Final Jeopardy betting question

[blackaces13]

Lets say that you (an average Jeopardy player) made it to Final Jeopardy against Ken Jennings, the current longtime champ, with $16,000 to his $24,000. The other player finished with a negative total so they are not participating in the final round.

What should you wager on the final question?

I think the answer is the same regardless of category or any other factors. Also realize that 2nd place doesn't get to keep their dollar amount, they get something like a weeks vacation which you are assured at worst anyway at this point. So your only concern is trying to win.

[Ulysses]

.

[blackaces13]

Yeah, this is pretty easy I guess. I thought it was interesting when it dawned on me today. For some reason I spent a large portion of my day thinking about optimum betting strategy against Ken Jennings. Go figure.

I also think that 95%+ of Jeopardy players in this spot would NOT bet $0. As smart as they may be I'm sure the proper strategy would elude them.

[Ulysses]

Somewhat more interesting. You have $15k or $17k, he has $24k.

[SnakeRat]

What are the rules for a tie?

Doesnt it matter if it is a category you are especially good in? Why doesn't optimum strategy change if you estimate that you have 90% chance of getting questions from that category correct? Wouldn't the best strategy in that case be to bet it all?

[blackaces13]

[ QUOTE ]
Somewhat more interesting. You have $15k or $17k, he has $24k.

[/ QUOTE ]

For 15K you can go ahead and bet anything from $3K on up. Actually, you should just go ahead and bet it all because you'll only win the times you get it right so betting it all gets you more actual money.

17K and you should bet 3k if you believe that you have greater than a 50% chance of getting the question right. Or zero again if you are less than 50% confident in answering correctly.

[blackaces13]

[ QUOTE ]
Why doesn't optimum strategy change if you estimate that you have 90% chance of getting questions from that category correct? Wouldn't the best strategy in that case be to bet it all?

[/ QUOTE ]

Well, this is why I thought it was interesting. It doesn't matter at all. The only way you win is if he gets it wrong and you a) get it right or B)bet nothing. He is obligated to bet $8001, forced is more like it.

So by betting, even if you are 99% likely to get it right, all you do is increase your chance of losing by that slight amount.

I suppose you could make a case that a slight decreased chance in winning would be worth it because of the extra 16K that you earn right then and there when you win. But if you were only 90% sure (which is nearly impossible anyway due to the general vagueness of the categories) then it likely doesn't make sense to risk the 10% costing you the win if Jennings misses (and he does miss) because you not only lose the 16K now, but more importantly your chance to continue winning on subsequent shows. This would be a tremendous opportunity cost considering you went toe to toe with Jennings for that long and were still close.

[benfranklin]

[ QUOTE ]

Doesnt it matter if it is a category you are especially good in? Why doesn't optimum strategy change if you estimate that you have 90% chance of getting questions from that category correct? Wouldn't the best strategy in that case be to bet it all?

[/ QUOTE ]

If you have $16K and bet it all, and he has $24K and bets $8001, then if you miss the final question you lose, and if you both get the final question, you lose. The only way to win is for you have to be right and for him to be wrong.

If you bet $0, he still has to bet $8001 in case you bet it all. Now, he still has to be wrong for you to win, but you don't also have to be right on the final question.

If you bet, you have to be right AND he has to be wrong.
If you don't bet, he just has to be wrong.

[ohkanada]

Simple, nada.

Ken

[Senor Choppy]

The answer depends on too many other factors.

If you have a 95% chance of getting the final jeopardy question correct but aren't that exceptional overall compared to most players, it would be throwing away money to not risk everything. Of course, if you were as good as Ken Jennings, and knew you could rack up a few million in winnings if you were somehow able to make it past him, then you'd want to maximize your chances of winning this round and not necessarily the most money, so you'd wager $0.

[FatOtt]

I think this is a more interesting question than just saying "Jennings must bet $8,001, so I should bet $0 and win whenever Jennings gets it wrong." Obviously, Jennings can see through this optimal strategy, in which case he would bet somewhere between $0 and $7,999 to counter it. In other words, this isn't an equilibrium solution. The equilibrium would be some kind of mixed strategy, so you'd be betting various amounts between $0 and $16,000.

Cool question.

[lu_hawk]

if the leader with $24k knows that you will bet the 'optimal' amount of $0 then he can bet $0-$7999 and be guaranteed to win. you need game theory to figure this out, but if there are two players who are smart enough to both realize what is going on then $0 is not optimal because it will be exploited.

[GuyOnTilt]

Zero

And Ken, knowing this, would bet what?

GoT

[felson]

"[if you have] 17K [then] you should bet 3k if you believe that you have greater than a 50% chance of getting the question right. "

This should be "if you believe that you have greater than a 50% chance of getting the question right, given that Ken has gotten it wrong."


Also here is a Jeopardy betting article (http://slate.msn.com/default.aspx?id=86351).

[benfranklin]

[ QUOTE ]
Zero

And Ken, knowing this, would bet what?

GoT

[/ QUOTE ]

This gets you into the various levels of hand reading. What does he have? What does he think I have? What does he think I think he has?

Since you are a first time player, Ken has no read on you. If I remember the shows I have seen, if he is in a position to be caught, he assumes that his opponent is betting it all, and bets whatever he has to to stay ahead by $1. I think that that is what you have to do in his situation, because the vast majority of first time players are going to think at the 1st level, not realizing that zero is a better bet than everything. Betting something between zero and everything would only work if Ken put you on a bet other than everything. If I'm playing, I think that Ken thinks that I am betting it all.

[Michael Davis]

Some 10 years ago, there was a stone cold match in the Tournament of Champions where the lady who was in the lead by a small amount bet nothing. She did this because she suspected her second-place opponent would also bet zero, and she was right. So, if both opponents know what is going on, there is the potential for a great, but unusual play to be made.

When I was in the college tournament, there was a complete jackass from Emory (I hope he somehow reads this, because he was one of the most vile, contemptible persons I've met, with antics including the holding of a knife at his opponents that was, perhaps, a half-joke). Anyways, this guy made a terrible move of educating the fish that this was the way to bet if you were in 2nd place but held 2/3 of your opponent's stack. Needless to say, if I had gotten the opportunity, I was going to play it the same way as the woman in my first example, praying that he wasn't bluffing.

-Michael

[Michael Davis]

Exactly. The number of players who are savvy enough to bet $0 is actually a somewhat small percentage, most just go out and bet whatever they need to beat the 1st place player, which is of course a terrible move. If you are in first, you generally have no choice but to bet so you can beat a person who tries to double up, unless, of course, they've somehow expressed that the correct move is to bet zero.

-Michael

[Ulysses]

[ QUOTE ]

And Ken, knowing this, would bet what?


[/ QUOTE ]

But he doesn't know this. That's the point. If we were playing Ken every day, it would be different. But we're not. We're playing him once and we know how he bets, while he has no idea how we bet. Thus, zero it is.

[GuyOnTilt]

But he doesn't know this. That's the point. If we were playing Ken every day, it would be different. But we're not. We're playing him once and we know how he bets, while he has no idea how we bet. Thus, zero it is.

I agree. I was just surprised no one mentioned multiple levels of thinking yet.

GoT

[Ulysses]

Nah, it really is that simple. Read the other responses to the thread and the Jeopardy betting article. Of course, if people were to start regularly wagering on Final Jeopardy in this manner, things would change.

[Ulysses]

Just read that article and was wondering about something. I haven't watched Jeopardy regularly for many, many years. I recall seeing a tie way back then and I believe both players got the money and came back. Does anyone know if that is (or was) correct?

[J.A.Sucker]

I don't think that zero is necessarily the correct answer. You are told what the category is before you bet, so you should have an idea as to what the odds are that you (and your opponent) will get the question correct. If you're playing Cliff Claven, and the topic is "Celebate Postman" you may bet differently than if it were something else. Likewise, if the category was "Talking Out of My Ass", then I might be inclined to bet all my money. /images/graemlins/grin.gif

[sprmario]

Ken should bet exactly $8000.

If you bet it all, he ties you if he gets it right and wins all the times you get it wrong as well.
If you bet zero, he ties you if he gets it wrong and wins all the times he gets it right.

The only times he loses absolutely is if he gets it wrong and you get it right betting any amount at all.

Given that he's Ken fuking Jennings the unbeatable machine, he should be happy to take a tie and come back the next day to kick your sorry arse.

[Michael Davis]

You are probably correct, but only to a small degree. The problem is that Final Jeopardy questions often have twists and the category title doesn't really fit what the question requires. A question supposedly about US Presidents might really turn out to be a geography question (cough, cough).

-Michael

[Michael Davis]

You are correct, and I think there are some great opportunities for implicit collusion here if people would wise up.

If you have a markedly inferior opponent, you should bet to tie, not to win.

-Michael

[blackaces13]

[ QUOTE ]
If you are in first, you generally have no choice but to bet so you can beat a person who tries to double up, unless, of course, they've somehow expressed that the correct move is to bet zero.

-Michael

[/ QUOTE ]

Actually, as one poster has already pointed out, Ken should be betting $8,000 on the number as opposed to $8,001 because by doing this he still continues his streak everytime he gets the correct answer, but he ALSO now protects himself from the small % of players who actually would be tricky and bet $0 by now tying when he misses as opposed to losing.

All he is risking by doing this is giving you another crack at him the following show should he get it wrong (which is the minority of the time anyway).

Besides, you probably got lucky to be that close anyway.

[blackaces13]

[ QUOTE ]
Some 10 years ago, there was a stone cold match in the Tournament of Champions where the lady who was in the lead by a small amount bet nothing. She did this because she suspected her second-place opponent would also bet zero, and she was right.

[/ QUOTE ]

WOW. That's amazing. If I ever saw a finish like this on Jeopardy I'd stand up and applaud in my own livingroom. (I don't get out much). /images/graemlins/smirk.gif