Thursday, October 15, 2015

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I’ll make this quick; I’ve got a baseball game to get back to watching.

‘Giant-killer’ Michael Baker was again timid on a late Daily Double – this time putting himself in a mind-games situation when he could have really turned up the heat on Josh.

Michael Baker	Josh Silverman	Dana Desprois
10,600	15,200	3,800

Tonight’s Final Jeopardy! category is:

THE MIDDLE EAST

Here’s your video:

First-order calculations

Michael has more than 2/3 of Josh’s total, so he can win on a double-stumper…

Michael		Josh		Dana
10,600		15,200		3,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	1,400	6,000

Second-order calculations

…but Josh can wager small against a bet like that, so an all-in wager is acceptable from Michael.

Michael		Josh		Dana
10,600		15,200		3,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	1,400	6,000
7,800*			3,200

What actually happened

Michael		Josh		Dana
10,600		15,200		3,800
4,601		6,001		3,000
5,999		21,201		800
min	max	min	max
	1,399	6,001*
10,600			3,199

4,601 isn’t enough, however, to cover that ‘small’ range out of Josh, so Michael gets the pink wager.

In the end, the Daily Double wager was moot, but here is the wagering situation in that case:

Michael		Josh		Dana
13,200		15,200		3,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
4,000	5,600	11,200	11,400	200*
	1,600	3,600	4,000
	9,200		7,600

Much more flexibility for Michael in this case.

The Final Jeopardy! clue

THE MIDDLE EAST

WITH AN AREA OF 4,000 SQUARE MILES, IT’S THE ONLY PRIMARILY ARABIC-SPEAKING COUNTRY IN THE MIDDLE EAST THAT HAS NO DESERT

[spoiler]What is Lebanon?[/spoiler]

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