July 1, 2015

Wednesday, July 1, 2015

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I’m thankful I had to be sober immediately after tonight’s episode, or I might be in the hospital.

Oh, hey – yet another Penultimate Wager. And this one’s really easy!

Brandon

Powell

Rena

Traube

Alex

Irvine

12,800

7,600

20,000

PENULTIMATE WAGER

Any nerd can tell you that double 12,800 is 25,600 – that’s an easy power-of-two calculation. Yet instead of going for $5,601, Alex wagered $5,000!

If Alex doesn’t want to risk so much, he should look to lock out Rena – remember that he’d have to have more than second + third to lock her out of contention.

$401 is perfect – and as much as $799 to maintain the crush over Brandon (so that Brandon would not have 2/3 of Alex’s score).

Anyway, Alex missed the clue. So here are our scores heading into Final:

Brandon	Rena	Alex
12,800	7,600	15,000

And we’ve got this category in play:

DOING BUSINESS INTERNATIONALLY

First-order calculations

Second doubles up

If Brandon doubles his score, he’ll have 25,600.

To cover this all-in wager, Alex will need to wager 10,600.

Brandon		Rena		Alex
12,800		7,600		15,000
12,800				10,600
25,600				25,600

min	max	min	max	min	max
				10,600

An incorrect response with that wager will leave Alex with 4,400.

To stay above his total, Brandon can wager up to 8,400.

Rena can wager up to 3,200.

Brandon		Rena		Alex
12,800		7,600		15,000
8,400		3,200		10,600
4,400		4,400		4,400

min	max	min	max	min	max
	8,400		3,200	10,600

Third doubles up

A successful doubling will put Rena at 15,200.

To cover this, Brandon should wager at least 2,400.

Alex would need to wager at least 200 if he so chooses. (Bad idea, I think.)

Brandon		Rena		Alex
12,800		7,600		15,000
2,400		7,600		200
15,200		15,200		15,200

min	max	min	max	min	max
2,400	8,400		3,200	10,600

				200

Rena would need to wager at least 2,800. She could also wager basically everything if she’s worried about Alex’s small 200 wager.

Brandon		Rena		Alex
12,800		7,600		15,000
2,400		2,800
10,400		10,400

min	max	min	max	min	max
2,400	8,400	2,800	3,200	10,600

		7,200*		200

Here’s where things stand after the first order:

Brandon		Rena		Alex
12,800		7,600		15,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,400	8,400	2,800	3,200	10,600

		7,200*		200

Second-order calculations

Second’s max vs. first

If Brandon makes the rational maximum wager of 8,400, Alex will need to wager 6,200 to cover him.

Brandon		Rena		Alex
12,800		7,600		15,000
8,400				6,200
21,200				21,200

min	max	min	max	min	max
2,400	8,400	2,800	3,200	10,600
				6,200
		7,200*		200

If he’s wrong with that wager, he’ll be left with 8,800.

To stay above him, Brandon can wager up to 4,000.

Rena might consider risking at least 1,200. We’ll leave that out of it.

Brandon		Rena		Alex
12,800		7,600		15,000
4,000		1,200		6,200
8,800		8,800		8,800

min	max	min	max	min	max
2,400	4,000	2,800	3,200	10,600
	8,400			6,200
		7,200*		200

Third’s max vs. first

Rena would have 10,800 with a correct response and a rational maximum wager.

Brandon		Rena		Alex
12,800		7,600		15,000
2,000		3,200		4,200
10,800		10,800		10,800

min	max	min	max	min	max
2,400	4,000	2,800	3,200	10,600
	8,400			6,200
	2,000	7,200*		200

Now, after two orders of analysis:

Brandon		Rena		Alex
12,800		7,600		15,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,400	4,000	2,800	3,200	10,600
	8,400			6,200
	2,000	7,200*		200

Zero wagers

Score differences:
Alex and Brandon: 2,200
Alex and Rena: 7,400
Brandon and Rena: 5,200

Brandon		Rena		Alex
12,800		7,600		15,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
2,400	4,000	2,800	3,200	10,600
4,400	5,200			6,200	7,400
	2,000	7,400*		200	2,200

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

What actually happened

Brandon		Rena		Alex
12,800		7,600		15,000
7,200		7,401		11,000
5,600		199		26,000

min	max	min	max	min	max
2,401	3,999	2,801	3,199	10,601
4,401	5,199	7,600		6,201	7,399
	1,999			201	2,199

No harm, no foul?

No: process > outcome here at The Final Wager.

The Final Jeopardy! clue