Tuesday, January 26, 2016

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I got really angry during Tuesday’s video. How much of that frustration stemmed from the wagers?

We’ll have to see, because this could be a tricky situation – particularly with Fred’s odd wagering pattern.

Fred Vaughn (2x)	Sonam Shah	Gerry Matatics
20,800	16,200	8,600

Tonight’s Final Jeopardy! category is:

20th CENTURY AMERICA

By the way, if you didn’t think Fred was TOC material, tonight’s game should put your doubts to rest. Over $20k without the benefit of a Daily Double is pretty, pretty, pretty good.

First-order calculations

Gerry needs to get it right to have a chance, which makes the rest of our analysis easier.

Fred		Sonam		Gerry
20,800		16,200		8,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,600		1,000	7,000	600*
	3,600

Second-order calculations

Fred can wager 2,400 to cover Sonam’s expected large wager, while Sonam should up her minimum wager.

Fred		Sonam		Gerry
20,800		16,200		8,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,600		2,200	7,000	600*
2,400	3,600

Zero wagers

Score differences:
Fred and Sonam: 4,600
Fred and Gerry: 12,200
Sonam and Gerry: 7,600

Fred		Sonam		Gerry
20,800		16,200		8,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,600	12,200	4,600	7,000	600*
2,400	3,600	9,200*

I don’t like the all-in from Sonam, but the math could suggest it.

What actually happened

Fred		Sonam		Gerry
20,800		16,200		8,600
7,500		12,201		8,598
13,300		3,999		2
min	max	min	max
11,601	12,199	4,601	6,999	8,600
2,401	3,599
		16,200

Turns out it would have worked on an easier clue. Why Sonam picked that number I can’t tell – it would have worked out (by $101) but I see no reason to anticipate Fred wagering 7,600.

Fred would have been better off forcing Sonam to get it right – or at least not giving her the chance at a win with that basic 1,001 wager to cover Gerry. No matter: he has now won 3 games and $49,600, and has a chance to break our drought tomorrow.

The Final Jeopardy! clue

20th CENTURY AMERICA

THE 1970 FOLLOW-UP LINE “WE’VE HAD A MAIN B BUS UNDERVOLT” WAS ADDRESSED TO A LISTENER IN THIS CITY

[spoiler]What is Houston? (As in “Houston, we’ve had a problem”)[/spoiler]

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