Thursday, May 28, 2015

It’s almost Friday! I could use a drink.

I’ll let you guess why.

*waits*

*waits*

*waits*

Ok, let’s just get right into it:

What actually happened

Dan		Ivan		Adrienne
20,000		15,200		15,700
19,999		15,200		14,701
39,999		0		30,401
min	max	min	max	min	max
11,401		4,801	5,599	15,700
				6,101	7,099
1,801	4,299				499

AGAIN! At least it’s not as bad as Tuesday’s wager.

In fact, I’d argue that Ivan’s wager is even worse, since he has no chance of winning unless the other two miss anyway.

Sorry – got a bit ahead of myself.

Dan Feitel	Ivan Tan	Adrienne Onofri
20,000	15,200	15,700

Tonight’s Final Jeopardy! category is:

AMERICAN LITERATURE

First-order calculations

Second doubles up

If Adrienne doubles her score, she’ll have 31,400.

To cover this all-in wager, Dan will need to wager 11,400.

Dan		Ivan		Adrienne
20,000		15,200		15,700
11,400				15,700
31,400				31,400
min	max	min	max	min	max
11,400

An incorrect response with that wager will leave Dan with 8,600.

To stay above his total, Adrienne can wager up to 7,100.

Ivan can wager up to 6,600.

Dan		Ivan		Adrienne
20,000		15,200		15,700
11,400		6,600		7,100
8,600		8,600		8,600
min	max	min	max	min	max
11,400			6,600		7,100

Third doubles up

A successful doubling will put Ivan at 30,400.

To cover this, Adrienne should wager at least 14,700. In this case, though, she will lose on an incorrect response, so she might as well wager everything.

I’m unconcerned about Dan here – might as well cover Adrienne.

Dan		Ivan		Adrienne
20,000		15,200		15,700
10,400		15,200		14,700
30,400		30,400		30,400
min	max	min	max	min	max
11,400			6,600	14,700*
					7,100

Here’s where things stand after the first order:

Dan		Ivan		Adrienne
20,000		15,200		15,700
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,400			6,600	14,700*
					7,100

Second-order calculations

Third’s max vs. first

If Ivan wagers 6,600, Adrienne can cover him with 6,100.

Dan		Ivan		Adrienne
20,000		15,200		15,700
		6,600		6,100
		21,800		21,800
min	max	min	max	min	max
11,400			6,600	14,700*
				6,100	7,100

An incorrect response with that wager will leave Adrienne with 6,100, so Ivan should cap his at 5,600.

Dan		Ivan		Adrienne
20,000		15,200		15,700
		5,600		6,100
		9,600		9,600
min	max	min	max	min	max
11,400			5,600	14,700*
				6,100	7,100

I don’t see much else, so after two orders of analysis:

Dan		Ivan		Adrienne
20,000		15,200		15,700
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,400			5,600	14,700*
				6,100	7,100

Zero wagers

Score differences:
Dan and Adrienne: 4,300
Dan and Ivan: 4,800
Adrienne and Ivan: 500

Dan		Ivan		Adrienne
20,000		15,200		15,700
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,400		4,800	5,600	14,700*
				6,100	7,100
	4,300				500

If for some reason Dan wants to put his life in the hands of his opponents, he can go for at least 1,800 (which would cover both maximum wagers except Adrienne’s proper cover bet).

Once again, what actually happened

Dan has now won 3 games and $85,598.

The Final Jeopardy! clue

AMERICAN LITERATURE

PUBLISHED A YEAR LATER, “GOOD WIVES” WAS A FOLLOW-UP TO THIS 1868 NOVEL

[spoiler]What is Little Women?[/spoiler]

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