Thursday, March 26, 2015

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I’m looking particularly dapper tonight, if I do say so myself.

Today on LearnedLeague, I’m facing off against Tucker Pope, the runner up of the most recent College Championship. He wore bow ties in his appearances, so I figured I’d give him a shout-out.

Here are our scores heading into Final tonight:

Jacqueline Hawkins	Laura Weiner	Al Cho
16,600	5,400	20,000

This is a complicated situation, but Al has a nice round number, which should make our calculations simpler.

Tonight’s Final Jeopardy! category is:

NAVY SHIPS

Let’s break it down.

First-order calculations

Second doubles up

If Jacqueline doubles her score, she’ll have 33,200.

To cover this all-in wager, Al will need to wager 13,200.

Jacqueline		Laura		Al
16,600		5,400		20,000
16,600				13,200
33,200				33,200
min	max	min	max	min	max
				13,200

An incorrect response with that wager will leave Al with 6,800.

To stay above his total, Jacqueline can wager up to 9,800.

Laura must respond correctly to have a shot, so all-in is the way to go.

Jacqueline		Laura		Al
16,600		5,400		20,000
9,800		1,400		13,200
6,800		6,800		6,800
min	max	min	max	min	max
	9,800	1,400*		13,200

Third doubles up

A successful doubling will put Laura at 10,800.

To stay above her, Jacqueline can wager at most 5,800.

Al could wager at most 9,200.

Jacqueline		Laura		Al
16,600		5,400		20,000
5,800		5,400		9,200
10,800		10,800		10,800
min	max	min	max	min	max
	5,800	1,400*		13,200
	9,800
					9,200

Here’s where things stand after the first order:

Jacqueline		Laura		Al
16,600		5,400		20,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	5,800	1,400*		13,200
	9,800
					9,200

Second-order calculations

This is the Intermediate Form of Shore’s Conjecture.

Shoretegic wagers

If Jacqueline chooses to stay above a double-up by Laura, she will have at most 22,400.

Al can cover that with a wager of 2,400.

Jacqueline		Laura		Al
16,600		5,400		20,000
5,800				2,400
22,400				22,400
min	max	min	max	min	max
	5,800	1,400*		13,200
	9,800			2,400
					9,200

To get above his “Shoretegic” total, Jacqueline must wager 1,000.

Jacqueline		Laura		Al
16,600		5,400		20,000
1,000				2,400
17,600				22,400
min	max	min	max	min	max
1,000	5,800	1,400*		13,200
	9,800			2,400
					9,200

Second’s max vs. first

If Jacqueline makes the rational maximum wager of 9,800, Al will need to wager 6,400 to cover her.

Jacqueline		Laura		Al
16,600		5,400		20,000
9,800				6,400
26,400				26,400
min	max	min	max	min	max
1,000	5,800	1,400*		13,200
	9,800			2,400
				6,400	9,200

If he’s wrong with that wager, he’ll be left with 13,600.

To stay above him, Jacqueline can wager up to 3,000.

Jacqueline		Laura		Al
16,600		5,400		20,000
3,000				6,400
13,600				13,600
min	max	min	max	min	max
1,000	3,000	1,400*		13,200
	5,800			2,400
	9,800			6,400	9,200

Now, after two orders of analysis:

Jacqueline		Laura		Al
16,600		5,400		20,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,000	3,000	1,400*		13,200
	5,800			2,400
	9,800			6,400	9,200

Zero wagers

Jacqueline and Al are separated by 3,400, so we add those to their respective minimum and maximum columns.

We also take into consideration Jacqueline covering a “Colbyesque” wager by Al (3,399), and Al forcing Laura to get it right if he goes big.

Jacqueline		Laura		Al
16,600		5,400		20,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,000	3,000	1,400*		13,200	14,600
3,400	5,800			2,400	3,400
6,800	9,800			6,400	9,200

What actually happened

Jacqueline		Laura		Al
16,600		5,400		20,000
5,799		3,000		13,300
10,801		8,400		6,700
min	max			min	max
3,401	5,799	5,400		13,201	14,599
6,801	9,799			2,401	3,399
1,001	2,999			6,401	9,199

Here at The Final Wager, I calculate the math. As long as you make a wager in a rational range, I’m happy.

Jacqueline and Al each had three ranges to choose from, which is highly unusual. Many players in the lead find it hard to rationalize a smaller-than-lockout wager, and I totally get that.

By the way, thank you to the Jeopardy! social media people for spoiling this result in advance on the Hometown Howdies.

The Final Jeopardy! clue

NAVY SHIPS

FIRST DESIGNATED AS ARMORED CRUISER NO. 1, THIS SHIP WAS COMMISSIONED IN 1895 & OPERATED ON OUR EAST COAST & IN THE CARIBBEAN

[spoiler]What is the U.S.S. Maine?[/spoiler]

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