Wednesday, July 8, 2015

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With the amount of work our players have given me lately, I’m tempted to ask for a raise. (It doesn’t help that my liquor cabinet is looking terribly empty these days.)

Let’s start with that terrible Penultimate Wager by one of our challengers.

Sawyer Morgan	Ian Bourland	Jenny Thorngate
11,000	10,400	11,800
PENULTIMATE WAGER
NAME-DROPPING SONG LYRICS for $800

Given our players’ proficiency with the rest of this category and the clue’s second-level status, I’d be tempted to go for $10,201 and end things right now. Even if Jenny is wrong, she can still win in Final.

The other option is no more than $199. This places Sawyer in Stratton’s Dilemma: if he covers Ian’s wager in Final, he’ll lose to Jenny if he’s wrong.

$3,000 does nothing if she’s right and puts her in third if she’s wrong. But she did get it right, and we have these scores heading into Final:

Sawyer	Ian	Jenny
11,000	10,400	11,800

Tonight’s Final Jeopardy! category is:

THE THOMAS JEFFERSON ADMINISTRATION

First-order calculations

Second doubles up

If Sawyer doubles his score, he’ll have 22,000.

To cover this all-in wager, Jenny will need to wager 7,200.

Sawyer		Ian		Jenny
11,000		10,400		14,800
11,000				7,200
22,000				22,000
min	max	min	max	min	max
				7,200

An incorrect response with that wager will leave Jenny with 7,600.

To stay above her total, Sawyer can wager up to 3,400.

Ian can wager up to 2,800.

Sawyer		Ian		Jenny
11,000		10,400		14,800
3,400		2,800		7,200
7,600		7,600		7,600
min	max	min	max	min	max
	3,400		2,800	7,200

Third doubles up

A successful doubling will put Ian at 20,800.

To cover this, Sawyer should wager at least 9,800. In this case, though, he will lose on an incorrect response, so he might as well wager everything. (Stratton’s Dilemma!)

Sawyer		Ian		Jenny
11,000		10,400		14,800
9,800		10,400		6,000
20,800		20,800		20,800
min	max	min	max	min	max
9,800*			2,800	7,200
	3,400

Here’s where things stand after the first order:

Sawyer		Ian		Jenny
11,000		10,400		14,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
9,800*			2,800	7,200
	3,400

Second-order calculations

Second’s max vs. first

If Sawyer makes the rational maximum wager of 3,400, Jenny will need to wager 400 to stay above him.

Sawyer		Ian		Jenny
11,000		10,400		14,800
3,400				400
14,400				14,400
min	max	min	max	min	max
9,800*			2,800	7,200
	3,400				400

In that case, Sawyer would have to wager 4,200 and respond correctly, and again, an all-in makes sense.

Ian might consider risking at least 4,800 – everything.

Third’s max vs. first

Sawyer might go for 2,200.

Sawyer		Ian		Jenny
11,000		10,400		14,800
2,200		2,800		1,600
13,200		13,200		13,200
min	max	min	max	min	max
9,800*			2,800	7,200
2,200	3,400				400
		4,800*

That downside means Ian should cap his wager at 1,600.

Sawyer		Ian		Jenny
11,000		10,400		14,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
9,800*			1,600	7,200
2,200	3,400		2,800		400
		4,800*

Zero wagers

Score differences:
Jenny and Sawyer: 3,800
Jenny and Ian: 4,400
Sawyer and Ian: 600

Sawyer		Ian		Jenny
11,000		10,400		14,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
9,800*		1,200	1,600	7,200	7,600
2,200	3,400		2,800		400
		4,800*

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

What actually happened

Sawyer		Ian		Jenny
11,000		10,400		14,800
10,900		10,400		7,201
21,900		20,800		22,001
min	max	min	max	min	max
11,000		1,201	1,599	7,201	7,599
2,201	3,399		2,799		399
		10,400

It looks like the writers are recycling Final Jeopardy! clues from the Teen Tournament that won’t be happening this season.

Tomorrow, Jenny will be our seventh consecutive different champion. Will we get another Penultimate Wager tomorrow? (I hope not.)

The Final Jeopardy! clue

THE THOMAS JEFFERSON ADMINISTRATION

OF THIS AGREEMENT, THOMAS JEFFERSON SAID HE “STRETCHED THE CONSTITUTION UNTIL IT CRACKED”

[spoiler]What is the Louisiana Purchase?[/spoiler]

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