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April 17, 2014

Daily analysis, Thursday, April 17

This one’s up a bit late thanks to Bolt Bus, which never has working WiFi. Maybe I’m just an optimistic sucker.The Final Wager - April 17, 2014

Strong performances by Sandie and Kristin, with Frédérique making a nice charge toward the end.

Sandie Baker: 15,400
Frédérique Delaprée: 6,200
Kristin McAuliffe: 13,200

The Final Jeopardy! category: 19th CENTURY PRESIDENTS

It’s tough to see on the surface, but this is a mind-boggling situation. It starts from the basics, in which Kristin needs to choose between the red pill (staying above Frédérique) and the blue pill (covering a zero by Sandie).

This might be easier to understand if you watch the video.

Basic strategy

Sandie should wager 11,000 to take her destiny into her own hands.

Kristin can wager at most 800 to stay above Frédérique, risking an automatic loss if Sandie wagers small; or, she can wager between 4,400 (to cover an “unsafe” wager by Sandie) and 7,000 (so as not to fall below Frédérique’s pre-Final total).

Frédérique should wager at most 1,800 to stay above an incorrect Sandie lockout wager; however, she’s justified in going for broke if she thinks Kristin will wager, say, 4,400, which is perfectly feasible.

Here’s where we’re at so far. Buckle your seat belts.

Mind games

First, look at a rational wager by Frédérique. If Frédérique gets it right with her 1,800 wager, she’ll have 8,000; in response, Kristin should cap her larger range at 5,200 to stay above this total.

If she thinks Kristin wagers 5,200, Sandie will need to wager 3,000.

But now look – if she gets it wrong, she’ll have 12,400 – double Frédérique’s total. An extra dollar could hurt her big time, so if she wants to wager this alternative amount, it has to be 3,000 exactly.

If Frédérique is afraid of this possibility, she should wager everything.

Here we have a bizarre equilibrium, in which each player is not really forced to wager for the tie, but has strong incentive to do so, particularly Sandie and Frédérique.

Again, this is an absurd situation, and without going several levels deep, Kristin’s wager is the only “bad” one; Frédérique’s is cagey, and I’m happy with it. The only reason she gets pink and not green is the math calls this a wager-to-tie scenario.

We’ll see what she does to wrap up the week. Congrats to Sandie on a fine run; we’ll see her in the TOC!

There is a general rule here, but I need to verify my math before posting it. Keep an eye out, if you’re interested.

The Final Jeopardy! clue for April 17, 2014 (19th CENTURY PRESIDENTS):

GOOD LOOKS WEREN’T ENOUGH AS HE BECAME THE ONLY FULL-TERM PRESIDENT REJECTED IN A BID FOR HIS PARTY’S 2nd TERM NOMINATION

Correct response: Who was Franklin Pierce?

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