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# Wise Wager?

 Britschgi on Mass Transit... Inside the Monkey Trap...

NOTE: This is my 3,000th post. I started in late October 2008 and have averaged over 300 posts per year and over 25 per month. Yay!

My wife and I were catching up on recorded episodes of Jeopardy last night and were stunned by what happened--both how one contestant bet and by Alex Trebek's comment about his bet.

When the second round ended, the score stood as follows:
Contestant A: \$4,000.
Contestant B: \$6,200.
Contestant C: \$12,400.

Focus on contestant C. He has a sure win in Final Jeopardy if he bets \$0. If he did that, he would end with \$12,400. The best B can do is bet \$6,200 and give the right answer, ending up with \$12,400. So they tie and C pockets \$12,400 plus goes on to play again, along with B.

Contestant A bets \$3,999, gets it wrong, and ends up with \$1. He was probably thinking that contestant B would bet it all and, if he got it wrong, end up with \$0, giving A second place and \$2,000 for second instead of \$1,000 for third. Of course, any bet between \$1 and \$3,999 would have worked from A's viewpoint.
Contestant B, sure enough, bets \$6,200 and gets it wrong. He ends up with \$0.
As we wait for contestant C's answer, my wife and I look knowingly at each other: his answer won't matter because he'll bet \$0.
WRONG.
Contestant C gets it wrong. But he bets \$1, bringing his final number down to \$12,399. So he got lucky because B got it wrong.

Alex, looking at the bet, says "A wise wager." Seriously, Alex? I thought we Canadians were better at math than that.

CATEGORIES: Game Theory

writes:

He must have though that all contestants need to bet at last \$1.

mattb writes:

David: The rules in Jeopardy have changed recently so that if there is a tie at the end of final Jeopardy, the contestants don't both win the money and come back the next day. Instead they go into a tie-breaker challenge where only one of them wins.

Given this rules change, a \$1 wager could be an optimal wager if the player who is ahead thinks that they really know the final jeopardy category well. This way if they get the question right there is no way that they can lose. In they bet \$0, and the second place player ends up doubling their money, they could end up with a very tough tiebreaker question that they don't know, or it could be an easy tiebreaker question where it comes down to who rings in first.

robc writes:

Even under the old rules, it might make sense to bet \$1 if you are confident in the question AND you think the #2 player is a real challenge.

On the other hand, if you thought #2 was a walk-over, you might play for the tie and only have 1 competitor to worry about the next day.

David R Henderson writes:

@mattb,