July 2, 2015

Thursday, July 2, 2015

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Nearly two seasons in the bag here on The Final Wager and I can’t believe people are still messing up.

No Penultimate Wager heart attacks tonight, but these are some tricky scores:

Alex

Irvine

Elsa

Angrist

Jon

Lubin

16,400

14,200

7,800

Tonight’s Final Jeopardy! category is:

EUROPEAN ARTISTS

Now let’s see what each player should do. Remember, we save the dollar changes until the end.

First-order calculations

Second doubles up

If Elsa doubles her score, she’ll have 28,400.

To cover this all-in wager, Alex will need to wager 12,000.

Alex		Elsa		Jon
16,400		14,200		7,800
12,000		14,200
28,400		28,400

min	max	min	max	min	max
12,000

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

To stay above his total, Elsa can wager up to 9,800.

Jon can wager up to 3,400.

Alex		Elsa		Jon
16,400		14,200		7,800
12,000		9,800		3,400
4,400		4,400		4,400

min	max	min	max	min	max
12,000			9,800		3,400

Third doubles up

A successful doubling will put Jon at 15,600.

To cover this, Elsa should wager at least 1,400.

Alex could wager at most 800.

Alex		Elsa		Jon
16,400		14,200		7,800
800		1,400		7,800
15,600		15,600		15,600

min	max	min	max	min	max
12,000		1,400	9,800		3,400

	800

Jon would need to wager at least 5,000. All in! All in!

Alex		Elsa		Jon
16,400		14,200		7,800
		1,400		5,000
		12,800		12,800

min	max	min	max	min	max
12,000		1,400	9,800	5,000*
					3,400
	800

Elsa might also consider 3,000 to cover that 800 wager by Alex.

Here’s where things stand after the first order:

Alex		Elsa		Jon
16,400		14,200		7,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
12,000		3,000	9,800	5,000*
		1,400			3,400
	800

Second-order calculations

Second’s max vs. first

If Elsa makes the rational maximum wager of 9,800, Alex will need to wager 7,600 to cover her.

Alex		Elsa		Jon
16,400		14,200		7,800
7,600		9,800
24,000		24,000

min	max	min	max	min	max
12,000		3,000	9,800	5,000*
7,600		1,400			3,400
	800

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

To stay above him, Elsa can wager up to 5,400.

Jon might consider risking at least 1,000.

Alex		Elsa		Jon
16,400		14,200		7,800
7,600		5,400		1,000
8,800		8,800		8,800

min	max	min	max	min	max
12,000		3,000	5,400	5,000*
7,600		1,400		1,000	3,400
	800		9,800

Third’s max vs. first

Not overly concerned here, but hey, math is math…

Alex		Elsa		Jon
16,400		14,200		7,800
5,200		3,000		3,400
11,200		11,200		11,200

min	max	min	max	min	max
12,000		3,000	5,400	5,000*
7,600		1,400	3,000	1,000	3,400
	800		9,800

Two orders deep:

Alex		Elsa		Jon
16,400		14,200		7,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
12,000		3,000	5,400	5,000*
7,600		1,400	3,000	1,000	3,400
	800		9,800

Zero wagers

Score differences:
Alex and Elsa: 2,200
Alex and Jon: 8,600
Elsa and Jon: 6,400

Alex		Elsa		Jon
16,400		14,200		7,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
12,000		4,400	5,400	6,400*
7,600	8,600	1,400	3,000	1,000	3,400
	800		6,400

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

What actually happened

Alex		Elsa		Jon
16,400		14,200		7,800
12,001		10,000		7,799
4,399		4,200		15,599

min	max	min	max	min	max
12,001		4,401	5,399	7,800
	799	1,401	2,999	1,001	3,399
7,601	8,599

No, no, no, Elsa! We were so close to having a good evening, too.

The Final Jeopardy! clue