Friday, January 25, 2008

Poetic Justice on Jeopardy

I know the results of one trial don't separate good decisions from bad ones. Still, one of my favorite things about always being right* is seeing people fail because they take stupid risks.

Thursday's episode of Jeopardy was a great example. Heading into Final Jeopardy, here were the scores:

Defending Champ: $12400
Challenger 1: $12600
Challenger 2: $800

Anyone who is at all familiar with the show should be able to come up with Challenger 2's proper strategy: Wager only a tiny amount or nothing at all. Her only chance to win comes when both of the other players bet big and answer incorrectly. Furthermore, both of the other players probably WILL make large wagers, based on players' tendencies, since their scores are so close to each other. Meanwhile, the difference between $1600 and $800 will surely not be a factor in determining whether she takes second or third place.

For a similar reason, I think it is also wrong for the defending champ to "go all-in" here**. If she does so and answers correctly, she will usually lose anyway if Challenger 1 also answers correctly. By making a smaller bet, she can probably win any time Challenger 1 is incorrect, regardless of the champ's own answer. If the champ makes a large wager, not only might she lose when Challenger 1 responds incorrectly, but she could encounter the nightmare scenario that actually happened, as we will soon see.

The wagers went as follows:

Champ: $12400
Challenger 1: $12345 (cute)
Challenger 2: $700

All three players answered incorrectly, leaving these final scores:

Champ: $0
Challenger 1: $255
Challenger 2: $100

Now what has happened? Both the champ and Challenger 2 have missed out on a free opportunity to come back tomorrow, because they made unnecessarily large wagers. Their prize wouldn't have been tremendous for that day, but the shot to come back the next day should be worth at least several thousand dollars to a good player.

Record of the game can be found here.

* Yes, I say this even after claiming Jason Schmidt was one of the better signings of the 2006-07 offseason.

** Wagering strategy in Final Jeopardy is actually a complex game theory problem. This site offers one take on it. Against a typical player in this spot, however, it is clearly correct for the defending champ NOT to make the maximum wager, because the leader entering Final Jeopardy will almost always bet enough to eclipse twice the score of the nearest competitor.


Eugene said...

Funny you should mention jeopardy -- I've been subscribing to your feed for the past year and I'm going to be on the show tonight. Let me know how I did!

Hells_Satans said...

On the surface your answer makes sense, but the right answer is too complex for that analysis.

You've assumed 2nd Place knows game theory but 1st place does not.

2nd place should do whatever is optimal regardless of whether or not 1st place knows how to bet. You can't assume 1st makes the bad bet in this case, which you have.

However, if you somehow know 1st place does NOT know, your advice is good!