Jeopardy final catergory.

[Beefy]

After playing your round of Jeopardy, it comes down to the final round. You have $14,400, the next player has $26,000, and the last guy has $7,300. The catergory comes up a neutral subject. How much should you bet?

[Damocles]

$8800

[maineman]

$11,601

[Beefy]

$11,601

I like the way you thought that out. I would probably bet it all, but this is a great amount. If I didn't bet it all, I would bet $1,000.

[Timshel]

Since your only chance of winning, assuming the leader bets rationally, is that you get the question correct and the leader misses it, you should bet it all. Why bet anything less?

[Damocles]

Since your only chance of winning, assuming the leader bets rationally, is that you get the question correct and the leader misses it, you should bet it all. Why bet anything less?
Because if the leader, for some reason, bets too much and the losing person bets it all and you and the winner both suck ass at the question, the loser doesn't end up winning by default.

[Timshel]

Because if the leader, for some reason, bets too much and the losing person bets it all and you and the winner both suck ass at the question, the loser doesn't end up winning by default.

In that case you should bet 201. 8800 does not help you unless you are assuming that the third place guy is irrational as well and if you assume that you need to be over his highest possilbe amount and correct.

To explain. The first place guy should bet 2801. The third place guy must count on the first place guy to be irrational but should assume you are not and that you will bet between 8800 and all of it. So he should bet to be over 5600 (which will be your highest likely score if wrong 14400-8800) if wrong. So third place guy should bet less than 1700.

With this betting if all three miss you still lose to the third place guy.

Assume the third place guy is not rational and bets it all. If you and the third place guy get it correct you need to be over double his current score. Also, 201 protects you if the thrid place guy is rational and you and the first place guy are incorrect.

I don't believe you should make the assumption that the first place guy will bet irrationally, because it does not help you determine your bet and you really have less guidance then. I still say you should bet it all because assuming he is not retarded you need him to miss while your answer is correct. If you have to be correct might as well go for the highest possible winnings.

[Timshel]

This question is poorly setup in my view because there is far too much space between contestants to make the logic of the final bet very relevant. Assuming they are rational, which is the only way you can approach it, player 1 has to miss and player 2 has to get it right. The bet matters little so long as it is over 8800. Since player 2 has to be right while 1 must be wrong, player 2 might as well bet it all.

If you set it up differently the logic becomes more interesting.

Say 1 has 20000, 2 has 15000 and 3 has 6000.

Then 2 should bet 2999.
Player 2 has to bet as if player 1 misses and should also bet as if he/she misses. If player 1 gets it right player 2's bet and answer do not matter. If player 1 gets it wrong and player 2 gets it correct player 2 wins and it does not matter. But if both are wrong, 2 bets 999 and player 1 bet rationally (10001) player 2 wins, even if player 3 is correct and bets it all.

[TheDanold]

Well you would never want to bet it all because rarely but sometimes the leader if he CAN be caught will bet it all, so leave yourself at least 2 dollars, because so many people try and leave themselves a dollar.
People aren't always rational, moreso when under pressure...

[TheDanold]

I would go with Maineman's amount IMHO, if you watch the show, there is often one contestant who does not place his bet rationally and it can be just about anything, usually this is the (dumber and more carefree because he thinks he has much less chance of winning) 3rd place guy.

The show is much easier than it used to be, I can run a lot of categories, when say 10 years ago, it was very rare that I could run a single category per show. Also Trebek is just lame trying to act more outgoing, it's just not his personality and it doesn't work.
Right now I'm enjoying 1 vs 100 more.

[uscitizen]

I would go with Maineman's amount IMHO, if you watch the show, there is often one contestant who does not place his bet rationally and it can be just about anything, usually this is the (dumber and more carefree because he thinks he has much less chance of winning) 3rd place guy.

The show is much easier than it used to be, I can run a lot of categories, when say 10 years ago, it was very rare that I could run a single category per show. Also Trebek is just lame trying to act more outgoing, it's just not his personality and it doesn't work.
Right now I'm enjoying 1 vs 100 more.

well I guess you would be better at 14 than 4 Dano ;)

[TheDanold]

well I guess you would be better at 14 than 4 Dano ;)
I'd guess you would be better than a 4 year old, but I don't like betting long-shots...