July 17, 2015

Friday, July 17, 2015

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I want Jennifer to keep winning, only so I can hear more of her stories.

She’ll need to win from behind this time…

Jennifer

Morrow

Lawrence

Dernulc

Julia

Lawrence

13,800

16,000

7,600

…with this category:

19th CENTURY AMERICANS

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First-order calculations

Second doubles up

If Jennifer doubles her score, she’ll have 27,600.

To cover this all-in wager, Lawrence will need to wager 11,600.

Jennifer		Lawrence		Julia
13,800		16,000		7,600
13,800		11,600
27,600		27,600

min	max	min	max	min	max
		11,600

An incorrect response with that wager will leave Lawrence with 4,400.

To stay above his total, Jennifer can wager up to 9,400.

Julia can wager up to 3,200.

Jennifer		Lawrence		Julia
13,800		16,000		7,600
9,400		11,600		3,200
4,400		4,400		4,400

min	max	min	max	min	max
	9,400	11,600			3,200

Third doubles up

A successful doubling will put Julia at 15,200.

To cover this, Jennifer should wager at least 1,400.

Lawrence could wager at most 800 if he lacks confidence in the category.

Jennifer		Lawrence		Julia
13,800		16,000		7,600
1,400		800		7,600
15,200		15,200		15,200

min	max	min	max	min	max
	9,400	11,600			3,200
1,400
			800

Julia would need to wager at least 4,800. Might as well go for broke in that case.

Jennifer		Lawrence		Julia
13,800		16,000		7,600
1,400				4,800
12,400				12,400

min	max	min	max	min	max
	9,400	11,600			3,200
1,400				4,800
			800

Here’s where things stand after the first order:

Jennifer		Lawrence		Julia
13,800		16,000		7,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	9,400	11,600			3,200
1,400				4,800
			800

Second-order calculations

Second’s max vs. first

If Jennifer makes the rational maximum wager of 9,400, Lawrence will need to wager 7,200 to cover her.

Jennifer		Lawrence		Julia
13,800		16,000		7,600
9,400		7,200
23,200		23,200

min	max	min	max	min	max
	9,400	11,600			3,200
1,400		7,200		4,800
			800

If he’s wrong with that wager, he’ll be left with 8,800.

To stay above him, Jennifer can wager up to 5,000.

Julia might consider risking at least 1,200.

Jennifer		Lawrence		Julia
13,800		16,000		7,600
5,000		7,200		1,200
8,800		8,800		8,800

min	max	min	max	min	max
	9,400	11,600		1,200	3,200
1,400	5,000	7,200		4,800
			800

Third’s max vs. first

We’ll ignore Lawrence’s 5,200 wager here – that’s asking a bit much.

Jennifer		Lawrence		Julia
13,800		16,000		7,600
3,000		5,200		3,200
10,800		10,800		10,800

min	max	min	max	min	max
	9,400	11,600		1,200	3,200
1,400	5,000	7,200		4,800
			800

Now, after two orders of analysis:

Jennifer		Lawrence		Julia
13,800		16,000		7,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,400	3,000	11,600		1,200	3,200
	9,400	7,200		4,800
	5,000		800

Zero wagers

Score differences:
Lawrence and Jennifer: 2,200
Lawrence and Julia: 8,400
Jennifer and Julia: 6,200

Jennifer		Lawrence		Julia
13,800		16,000		7,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,400	3,000	11,600		1,200	3,200
4,400	9,400	7,200	8,400	4,800
2,200	5,000		800

Then we line the wagers up and adjust as appropriate.

What actually happened

Jennifer		Lawrence		Julia
13,800		16,000		7,600
4,000		11,601		7,201
17,800		4,399		399

min	max	min	max	min	max
4,401	4,999	11,601		7,600
3,000 !		7,201	8,399	1,201	3,199
	9,399		799

Looks like someone’s been studying wagering “theory“!

Cory WHAAAAAT

Either way, that brings Jennifer’s total up to $37,000 after 2 victories.

Have a great weekend!

The Final Jeopardy! clue