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March 26, 2015

Thursday, March 26, 2015

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I’m looking particularly dapper tonight, if I do say so myself.The Final Wager – March 26, 2015

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.

Jacqueline hometown howdy

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
Correct response: Show
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One Comment
  1. Shane permalink

    About that spoiler, the same could be said for Alex and Gautam as well.

What do you think?