Monday, December 21, 2015

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Last month I asked you a question:

Love my facial hair? Hate my facial hair? Either way, I think you’ll enjoy tonight’s video.

In part because these scores are so fascinating.

Liz Quesnelle	Jay O’Brien	Shoshana Gordon Ginsberg
15,000	3,800	10,000

Shoshana has exactly 2/3 of Liz’s score. In days of yore, the prescription would have been for Liz to wager 5,000 and Shoshana to pick between 0 and 10,000.

But times have changed, and we’ve got some mind games to consider. The last time we had this situation – nearly 11 months ago – things turned ugly.

Here’s the Final Jeopardy! category:

PUBLISHING

Shoshana works as a children’s librarian, so I think it’s safe to say she likes this.

First-order calculations

If Liz goes for the lockout and misses, she’ll fall below Shoshana by a dollar, so wagering 5,000 even is a possibility, risking the tie in both directions.

Liz		Jay		Shoshana
15,000		3,800		10,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
5,000+ !					0 !

Second-order calculations

Since the 5,000 wager is rational from Liz, Shoshana might wager 10,000, aiming for a possible tiebreaker.

On the other hand, if Liz thinks Shoshana will wager zero, she could wager up to 4,999. (I’m subtracting the extra dollar here in advance, which is unusual for me, but makes things better to look at.)

Liz		Jay		Shoshana
15,000		3,800		10,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
5,000+ !					0 !
	4,999			10,000 !

Since Shoshana is probably going to bet big, Liz should feel safe tacking on the extra dollar. Some other things she could take into account:

What actually happened

Liz		Jay		Shoshana
15,000		3,800		10,000
5,001		3,799		7,500
20,001		7,599		17,500
min	max
5,001	7,399			0 !
5,000 !				10,000 !
	4,999

Well, Shoshana liked the category, indeed, but deprived herself of a tiebreaker. Liz rendered that point moot, however, so we can all sleep easy tonight.

Liz returns tomorrow, once again at the first podium – this time as the returning champ.

The Final Jeopardy! clue

PUBLISHING

IN 1927 THE PUBLISHER OF THE MODERN LIBRARY WIDENED ITS SCOPE AND TOOK THIS NAME, MEANT AS A JOKE ABOUT HOW IT WOULD SELECT TITLES

[spoiler]What is Random House?[/spoiler]

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