July 14, 2015

Tuesday, July 14, 2015

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I don’t know how you feel about this whole carousel of champs thing, but I do know the 4- and 3-time champs on the TOC bubble are lovin’ it.

Phil Salathe is our tenth consecutive different player at podium #1 – and he is trailing heading into Final.

Phil

Salathe

Ben

Hemmens

Val

Narehood

13,400

16,200

4,400

Tonight’s Final Jeopardy! category is:

HISTORIC AMERICANS

For the first time in a while, we have a Shore’s Conjecture situation.

First-order calculations

Second doubles up

If Phil doubles his score, he’ll have 26,800.

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

Phil		Ben		Val
13,400		16,200		4,400
13,400		10,600
26,800		26,800

min	max	min	max	min	max
		10,600

An incorrect response with that wager will leave Ben with 5,600.

To stay above his total, Phil can wager up to 7,800.

Val must respond correctly to have a shot, so all-in is the way to go.

Phil		Ben		Val
13,400		16,200		4,400
7,800		10,600		1,200
5,600		5,600		5,600

min	max	min	max	min	max
	7,800	10,600		1,200*

Third doubles up

A successful doubling will put Val at 8,800.

To stay above her, Phil can wager at most 4,600.

Ben could wager at most 7,400.

Phil		Ben		Val
13,400		16,200		4,400
4,600		7,400		4,400
8,800		8,800		8,800

min	max	min	max	min	max
	4,600	10,600		1,200*
	7,800
			7,400

Here’s where things stand after the first order:

Phil		Ben		Val
13,400		16,200		4,400
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	4,600	10,600		1,200*
	7,800
			7,400

Second-order calculations

Shoretegic wagers

If Phil chooses to stay above a double-up by Val, he will have at most 18,000.

Ben can cover that with a wager of 1,800.

Phil		Ben		Val
13,400		16,200		4,400
4,600		1,800
18,000		18,000

min	max	min	max	min	max
	4,600	10,600		1,200*
	7,800	1,800
			7,400

To get above Ben’s “Shoretegic” total, Phil must wager 1,000.

Phil		Ben		Val
13,400		16,200		4,400
1,000		1,800
14,400		18,000

min	max	min	max	min	max
1,000	4,600	10,600		1,200*
	7,800	1,800
			7,400

Second’s max vs. first

If Phil makes the rational maximum wager of 7,800, Ben will need to wager 5,000 to cover him.

Phil		Ben		Val
13,400		16,200		4,400
7,800		5,000
21,200		21,200

min	max	min	max	min	max
1,000	4,600	10,600		1,200*
	7,800	1,800
		5,000	7,400

If he’s wrong with that wager, he’ll be left with 11,200.

To stay above him, Phil can wager up to 2,200.

Phil		Ben		Val
13,400		16,200		4,400
2,200		5,000
11,200		11,200

min	max	min	max	min	max
1,000	2,200	10,600		1,200*
	4,600	1,800
	7,800	5,000	7,400

Now, after two orders of analysis:

Phil		Ben		Val
13,400		16,200		4,400
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,000	2,200	10,600		1,200*
	4,600	1,800
	7,800	5,000	7,400

Zero wagers

Score differences:
Ben and Phil: 2,800
Ben and Val: 11,800
Phil and Val: 9,000

Phil		Ben		Val
13,400		16,200		4,400
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,000	2,200	10,600	11,800	1,200*
2,800	4,600	1,800	2,800
5,600	7,800	5,000	5,600

Val’s forced into her wager, but Phil and Ben have a host of options.

If I’m Ben, I take my destiny into my own hands.

If I’m Phil, I make the Shoretegic play.

What actually happened

Phil		Ben		Val
13,400		16,200		4,400
4,599		10,601		4,400
17,999		26,801		0

min	max	min	max
2,801	4,599	10,601	11,799	4,400
5,601	7,799	1,801	2,799
1,001	2,199	5,001	5,599

A triple green! And a new champion! Oh, what a night!

I thought this was a tough clue – nice job by the two gentlemen to get it.

The Final Jeopardy! clue