 knows this and the other two both know P3 knows, etc, doesn't this change what they should bet?

Slick,

You're right, I am making certain assumptions, but in order for them not to hold it would require such severe probabilities to be assigned to the player getting the question right, such as <5% or something that they can pretty much be ignored imo.

I think my analysis hold up with any sort of realistic real-world situation where you assume that each player has between a 20% and 85% chance of getting the question right.

For instance, I would bet that the leader going into final Jeopardy bets over the amount needed to result in double 2nd place current score close to 100% of the time, barring some sort of miscalculation or admitted blunder. Now, as you say, if they think there is literally ZERO chance of them getting the question right they shouldn't, but that is just so unlikely given that they are in the lead to begin with and the categories are often a bit vague that its not worth considering imo.

his analysis ignores this - but he's right that in most situations, the contestants should bet the amounts he's suggesting. it's really player 1 who screws up here, he just bets a random amount, not analyzing what might happen if all three players miss the question (which seems to be happening a lot).

rarely true. final jeopardy is almost never straightforward and even if it purports to be about one thing, it is often about another - the setup of the question will be about that subject, but the answer will not be. basically the jeopardy writers want to confound your ability to wager correctly based on the first 2 criteria you list.

I pretty much expect final jeopardy blunders but what really tilts me is when the 2nd or 3rd place guy gets a daily double right at the end of double jeopardy and doesn't make a bet big enough to put him in first or close to it. WTF? Anyone who watches this show for a small amount of time will quickly realize how huge of an advantage it is to be leader going into final. Seems ******ed to not go for it, basically you're hoping your opponents screw up in order for you to win, instead of putting the onus of winning on you.

I believe it would, but this is so far beyond what any typical people will actually do on the show that you'd be foolish to even consider it if you were playing. Its like trying to use 5th level thinking for play money.

and this was PRECISELY what happened in this game. player 1 got a daily double on what turned out to be the last question of double jeopardy. he had $8800, leader had $13800, he wagered 4000, which is pretty much the worst wager - he doesn't go into first if he gets it correct, but if he misses it, he falls into third place and has to hope both his opponents miss final jeopardy for him to win.

+1.

LOL, exactly what happened. This is what initially set me off as I was watching it, the hate for player 1 started burning from deep within me. I thought to myself, "if this idiot bets his entire roll here and they both get it wrong my head is going to explode."

Then that happened, to my surprise my head was still intact so I decided to write a really long-winded angry Jeopardy post on OOT, that'll show 'em. BTW, I omitted the initial daily-double debacle from my OP because it was already too long. Glad you guys picked up on it.

You either bet everything or you bet a maximum amount to still be able to catch the leader/stay clear of third, betting any amount in between is so, so wrong.

In today's situation, I believe the optimal bet for player A in that daily double would be anywhere between $5,000 and $5,200. You could say between $5,001 and $5,199 but I don't think ties really decrease your EV (except for having to play that opponent as opposed to a random opponent in the next game). This is basically the same thing Dudd said, not really sure why i typed it again.

That's awesome, sounds like I should dvr Jeopardy.

Somewhat unrelated... let's say you go into final jeopardy with only 2 players because one guy was eliminated by having less than zero (right?) and the other two players have $1,001 (p1) and $1,000 (p2)? If they both play perfectly and let's say they somehow know each have 50% chance of getting the answer right how much should they bet? I assume there is a right answer... or is there a huge continuum of best responses?

starting to dvr jeopardy may have been one of the best dvr related decisions i've ever made

my guess would be that p1 bets $999 and p2 bets $1

well if it's a topic you're not confident in i can see betting the minimum (e.g. potent potables if you don't drink). but yeah generally this is correct.