Monday, April 6, 2015

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Happy Easter! Happy Passover! Here’s hoping for a Happy Keith tonight, too.

These are some good scores heading into Final.

Kerry Greene	Brian Carrick	Eric Simmonds
11,800	18,800	14,800

Will our champ be able to pull out the come-from-behind victory again?

Tonight’s Final Jeopardy! category is:

NYC LANDMARKS

Let’s get to it, because this is a fun one. Remember, we save the dollar changes until the end.

First-order calculations

Second doubles up

If Eric doubles his score, he’ll have 29,600.

To cover this all-in wager, Brian will need to wager 10,800.

Kerry		Brian		Eric
11,800		18,800		14,800
		10,800		14,800
		29,600		29,600
min	max	min	max	min	max
		10,800

An incorrect response with that wager will leave Brian with 8,000.

To stay above his total, Eric can wager up to 6,800.

Kerry can wager up to 3,800.

Kerry		Brian		Eric
11,800		18,800		14,800
3,800		10,800		6,800
8,000		8,000		8,000
min	max	min	max	min	max
	3,800	10,800			6,800

Third doubles up

A successful doubling will put Kerry at 23,600.

To cover this, Eric should wager at least 8,800. In this case, though, he will lose to Brian on an incorrect response, so he might as well wager everything.

Kerry		Brian		Eric
11,800		18,800		14,800
11,800		4,800		8,800
23,600		23,600		23,600
min	max	min	max	min	max
	3,800	10,800		8,800*
					6,800
		4,800

Here’s where things stand after the first order:

Kerry		Brian		Eric
11,800		18,800		14,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,200	3,800	10,800		8,800*
					6,800
		4,800

Second-order calculations

Second’s max vs. first

If Eric makes the rational maximum wager of 6,800, Brian will need to wager 2,800 to cover him. We’ll ignore that, though, given it would allow both Eric and Kerry to pass him.

Kerry could pass that wager from Eric by wagering at least 9,800 (read: everything).

Kerry		Brian		Eric
11,800		18,800		14,800
9,800		2,800		6,800
21,600		21,600		21,600
min	max	min	max	min	max
2,200	3,800	10,800		8,800*
					6,800
9,800*		4,800

Third’s max vs. first

Eric could cover Kerry’s maximum wager by putting up 800. Brian‘s 3,200 wager makes no sense here.

Kerry		Brian		Eric
11,800		18,800		14,800
3,800		3,200		800
15,600		15,600		15,600
min	max	min	max	min	max
2,200	3,800	10,800		8,800*
				1,200	6,800
9,800*		4,800		800

Now, after two orders of analysis:

Kerry		Brian		Eric
11,800		18,800		14,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,200	3,800	10,800		8,800*
				1,200	6,800
9,800*		4,800		800

Zero wagers

Kerry		Brian		Eric
11,800		18,800		14,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
3,000	3,800	10,800		8,800*
				1,200	3,000
9,800*		4,800	7,000	4,000	6,800

Lots happening here – 3,000, 4,000, 7,000…

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

What actually happened

Kerry		Brian		Eric
11,800		18,800		14,800
11,800		12,000		8,801
23,600		6,800		5,999
min	max	min	max	min	max
3,001	3,799	10,801		14,800
		4,801	6,999	1,201	2,999
11,800				4,001	6,799

In many situations, I’d give Kerry’s wager a red. Eric, however, has some wagers that could keep her (mostly) at bay – but note that my preferred range for Kerry would cover a zero/incorrect response from Eric.

Eric almost left $5,999 on the table. He finished in third anyway.

Brian’s wager was fine – technically, he could have gone for $799 or $800 more – but with so many moving parts below him, I’d recommend sticking to the bare minimum.

The Final Jeopardy! clue

NYC LANDMARKS

THE LOBBY OF THIS LANDMARK HAS AN ART DECO CEILING FRESCO BY EDWARD TRUMBULL CALLED “TRANSPORT AND HUMAN ENDEAVOR”

[spoiler]What is the Chrysler Building?[/spoiler]

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