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November 22, 2013

Wagering in the 2008 College Championship Finals

In my previous Wagering Practice post, I gave you the following situation, from the 2008 College Championship Finals.

2008 Jeopardy! College Championship finals Slide01

When I picked this situation for my example, I didn’t realize how complicated it was. In fact, under one entirely feasible scenario, the three players might be separated by a total of just $2.

This underscores how important it is to know wagering theory backwards and forwards before you go into battle.

I’m going to break this up into two slideshows. The first shows the wagers you would calculate under “basic” game theory conditions. The second delves more deeply into the “mind game” aspect of wagering, which has a potential to rear its head every so often.

Let’s begin. (Click the upper-left square to enter the slideshow.)

Ok, so this seems like an easy puzzle.

But riddle me this, Batman: how did it happen that Joey wagered much less than he was “supposed” to, yet still managed to win by just $400 – even though both he and Danielle responded correctly?

2008 College Championship final Slide08

This is where things get tricky – the “mind games” aspect of wagering, which has the potential to take on subtle nuances in the multiple-game format. For example, Joey is in the lead overall, but if he gets it wrong and wagers 16,401, he’s going to lose to Danielle – even if Danielle wagers everything!

I’d also like to point out that had Danielle wagered 10,201 instead, and both she and Joey responded incorrectly, we’d have this situation:

2008 College Championship final Slide09

Joey beats Danielle by a dollar – who beats Andrew by a dollar! What is going on here?

Let’s delve into the “second-order” calculations – how Joey and Danielle each might respond to suboptimal wagers by the other.

Joey’s wager makes a little more sense in this light. Danielle should aim at the low end of that range only if she thinks Joey will wager zero. She must have been scared of that, which is why she stayed below 3,400.

2008 College Championship final Slide20

But on Jeopardy!, you play to win – not to not lose. Danielle’s 3,000 was a fearful wager, one that cost her the trophy, an additional $50,000, and a trip to the Tournament of Champions. Joey’s was, too – but his bluff won this hand of poker.

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