June 24, 2015

Wednesday, June 24, 2015

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It’s been a wild week, wagering-wise. And for Wednesday, I briefly considered heading to the gym.

Who knows what would have transpired? I liked Shayna’s Penultimate Wager (although I haven’t really looked into it).

Here are our scores heading into Final:

Matt

Pressman

Shayna

Kravetz

Pat

Devane

15,200

18,700

8,200

With this category:

WORLD LEADERS IN THE NEWS

Everyone’s going to have some mind games to deal with.

First-order calculations

Second doubles up

If Matt doubles his score, he’ll have 30,400.

To cover this all-in wager, Shayna will need to wager 11,700.

Matt		Shayna		Pat
15,200		18,700		8,200
15,200		11,700
30,400		30,400

min	max	min	max	min	max
		11,700

An incorrect response with that wager will leave Shayna with 7,000.

To stay above her total, Matt can wager up to 8,200.

Pat can wager up to 1,200.

Matt		Shayna		Pat
15,200		18,700		8,200
8,200		11,700		1,200
7,000		7,000		7,000

min	max	min	max	min	max
	8,200	11,700			1,200

Third doubles up

A successful doubling will put Pat at 16,400.

To cover this, Matt should wager at least 1,200.

Shayna could wager at most 2,300.

Matt		Shayna		Pat
15,200		18,700		8,200
1,200		2,300		8,200
16,400		16,400		16,400

min	max	min	max	min	max
1,200	8,200	11,700			1,200

			2,300

Pat would need to wager at least 5,800. That means all-in; I prefer this approach.

Matt		Shayna		Pat
15,200		18,700		8,200
1,200				5,800
14,000				14,000

min	max	min	max	min	max
1,200	8,200	11,700		5,800*
					1,200
			2,300

Here’s where things stand after the first order:

Matt		Shayna		Pat
15,200		18,700		8,200
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,200	8,200	11,700		5,800*
					1,200
			2,300

Second-order calculations

Second’s max vs. first

If Matt makes the rational maximum wager of 8,200, Shayna will need to wager 4,700 to cover him.

Matt		Shayna		Pat
15,200		18,700		8,200
8,200		4,700
23,400		23,400

min	max	min	max	min	max
1,200	8,200	11,700		5,800*
		4,700			1,200
			2,300

If she’s wrong with that wager, she’ll be left with 14,000.

To stay above her, Matt can wager up to 1,200. This gives us our first wager-to-tie range.

Matt		Shayna		Pat
15,200		18,700		8,200
1,200		4,700		5,800
14,000		14,000		14,000

min	max	min	max	min	max
1,200	1,200	11,700		5,800*
	8,200	4,700			1,200
			2,300

Third’s max vs. first

If Pat goes for that 1,200 amount, Matt could stay above him with a wager of 5,800, while it’s 9,300 for Shayna.

Matt		Shayna		Pat
15,200		18,700		8,200
5,800		9,300		1,200
9,400		9,400		9,400

min	max	min	max	min	max
1,200	1,200	11,700		5,800*
	5,800	4,700	9,300		1,200
	8,200		2,300

Now, after two orders of analysis:

Matt		Shayna		Pat
15,200		18,700		8,200
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,200	1,200	11,700		5,800*
	5,800	4,700	9,300		1,200
	8,200		2,300

Zero wagers

Score differences:
Shayna and Matt: 3,500
Shayna and Pat: 10,500
Matt and Pat: 7,000

Matt		Shayna		Pat
15,200		18,700		8,200
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,200	1,200	11,700		5,800*
3,500	5,800	4,700	7,000		1,200
7,000	7,000		2,300

Note that to cover an “unsafe” (or “Colbyesque“) wager from Shayna, Matt will have to wager 7,000 – exactly the amount by which he leads Pat.

What actually happened

Matt		Shayna		Pat
15,200		18,700		8,200
7,000		3,498		8,199
22,200		22,198		16,399

min	max	min	max	min	max
7,000 !		11,701		8,200
3,501	5,799	4,701	6,999		1,199
1,200 !			2,299

Impressive wagering by Matt – he clearly knew what he was doing. Well done, sir.

Shayna, not so much. If she wanted to play conservatively, she should have risked no more than 2,299 to keep Pat out of contention.

Matt has now won 2 games and $36,000, and I deem his the second-best wager this season after Christine Kim’s True Penultimate Wager in January.

The Final Jeopardy! clue