July 7, 2015

Tuesday, July 7, 2015

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Lots to discuss tonight – I’m pretty excited.

The Penultimate Wager is quite intriguing – I’ll edit this post in a bit to include information on that. I also talk about it in the video.

Anyway, here are our scores heading into Final:

Jess

Lindoerfer

Sawyer

Morgan

Bridget

Ker

8,400

7,600

10,200

Tonight’s Final Jeopardy! category is:

INTERNATIONAL COMPETITIONS

First-order calculations

Second doubles up

If Jess doubles her score, she’ll have 16,800.

To cover this all-in wager, Bridget will need to wager 6,600.

Jess		Sawyer		Bridget
8,400		7,600		10,200
8,400				6,600
16,800				16,800

min	max	min	max	min	max
				6,600

An incorrect response with that wager will leave Bridget with 3,600.

To stay above her total, Jess can wager up to 4,800.

Sawyer can wager up to 4,000.

Jess		Sawyer		Bridget
8,400		7,600		10,200
4,800		4,000		6,600
3,600		3,600		3,600

min	max	min	max	min	max
	4,800		4,000	6,600

Third doubles up

A successful doubling will put Sawyer at 15,200.

To cover this, Jess should wager at least 6,800. In this case, though, she will lose on an incorrect response, so she might as well wager everything.

Jess		Sawyer		Bridget
8,400		7,600		10,200
6,800		7,600		5,000
15,200		15,200		15,200

min	max	min	max	min	max
6,800*			4,000	6,600
	4,800
				5,000

Sawyer could also cap his wager at 2,400 if he’s worried about the 5,00 wager from Bridget.

Second-order calculations

Second’s max vs. first

If Jess makes the rational maximum wager of 4,800, Bridget will need to wager 3,000 to cover her.

Jess		Sawyer		Bridget
8,400		7,600		10,200
4,800				3,000
13,200				13,200

min	max	min	max	min	max
6,800			4,000	6,600
	4,800
			2,400	5,000

Not a smart wager.

Third’s max vs. first

Jess		Sawyer		Bridget
8,400		7,600		10,200
3,200		4,000		1,400
11,600		11,600		11,600

min	max	min	max	min	max
6,800			4,000	6,600
3,200	4,800
			2,400	5,000

An incorrect response with that wager will leave Bridget with 3,600.

Jess		Sawyer		Bridget
8,400		7,600		10,200
3,200		2,400		1,400
5,200		5,200		8,800

min	max	min	max	min	max
6,800			4,000	6,600
3,200	4,800
			2,400	5,000

Now, after two orders of analysis:

Jess		Sawyer		Bridget
8,400		7,600		10,200
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
6,800			4,000	6,600
3,200	4,800
			2,400	5,000

Zero wagers

Score differences:
Bridget and Jess: 1,800
Bridget and Sawyer: 2,600
Jess and Sawyer: 800

Jess		Sawyer		Bridget
8,400		7,600		10,200
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
6,800		1,600	2,400	6,600
3,600	4,800	2,600	4,000
	800			5,000	5,200

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

What actually happened

Jess		Sawyer		Bridget
8,400		7,600		10,200
6,801		3,990		6,601
1,599		11,590		3,599

min	max	min	max	min	max
8,400		1,601	2,399	6,601
3,601	4,799	2,601	3,999
	799			5,001	5,199

Congrats to Sawyer, who is a good friend of The Final Wager. Here’s hoping he can repeat Wednesday!

The Final Jeopardy! clue