Friday, June 19, 2015

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Man, good thing it’s Friday. That’s all I can say.

OK, first of all, I was mad about that Daily Double about a Dutch-named place (ugh, Spuyten Duyvil). And then Jennifer had the Penultimate Wager and totally blew it. More on that below.

And don’t worry, you’ll be getting a video soon.

Here’s where we’re sitting right now:

Brennan Bushee	Chad Capule	Jennifer Shepherd
12,400	9,200	12,000

The category is almost inconsequential given these scores.

First-order calculations

Second doubles up

If Jennifer doubles her score, she’ll have 24,000.

To cover this all-in wager, Brennan will need to wager 11,600.

Brennan		Chad		Jennifer
12,400		9,200		12,000
11,600				12,000
24,000				24,000
min	max	min	max	min	max
11,600

An incorrect response with that wager will leave Brennan with 800.

To stay above his total, Jennifer can wager up to 11,200.

Chad can wager up to 8,400.

Brennan		Chad		Jennifer
12,400		9,200		12,000
11,600		8,400		11,200
800		800		800
min	max	min	max	min	max
11,600			8,400		11,200

Third doubles up

A successful doubling will put Chad at 18,400.

To cover this, Jennifer should wager at least 6,400.

Brennan would need to wager at least 6,000, but we’ll return to this only if there’s a good reason.

Brennan		Chad		Jennifer
12,400		9,200		12,000
6,000		9,200		6,400
18,400		18,400		18,400
min	max	min	max	min	max
11,600			8,400	6,400	11,200
6,000

If Jennifer is incorrect with that wager, Chad can wager up to 3,600 to stay above her total.

Brennan		Chad		Jennifer
12,400		9,200		12,000
		3,600		6,400
		5,600		5,600
min	max	min	max	min	max
11,600			3,600	6,400	11,200
			8,400
6,000

Here’s where things stand after the first order:

Brennan		Chad		Jennifer
12,400		9,200		12,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,600			3,600	6,400	11,200
			8,400
6,000

Second-order calculations

Third’s max vs. second

Against Jennifer, Chad can wager at most 3,600. With a correct response, he’ll have 12,800.

To cover this, Jennifer should wager at least 800.

Brennan		Chad		Jennifer
12,400		9,200		12,000
		3,600		800
		12,800		12,800
min	max	min	max	min	max
11,600			3,600	6,400	11,200
			8,400	800
6,000

If she’s wrong with that minimum wager, Jennifer will have 11,200, so Chad should wager at least 2,000.

Brennan		Chad		Jennifer
12,400		9,200		12,000
		2,000		800
		11,200		11,200
min	max	min	max	min	max
11,600		2,000	3,600	6,400	11,200
			8,400	800
6,000

Now, after two orders of analysis:

Brennan		Chad		Jennifer
12,400		9,200		12,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,600		2,000	3,600	6,400	11,200
			8,400	800
6,000

Zero wagers

Score differences:
Brennan and Jennifer: 400
Brennan and Chad: 3,200
Jennifer and Chad: 2,800

Brennan		Chad		Jennifer
12,400		9,200		12,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
11,600		3,200	3,600	6,400	11,200
6,000	6,400	6,400	8,400	800	2,800
	400

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

What actually happened

Brennan		Chad		Jennifer
12,400		9,200		12,000
11,601		1,800		11,500
24,001		11,000		23,500
min	max	min	max	min	max
11,601		3,201	3,599	6,401	11,199
6,001	6,399	6,401	8,399	801	2,799
	399

Not sure what Jennifer is doing here, either – but that’s not really a surprise.

Thanks in part to her Christmas present of a Penultimate Wager, Brennan completed his sweep of the week, taking down $126,404.

The Penultimate Wager

Brennan	Chad	Jennifer
12,400	9,200	10,000

It’s the $2000 clue in BRONTE-SAURUS – a category that had given our players problems (they missed the $800, $1200, and $1600 clues).

The right play is to try for first place. I’d go between $2,401 and $3,600 – if she’s wrong with that bigger end, she’ll beat Brennan by a dollar with a zero wager if he goes for the lockout.

With that $2,000 wager, she gains nothing if she’s right and falls to third anyway if she’s wrong. And we all saw how it shook out in the end.

The Final Jeopardy! clue

20th CENTURY SCIENTISTS

EVERYTHING CHANGED IN 1924 AFTER HE OBSERVED, “I HAVE FOUND A CEPHEID VARIABLE IN THE ANDROMEDA NEBULA”

[spoiler]Who was Edwin Hubble?[/spoiler]

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