But they’re not synonyms. The French and Indian war was just one theater of a global war. It would be like saying the Winter War and WWII are synonymous.
In particular, the FJ clue referenced a Churchill quote. I very much doubt Churchill called it “The French and Indian War.”
Yes, but the analysis is exactly the same if Mattea had bet $2, or $99. If she is correct, she wins. If she is incorrect, she risks falling to second.
Obviously, a lot depends on how much the second-place player wagers. Without knowing that, there’s no obvious correct wager for the leader. But if you assume that the second-place player will double her score, then the leader’s wager is almost irrelevant (unless it’s $0).
Exactly correct. Either she bets nothing, ensuring a tie, or something, which ensures a victory if she’s correct. Since she bet something, she should have bet more so as to earn more money.
She had $20,400
2nd had $10,200
3rd had $8,000
The ‘correct’ amount, IMO would be $4,399. That ensures her beating the 3rd place player, even if that player doubles up.
He would have, if that’s what it was called. 
As a product of late-20th century American school system, I’ve never heard of the Seven Years War. Off to wikipedia.
If you assume that the second-place player has wagered everything, then you’re right.
I just don’t think that’s a justified assumption. The player in second doesn’t have to bet all their money. There is no correct, perfect answer on how much to wager on Final Jeopardy. The perfect bet for you depends on how much the other players bet, and you don’t know that until it’s too late.
I think it’s very justified. These are humans betting in Jeopardy, not IBM’s Watson programmed with Game Theory. The humans pretty much always bet the same way in these situations.
Obviously I agree with @K364 that it is a justified assumption. But evidently you don’t. What, then, do you think the second-place player might bet? And why?
You posted this upthread:
The correct amount for the leader to bet is $4,399. If she’s wrong, she’ll be left with $16,001. So the player in second only needs to bet $5,801 to tie, $5,802 to win.
Assuming 1st is going to make a sane bet, 2nd MUST get the question correct. Therefore 2nd might as well bet everything.
Which then begs the question: why wouldn’t second-place bet more, so as to win more money?
I think we can all agree that the second-place person will lose the game if his answer is wrong. So why not bet it all?
It used to be, in the event of a tie after FJ between #1 and #2, that both would return as co-champions. Is this no longer the case? Do they go to a tie-breaker?
If not, then the correct bet for Mattea would have been $0. At worst she would have come back as co-champion.
Nope. They have a one question buzz off to win.
If you know you’re going to get the question right, then everyone should bet everything, always. Unfortunately, I sometimes get Final Jeopardy wrong, and my wager should take that into account (however remote the possibility might be).
If the second-place player bets everything, and gets it wrong, they risk finishing in third place, which pays less than second.
Which, in fact, is exactly what happened.
But he bet everything, knowing that was his best chance to win. Which is, after all, the ultimate goal.
It would seem to me that, if winning is the most important thing, then it makes sense to take the minimum risk you would need to win.
Assuming how the other player will bet always seems a bad idea to me. You should bet based on the worst case scenario of what the other player will bet, or at least the worst case scenario where you could actually win.
So what do you think that Mattea should have bet in FJ? What was her worst case scenario?
This is exactly why the prize difference between 2nd and 3rd should be greater, IMHO. A $1,000 difference isn’t enough to change the way anyone should play. From a practical standpoint, its either win, or not get enough to cover your expenses whether you come in 2nd or 3rd. So in this game, the only correct bet for 2nd place was $10,200. If he is right, and 1st place bets $0, he has a coin toss chance at $20,400. If he is wrong, he loses $1000. If there was more incentive to finish in 2nd, say the 3 highest placed 2nd place players from a given season were given a chance at coming back, it would have a huge difference in the way people would bet.
I thought the goal was to maximize the amount of money you win.
In the particular case under discussion, the second place player wagered everything. As it turned out, there was no way they could have won (Mattea got FJ correct, and clinched the win), and by betting everything they dropped to third. And you also say that there’s no reason not to bet everything.
I stand by my claim that there is no correct answer on how much to bet in Final Jeopardy*. You can make guesses about what the other players will do, choose your own wager accordingly; but those other players are trying to guess what you’ll do. It’s guesses all the way down.
* Well, there is the trivial case that your finishing position is already guaranteed.
I think they should give 2nd and 3rd exactly what they have at the end of FJ. (maybe with a $1000 minimum for $0). It would make betting more active.