Tuesday, July 28, 2015

[php snippet=22]

The good news: if you read my Fact Primers and my This Day in History entries, you did pretty well tonight.

The bad news: I’m down to coffee.

No rest for the weary, even in the last week of the season.

Suzanne Vito	Jonathan Marcus	Melissa Hodges
9,600	10,100	5,800

Tonight’s Final Jeopardy! category is:

TELEVISION OF THE 2000s

I’ll put the calculations below, but I’m just going to get to the results. I think this is the first time I’ve ever had to do this.

What actually happened

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
9,600		10,100		0
19,200		20,200		5,800
min	max	min	max	min	max
2,001	3,799	9,101		4,301	4,799
	8,599	1,501	4,299

While, yes, Melissa’s wager could have worked out in her favor, she doesn’t cover the very rational 2,001 wager out of Suzanne. In fact, given Jonathan’s indefensible all-in wager, Melissa could have put up everything but a dollar!

I see absolutely no reason for Suzanne to wager everything here, either, unless she happens to know that Jonathan has had zero contact with pop culture in the past 15 years.

The Final Jeopardy! clue

TELEVISION OF THE 2000s

BLANCO IS THE LAST NAME OF THE MAIN CHARACTER IN “METÁSTASIS”, A COLOMBIA-SET VERSION OF THIS SHOW

[spoiler]What is Breaking Bad?[/spoiler]

[php snippet=22]

And now, on to the calculations.

First-order calculations

Second doubles up

If Suzanne doubles her score, she’ll have 19,200.

To cover this all-in wager, Jonathan will need to wager 9,100.

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
9,600		9,100
19,200		19,200
min	max	min	max	min	max
		9,100

An incorrect response with that wager will leave Jonathan with 1,000.

To stay above his total, Suzanne can wager up to 8,600.

Melissa can wager up to 4,800.

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
8,600		9,100		4,800
1,000		1,000		1,000
min	max	min	max	min	max
	8,600	9,100			4,800

Third doubles up

A successful doubling will put Melissa at 11,600.

To cover this, Suzanne should wager at least 2,000.

(Jonathan would need to wager at least 1,500, but this is somewhat questionable.)

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
2,000		1,500		5,800
11,600		11,600		11,600
min	max	min	max	min	max
2,000	8,600	9,100			4,800
		1,500

Melissa would need to wager at least 1,800.

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
2,000				1,800
7,600				7,600
min	max	min	max	min	max
2,000	8,600	9,100		1,800	4,800
		1,500

She’d also need to wager at least 2,800 against that weird Jonathan wager.

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,000	8,600	9,100		2,800	4,800
				1,800
		1,500

Second-order calculations

Third’s max vs. first

4,800 from Melissa means

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
1,000		500		4,800
10,600		10,600		10,600
min	max	min	max	min	max
2,000	8,600	9,100		2,800	4,800
				1,800
1,000		1,500

An incorrect response with that wager will leave Jonathan with 1,000.

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
1,000		500		2,800
8,600		9,600		8,600
min	max	min	max	min	max
2,000	8,600	9,100		2,800	4,800
				1,800
1,000		1,500

Now, after two orders of analysis:

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,000	8,600	9,100		2,800	4,800
				1,800
1,000		1,500

Zero wagers

Score differences:
Jonathan and Suzanne: 500
Jonathan and Melissa: 4,300
Suzanne and Melissa: 3,800

Suzanne		Jonathan		Melissa
9,600		10,100		5,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,000	3,800	9,100		4,300	4,800
	8,600
1,000		1,500	4,300