OP is basically right, still, FJ wagering is a mixed strategy not an absolute one. if P2 knows P3 is betting small, then he can bet small and lock out P1.

-ChipsAhoya

fast forward through interviews FTW.

-ChipsAhoya

but in this situation is having $8800 and $3800 really any different going into final jeopardy against opponents with $13800 and $12000?

i think you have to take the risk as no matter what the category you should have a greater than 5% chance of answering correctly (just pulled that percentage out of the air, but just trying to show the principle)

This is a good example, I don't know what you mean by "plays perfectly" but in a real life situation on national TV final Jeopardy here you can take it to the bank that player 1 is betting $1000 or $1001.

He pretty much has to since in his mind he has to believe that there is a good chance that player 2 is just gonna bet $1K, and he certainly would look like a shmohawk if he bet less than $1K, got it right, and still lost. Virtually no one in the world would risk this happening against a random person whom they know nothing about.

So, with that in mind, played 2 can pretty much bet anywhere from 0-$998 if all he cares about is winning/losing and he'll basically win everytime P1 gets it wrong. I haven't thought about this too hard but taking the actual $ into consideration it seems to make sense that he bet $998 when he believes there is a >50% chance he will get the final question right, and bet 0 if he believes there is a <50% chance he gets it right, from a strictly EV standpoint.

EDIT: Chips is 1000% correct here, but my position is that you can pretty much never be sure that randoms on Jeopardy are going to be betting in such a manner, and a leader failing to bet enough to cover a 2nd place double up is far, far, far too risky to ever be practical imo. There are definitely counter examples that can be conjured up, but they will almost certainly rely on assumptions regarding knowledge of opponents, categories, or questions that are highly unrealistic.

EDIT 2: Like P3 is Chris Ferguson and he doesn't know that you know who he is.

Having 8800 is a huge difference because now you can catch Player 2 if he gets the question wrong. If you have 4800 dollars going into final Jeopardy, you have to hope both players miss the question and the second place player bets enough to let you catch him, which he should never do, his max bet should be 2400 since he can only win if the first place player gets it wrong (assuming the standard bet of 10201 for the first place player). If you have >6000 dollars entering Final Jeopardy, now second place not only has to hope for the first place player to get it wrong, but he must wager enough so that he doesn't get passed by the third place player, which then allows the third place player to bet small and hope to win if both of them get it wrong. Obviously then the second place player can bet small himself banking on third place also betting small, but that rarely if ever happens. That's what makes the 4000 dollar daily bet so horrible, even if you get it right you're still trailing and have to hope for the leader to screw up, but if you get it wrong you're drawing pretty slim. Better to either sit on your winnings and hope to catch them both in final jeopardy or go for the gusto and try to take the lead.

Exactly. I mean there has to be a huge negative utility to being in first, getting the question right, and still losing. That itself should deter just about anyone from betting less than the minimum needed to cover a 2nd place double-up. And the same concept applies to the 2nd place player vs. 3rd place.

"Who are three people who have never been in my kitchen?"

Yeah, let's revel in lack of knowledge and critical thinking abilities, particularly in a contestant on a game show which rewards both of these

Oh apparently a couple days ago (like Thursday or Friday) a guy I went to college with / was a regular in my first regular home poker game was on Jeopardy. He lost. Off-topic but I don't care.

So glad I watched Jeopardy tonight and then read this thread. The main bet that tilted me has already been discussed which was of course the bet of $4000 on the last Daily Double during Double Jeopardy. As others have already covered that was a horrid bet.

Also, I somewhat simmed this thread, but why did P2 bet $13,000? He over bet by a decent amount which it would have been lol if it came back to bite him.

Right this happens all the time, so tilting.

But what is p1 is a stone expert on acting families, the worlds foremost scholar on acting families. He should make a bigger wager if he is going to know the answer over a certain percentage of the time for the times they get it wrong and he will win more money.

What would they percentage have to be?

How can you have this line of logic without getting into a huge levelling war? If P3 shouldn't bet any more than $2399, the P2 has no reason to bet $10,201, and instead should bet $1301. Then P2 can't lose to P1, and has a nice chunk of cash those times they miss the question but still win contest.

There is nothing wrong with Player 2's bet or player 3's bet. If you win you keep that amount of cash, so if he thinks he is greater than 50/50 to get FJ right he is just flipping a weighted coin for 13k/11k. The only real problems here are they may have left too much behind, but w/e it's like maybe $500 for P2 and like $60 in ev for P3.

The biggest fail here is the short stack not betting zero and hoping both of them get it wrong.

dd,

I've addressed this a few times already but it basically comes down to the fact that it is completely insane for P2 to ever assume that P3 is thinking on this level and he simply must bet enough to cover a P3 double up. I also think that in practice you will find that the leader going into FJ bets enough to accomplish this +99% of the time, so there really isn't an elaborate leveling thing going on here at all.

P3 simply can and should use the knowledge that P2 is betting at least a certain amount to her advantage. P2 still must bet it though, because he can never assume that she's thinking this, they don't know each other at all, and looking like a MASSIVE tard on national TV is enough to make most people in P2's spot bet enough to cover even in the extremly unlikely event that he did suspect P3 was capable of thinking on this level.

Its actually pretty cut and dried of you think about it, and P3 is bound by the same principles with regard to P1. There's nothing fancy going on here and certainly nothing approaching leveling wars.

There is a whole lot wrong with P3's bet if she wants to win and get to play again. Assuming P2 will bet enough to cover her double up (which I think is a very conservative assumption and happens close to 100% of the time) she is denying herself a SURE win by betting that amount in the event that P2 gets it wrong. Also worth noting, if P2 gets it right she will NEVER win anyway.

FWIW I wasn't really criticizing P2's bet, but P1 and P3 both made huge blunders.

I'm pretty sure that maximizing your chances to win the game carries far more importance than maximizing your nominal dollar totals, given the ruleset that winners get to keep coming back to rack up more money and that second and third place finishers get token amounts of money, not their final score.

FJ is not a fixed strategy like you imply it is, OP.

The contestants were stupid, but it's a mixed strategy that works best. Your thoughts about P2 betting large:

Is certainly not accurate, and if it is, it's a huge leak in P2's game. Game Theory Optimal (GTO) strategy dictates a mixed strategy and not a simple level one analysis like you think is correct.

Just saw this on Tivo. The $4000 daily double wager by leather jacket was much worse than the final jeopardy wagering imo. So bad. And people make that mistake on almost every single show.

All of this is assuming that the only thing players should care about is winning though. It ignores the value of betting larger to maximize the amount of $$$ won.

Let's say P3 thinks he has a 90% chance of getting the question correct and estimates that if he wins, his total EV in future games as returning champion is $10,000. Ignoring the cases when P2 gets the question correct, as then P3's wager doesn't matter at all:

If he bets $2,399, his EV is:
(90%) * ($11,900 + $2,399 + $10,000) + (10%) * ($11,900 - $2,399 + $10,000) = $23,819.2

If he bets $11,900, his EV is:
(90%) * ($11,900 + $11,900 + $10,000) + (10%) * ($11,900 - $11,900) = $30,420

Betting everything is clearly correct because even though he loses 10% of the time and wins nothing, the extra $9,501 that he wins 90% of the time is worth way more than winning the game and coming back an extra 10% of the time.

Obviously you can tweak the numbers to get a different result. If the dude is Ken Jennings, his EV for future games would be estimated at much higher than $10,000 and that would radically change things. But it's way too simplistic to say he's wrong to bet anything more than $2,399, because maximizing winning % isn't the only thing that matters.

Edit: Also, the chances, however small, that P2 bets less than what will guarantee him a win with a correct answer make it even more +EV for P3 to bet as much as possible.

Ok kyleb, as P2 you play your GTO strategy, get the question right, and still lose. But when all your friends are making fun of you the next 10 years, you can throw "GTO mother-****er, look it up!" right back in their faces. You'll have the last laugh.

Brocktoon,
You post in your OP that P1 should bet 0 (which I agree with) and than also say P3 is stupid for making a wager that is correct if we assume P1 bets 0.

Dudd,
I agree, especially because experience should give you a decent edge in future games, however you could easily be passing up 5-6k in ev without really increasing your win probability that much.
In a spot with stacks of 3k 5k 10.1k, shoving and passing up potential future games would be pretty reckless as the big stack unless the category was something like Your First Name, however in this case I feel he could have reasonably estimated his P(correct answer) to be large enough that shoving was the correct play.

Edit: GTO is fine, but playing vs. real people in a one time game that isn't repeated soul reading and wagering >>>> GTO
Edit: Ungoliant 10k is much too low an estimate for value as returning champ.

The only flaw in that EV calculation is that they aren't independent events, when you get the question correct your opponent is also more likely to get the question correct, and conversely when you get it wrong your opponent is also more likely to get it wrong.

Game theory optimal play is a huge leak on Jeopardy, players don't play anywhere close to optimal so you should be exploiting their mistakes, not trying to make yourself unexploitable.

I wonder if you're being serious or not. If so, you must suck at poker.

Maybe. I don't think it's that far off, but if you plug in $50,000 instead, betting everything is still slightly +EV over $2,399. The main point is, that $9,501 he's giving up by betting so low has to be factored in. It's not automatically optimal just because it allows him to always win.

Of course. You should modify your bet sizing based on probability of bet sizing based on their Daily Double wagering and such. Just talking about the GTO strategy.