Friday, March 20, 2015

Let’s see how we finish our week.

Here are our scores heading into Final:

Gina Shaddox	Lesley Cooksey	Alex Navissi
7,600	4,800	6,800

Tonight’s Final Jeopardy! category is:

UNWANTED FIRSTS

Let’s see what each player should do. Remember, we save the dollar changes until the end.

First-order calculations

Second doubles up

If Alex doubles his score, he’ll have 13,600.

To cover this all-in wager, Gina will need to wager 6,000.

Gina		Lesley		Alex
7,600		4,800		6,800
6,000				6,800
13,600				13,600
min	max	min	max	min	max
6,000

An incorrect response with that wager will leave Gina with 1,600.

To stay above her total, Alex can wager up to 5,200.

Lesley can wager up to 3,200.

Gina		Lesley		Alex
7,600		4,800		6,800
6,000		3,200		5,200
1,600		1,600		1,600
min	max	min	max	min	max
6,000			3,200	2,800

Third doubles up

A successful doubling will put Lesley at 9,600.

To cover this, Alex should wager at least 2,800.

(Gina would need to wager at least 2,000, but this is somewhat questionable.)

Gina		Lesley		Alex
7,600		4,800		6,800
2,000		4,800		2,800
9,600		9,600		9,600
min	max	min	max	min	max
6,000			3,200	2,800	5,200
2,000

If Alex is incorrect with that wager, Lesley can wager up to 800 to stay above his total.

Gina		Lesley		Alex
7,600		4,800		6,800
		800		2,800
		4,000		4,000
min	max	min	max	min	max
6,000			800	2,800	5,200
			3,200
2,000

Here’s where things stand after the first order:

Gina		Lesley		Alex
7,600		4,800		6,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
6,000			800	2,800	5,200
			3,200
2,000

Second-order calculations

Second’s max vs. first

If Alex makes the rational maximum wager of 5,200, Gina will need to wager 4,400 to cover him.

Gina		Lesley		Alex
7,600		4,800		6,800
4,400				5,200
12,000				12,000
min	max	min	max	min	max
6,000			800	2,800	3,600
2,000			3,200		5,200
4,400

If she’s wrong with that wager, she’ll be left with 3,200.

To stay above her, Alex can wager up to 3,600.

Lesley may risk up to 1,600, but we’ll ignore that.

Gina		Lesley		Alex
7,600		4,800		6,800
4,400		1,600		3,600
3,200		3,200		3,200
min	max	min	max	min	max
6,000			800	2,800	3,600
2,000			3,200		5,200
4,400

Third’s max vs. second

Against Alex, Lesley can wager at most 800. With a correct response, she’ll have 5,600.

To stay above this, Alex can wager at most 1,200.

Gina		Lesley		Alex
7,600		4,800		6,800
		800		1,200
		5,600		5,600
min	max	min	max	min	max
6,000			800	2,800	3,600
2,000			3,200		1,200
4,400					5,200

If he is correct, Alex will have 8,000.

To account for this, Lesley will need to wager at least 3,200. You could make the argument she needs to wager this amount, I suppose, but I’d rather cap at 800.

Gina		Lesley		Alex
7,600		4,800		6,800
		3,200		1,200
		8,000		8,000
min	max	min	max	min	max
6,000			800	2,800	3,600
2,000		3,200	3,200		1,200
4,400					5,200

Now, after two orders of analysis:

Gina		Lesley		Alex
7,600		4,800		6,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
6,000			800	2,800	3,600
2,000		3,200	3,200		1,200
4,400					5,200

Zero wagers

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

Gina		Lesley		Alex
7,600		4,800		6,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
6,000			800	2,800	3,600
2,000	2,800	3,200	3,200	800	1,200
4,400					5,200

What actually happened

Gina		Lesley		Alex
7,600		4,800		6,800
2,400		4,799		6,700
5,200		1		13,500
min	max	min	max	min	max
6,001			799	2,801	3,599
2,001	2,799	3,200		801	1,199

Alex’s wager worked out – it’s not as bad as I’d normally say, because Gina showed in Thursday’s game that she wasn’t very well prepared when it came to wagering.

The Final Jeopardy! clue

UNWANTED FIRSTS

JEAN VALLIERE, BURNED IN 1523, IS CONSIDERED THE FIRST MARTYR OF THIS RELIGIOUS GROUP

[spoiler]Who are the Huegenots?[/spoiler]

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