Tuesday, June 9, 2015

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We had a fun situation last night. How will tonight’s compare?

This is one of the tighter games in recent memory, with Phil leapfrogging Chris into second on the penultimate clue.

Chris Wonderly	Phil Arevalo	Holly Cooper
10,800	11,800	11,900

Tonight’s Final Jeopardy! category is:

HUMANITIES & HISTORY

Strange one, eh?

The scores are so close that the wagering calculations are very easy.

First-order calculations

Second doubles up

If Phil doubles his score, he’ll have 23,600.

To cover this all-in wager, Holly will need to wager 11,700.

Chris		Phil		Holly
10,800		11,800		11,900
		11,800		11,700
		23,600		23,600
min	max	min	max	min	max
				11,700

An incorrect response with that wager will leave Holly with 200.

To stay above her total, Phil can wager up to 11,600.

Chris can wager up to 10,600.

Chris		Phil		Holly
10,800		11,800		11,900
10,600		11,600		11,700
200		200		200
min	max	min	max	min	max
	10,600		11,600	11,700

Third doubles up

A successful doubling will put Chris at 21,600.

To cover this, Phil should wager at least 9,800.

Holly would need to wager at least 9,700, but this would put her at risk against Phil.

Chris		Phil		Holly
10,800		11,800		11,900
10,800		9,800		9,700
21,600		21,600		21,600
min	max	min	max	min	max
	10,600	9,800	11,600	11,700
				9,700

If Phil is incorrect with that wager, Chris can wager up to 8,800 to stay above his total. We can further cap Chris at 8,600 just in case Holly aims to cover him.

Chris		Phil		Holly
10,800		11,800		11,900
8,800		9,800		9,700
2,200		2,000		2,200
min	max	min	max	min	max
	8,600	9,800	11,600	11,700
	10,600
				9,700

Here’s where things stand after the first order:

Chris		Phil		Holly
10,800		11,800		11,900
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	8,600	9,800	11,600	11,700
	10,600
				9,700

Because everyone’s so bunched up, there is very little room for mind games.

Zero wagers

Score differences:
Holly and Phil: 100
Holly and Chris: 1,100
Phil and Chris: 1,000

Chris		Phil		Holly
10,800		11,800		11,900
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,200	8,600	9,800	11,600	11,700
				9,700
	10,600	200	1,000		100

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

What actually happened

Chris		Phil		Holly
10,800		11,800		11,900
10,000		11,800		6,000
20,800		23,600		5,900
min	max	min	max	min	max
2,201	8,599	9,801	11,599	11,701
				9,701
	10,599	201	999		99

Well, color me confused by these wagers. The gentlemen’s wagers fall to the minimum proper bet of the next player up. And 6,000? There’s no wagering website that will agree with that.

The Final Jeopardy! clue

HUMANITIES & HISTORY

ECHOING THE MORSE CODE FOR V, IN WWII THE BBC’S “V FOR VICTORY” CAMPAIGN USED THIS CLASSICAL WORK AS A THEME • • • —

[spoiler]What is Beethoven’s Fifth?[/spoiler]

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