That’s what I do. Every time they reveal the category, I give my best guess as to the final “question”. Oddly enough, the times I’m correct (not very often at all, but often enough to give my life hope and meaning) it’s on categories I know very little about. I think that’s because, ultimately, the answers aren’t really all that difficult, and are scraped off the top layer of that category’s content.
If the category was “Physics”, I think Chronos would guess something pretty obscure. I’d probably go with “centripetal” or something equally high school level. When it comes time to actually answer the question, Chronos will have a100% chance, I will have a roughly green% chance.
If I’m up there I don’t give a flying crap about the difference between second and third. I wanna win, and I want as much money as humanly possible. Since the only way to win is to get the question correct, the logical thing to do is to bet everything to maximize my winnings if, in fact, I win.
If I only bet $501 and win, I might be losing $9000 in winnings, versus the $1000 I might win if I finish in second instead of first. Since I really have no way of knowing the likelihood that P1 and P2 will get the question right or wrong, I may as well adopt the strategy that will possibly increase my haul by $9000, instead of the strategy that will possibly increase it by $1000.
cmosdes’s math looks right, but assumes a likelihood of 85% that players will get the answer right. I’ve looked up a few references that suggest that the response percentage on Final is actually about half right and half wrong, which matches my impression from watching the show.
But that extra $80 of expected value may be meaningless to him. Say you’re offered a game - you can take $10, or you can take a 1/1000 chance of winning $5000. Pure expected value math would tell you to take the $10 - your expected value of the bet is only $5. But for me, an extra $10 isn’t of any great value, while $5000 would be, so I’d take the 1/1000 chance every time. Same thing here - I wouldn’t ever make my bet based on 2nd or 3rd - the $1k difference isn’t worth wasting my time on if I’m on a game show. I’m playing to win, to get as much money as I can, and to come back the next day.
Exactly. There is one exception I can think of, though. In the course of a tournament (College Tournament, Teen Tournament, etc.) where they have wild card spots, it would make sense for p3 to try to retain as much money as possible. Even if p1 or p2 get it right, and he has enough money (even after getting it wrong) he could qualify for a wild card spot.
When I was on College Jeopardy, I was in second, but couldn’t catch the player in first. I bet enough that I would have a sizable chunk if I won and qualify for a wild card spot. I didn’t want to bet it all, because if I got it wrong, I hoped I would still have enough for a wild card spot (I didn’t).
You and RickJay make excellent points. If he is going to win, he might as well win an extra $9k. After all, he isn’t going to get 100s of chances at this to have it pay off over a long haul. He has one chance and if that really small chance just happens to hit, he might as well get all he can out of it.
Perhaps a more interesting question would be what to do if standing pat would give you a shot at first place if all 3 got it wrong while betting it all would almost certainly result in you losing if all 3 got it wrong. For example, if the totals after DJ were $11k, $10k and $9k, what would you bet if you were p3? I’d probably bet $6.5k. p1 should bet $9k and p2 should bet $8k.