Final Jeopardy Strategy

What would you bet if you were in each player's shoes:

Final Jeopardy Category: Medieval Japanese Opera
Player 1: $5,000
Player 2: $14,000
Player 3: $15,000

And what would your bet be if the Final Jeopardy Category were: US State Capitals? (same amounts for each player)

Quote: s2dbaker

What would you bet if you were in each player's shoes:

Final Jeopardy Category: Medieval Japanese Opera
Player 1: $5,000
Player 2: $14,000
Player 3: $15,000

And what would your bet be if the Final Jeopardy Category were: US State Capitals? (same amounts for each player)

For the first one, I'd bet zero across the board, even as the leader. But there's probably only about 3-5% of categories with which I'd do that.

For state capitals, as player three, I'd have to assure a win with a correct answer, so I'd bet $13,001. (There is an exception. I'd bet $13,000 if I felt that player two was weak, or at least weaker than a random contestant that would replace him/her in the next game I'd be playing...)

As Player Two, I'd have to assume player three is using my strategy, so there would be no way to beat him with a correct answer. Therefore, I'd hope for a difficult answer and bet $0. I could also bet up to $4000 if I felt like player three might have a weakness with capitals, and I might be able to win something even if he loses. But when the rubber meets the road, I think I bet $0.

As player one, I'd have no chance against the above two scenarios in tandem. But, I think I'd bet $0 anyway, because while Player Three is very likely to employ my above strategy, my player two strategy is often not chosen by the 2nd place player. So I'd hope for a hard question and a overachieving Player Two and sneak in with $5000.

I will also say that I do feel confident that I could sometimes snag a State Capitals question that many would miss, so I'd be tempted to change my strategy because it's strong for me. But I'd use the system above for about 85-90% of categories.

Also, I watched Jeopardy every night in gradeschool (when Alex Trebek started) and I believe it made me smarter in the classroom. Often I would remember facts from the show and it would help me on tests and in classroom activities.

I think the better question is what would you bet for a category that you were average in, and felt you opponents were average in as well.

Quote: Wizard

I think the better question is what would you bet for a category that you were average in, and felt you opponents were average in as well.

I think my basic outline above is the best play for the average category. There's always a lot of "well, if he does this, she'll do this, then he'll do this..." circular logic, but if you are in first place, I don't see how you bet anything other than the amount that will allow you to win when correct. So the other two players have to go under that assumption.

Suppose each player had a 50/50 chance of answering the question correctly. Is there now a way to quantify the correct strategy? In my example, I think player 1 always bets zero because betting anything else would reduce his chances. So I think in the next round, I'll up player one's pool to $10,000.

Quote: s2dbaker

Suppose each player had a 50/50 chance of answering the question correctly. Is there now a way to quantify the correct strategy? In my example, I think player 1 always bets zero because betting anything else would reduce his chances. So I think in the next round, I'll up player one's pool to $10,000.

I think if it's exactly 50/50, then there is no correct strategy for player 3. If it's 51% chance of winning, you bet enough to beat #2 by a dollar, if it's 49% you bet zero.
edit: player 3 (the player in 1st place)

Scenario 1 - Bet $0 in all 3 player situations, as I know nothing about the topic.
Scenario 2 - Bet it all in all 3 player situations, as I am dynamite at geography in general and know all the state capitals.

Final Jeopardy Category: Medieval Japanese Opera
Player 1: $5,000
Player 2: $14,000
Player 3: $15,000

Let's say each player has a 60% chance of getting the question right.

I think player 1 should bet $0, or very little, hoping 2 and 3 go high, and both miss.

I think player 3 should bet big, to lock in a win if right, so $13,011.

I think player 2 should bet anything $3,999 or under, I don't think it matters much what.

A spectacular site, the Jeopardy Archive, has every clue, question, and result of just about every game for the past 27 seasons. They also have the Wagering Calculator. Here is the strategy suggested:

Player A: $15,000
Player B: $14,000
Player C: $5,000

Four-fifths for first place
Strong form of Shore's Conjecture

Player C: There's no way you can cover a rational wager by Player B, but if Player B decides for some reason to wager everything, you can eke out a win on a Triple Stumper if you wager no more than $3,000.

Player B: Your score is within 4/5ths of Player A's, so wager between $2,001 (venusian) and $3,999 (martian), beating Player A's maximum safe bet of the difference between your scores while still covering against a doubled score on Player C's part.

Player A: Wager $13,001 to cover Player B. If you feel like using Shoretegy, try wagering $3,001.

"Venusian"? "Martian"? "Shortegy"? When you use the calculator, these odd words can be looked up in the J-Archive Glossary.

I think that we can come up with a better method than, a 4/5th strategy. I'll do some number crunching when I get home.

I generally suck at Final and the odds are very high that I would be in last place so I'll bet 0 :)

Yes, the category matters the least in determining your Final Jeopardy wager. Wagering strategy has been mathematically analyzed to death and laid out in the websites quoted above. Most people don't bother to learn it, even if they are going on the show. I did, and it is the most useful thing you can do, better than studying.