I was watching teen jeopardy tonight, and the category for final jeopardy was one that I thought would be hard: other countries' presidents. The three contestants were somewhat close: 9600, 10400, 11600, or thereabouts.

It's important to maximize your chances of winning. In this teen tournament, you get $10,000 for making the semifinals (which is where they were) and a minimum of $25,000 for making the finals.

So, the person with 9600 should bet 2001. She'll win if she gets it right and the other two don't get it right. But she shouldn't wager more than that because the other two will always beat her if they get it right and wager enough. 10400 should wager enough to beat the 9600 if the 9600 goes all in, and they both get it right. 9600x2 = 19200. 19200-10400 = 8800. So the 10400 person should wager 8801. The 11600 contestant should wager enough to beat the 10400 if they go all in. 10400x2 = 20800. 20800-11600 = 9200. So the 11600 contestant should wager 9201.

9600 should wager 2001
10400 should wager 8801
11600 should wager 9201

If they all get it right, the person on top still wins. But like I said, this was a hard category. So what if they all lose? It should pan out like this:

9600 - 2001 = 7599
10400 - 8801 = 1599
11600 - 9201 = 2399

But 2nd and 3rd place were girls. They both thought they were smart, and so they wagered everything. The top guy wagered correctly: not everything, but enough to win if he got it right and 2nd place wagered everything and got it right.

Everyone got it wrong. The two girls ended up with $0, and the only boy gets a ticket to the finals just because he wagered correctly.