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December 15, 2014

The Final Wager – Mon 15 Dec 2014

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I spent some time this weekend programming my automated calculator, so let’s see how it did.The Final Wager – December 15, 2014

Boy, did I get to test a doozy of a situation.

Ryan Pensyl Alysha Rooks Rex Marzke
7,400 10,400 10,800

Tonight’s Final Jeopardy! category is:

POETRY

Let’s see what each player should do. Remember, we save the dollar changes until the end.

First-order calculations

Second doubles up

If Rooks doubles her score, she’ll have 20,800. To cover this all-in wager, Rex will need to wager 10,000.

An incorrect response with that wager will leave Rex with 800. To stay above his total, Rooks can wager up to 9,600. Ryan can wager up to 6,600.

Third doubles up

A successful doubling will put Ryan at 14,800. To cover this, Rooks should wager at least 4,400.

(Rex would need to wager at least 4,000, but this is somewhat questionable.)

Second-order calculations

Second’s max vs. first

If Rooks makes the rational maximum wager of 9,600, Rex will need to wager 9,200 to cover her.

If he’s wrong with that wager, he’ll be left with 1,600.

To stay above him, Rooks can wager up to 8,800. Ryan may risk up to 5,800.

Third’s max vs. second

Against Rooks, Ryan can wager at most 1,400. With a correct response, he’ll have 8,800. To stay above this, Rooks can wager at most 1,600.

(Rex could restrict his maximum to 2,000, but it’s not compelling.)

Zero wagers

How does each player cover – or stay above – a zero wager by each other player?

Then we add a dollar to the minimum wagers, and subtract a dollar from the maximum wagers.

What actually happened

The calculator worked out pretty nicely. Of course, it’ll probably fail on an impossibly simple task…

The Final Jeopardy! clue

POETRY

THE NARRATOR MISTAKES THE PRESENCE OF THIS CREATURE FOR THE WIND & LATER CALLS IT PROPHET

Correct response: Show

 

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