June 3, 2015

Wednesday, June 3, 2015

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I’m sad Dan Feitel is gone – he was fun to watch, and he certainly kept things interesting. Will our new champ begin a streak of his own?

Things aren’t looking good for Jacob right now.

Jacob

Johnson

Pete

Miranti

Jami

Griffeth

5,200

15,000

16,800

“It’ll all come down to wagering and our players’ knowledge of:” *glink*

BRITISH CITIES

Well, this one should be fun.

First-order calculations

Second doubles up

If Pete doubles his score, he’ll have 30,000.

To cover this all-in wager, Jami will need to wager 13,200.

Jacob		Pete		Jami
5,200		15,000		16,800
		15,000		13,200
		30,000		30,000

min	max	min	max	min	max
				13,200

If Jami is wrong, she’ll have 3,600.

To stay above her total, Pete can wager up to 11,400.

Jacob can wager up to 1,600.

Jacob		Pete		Jami
5,200		15,000		16,800
1,600		11,400		13,200
3,600		3,600		3,600

min	max	min	max	min	max
	1,600		11,400	13,200

Third doubles up

A successful doubling will put Jacob at 10,400.

To stay above him, Pete can wager at most 4,600.

Jami could wager at most 6,400 if she is so inclined.

Jacob		Pete		Jami
5,200		15,000		16,800
5,200		4,600		6,400
10,400		10,400		10,400

min	max	min	max	min	max
	1,600		4,600	13,200
			11,400
					6,400

Here’s where things stand after the first order:

Jacob		Pete		Jami
5,200		15,000		16,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	1,600		4,600	13,200
			11,400
					6,400

Notice that Pete can both (1) stay above Jacob no matter what and (2) cover a zero wager from Jami. Therefore, we are in Shore’s Conjecture.

Because Jacob can stand pat and beat Jami on a cover wager, this is the Strong Form.

Second-order calculations

Shoretegic wagers

If Pete chooses to stay above a double-up by Jacob, he will have at most 19,600.

Jami can cover that with a wager of 2,800.

Jacob		Pete		Jami
5,200		15,000		16,800
		4,600		2,800
		19,600		19,600

min	max	min	max	min	max
	1,600		4,600	13,200
			11,400	2,800
					6,400

To stay above Jami’s “Shoretegic” total, Pete can wager up to 1,000.

Jacob		Pete		Jami
5,200		15,000		16,800
		1,000		2,800
		14,000		19,600

min	max	min	max	min	max
	1,600		4,600	13,200
			1,000	2,800
			11,400		6,400

First’s max vs. third

Let’s say Jami plans to stay above Jacob. In that case, Pete would need to wager 8,200 to cover her.

Jacob		Pete		Jami
5,200		15,000		16,800
		8,200		6,400
		23,200		23,200

min	max	min	max	min	max
	1,600		4,600	13,200
			1,000	2,800
		8,200	8,200		6,400

Third’s max vs. first

I don’t like this one so much, but I’ll put it in anyway, because it doesn’t hurt to restrict wagers. This one really only applies to Pete.

Jacob		Pete		Jami
5,200		15,000		16,800
1,600		8,200		10,000
6,800		6,800		6,800

min	max	min	max	min	max
	1,600		4,600	13,200
			1,000	2,800
		8,200	8,200		6,400

If Jacob is scared of this possibility, he could wager everything.

Now, after two orders of analysis:

Jacob		Pete		Jami
5,200		15,000		16,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	1,600		4,600	13,200
			1,000	2,800
5,200		8,200	8,200		6,400

Zero wagers

Score differences:
Jami and Pete: 1,800
Jami and Jacob: 11,600
Pete and Jacob: 9,800

Jacob		Pete		Jami
5,200		15,000		16,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	1,600	3,600	4,600	13,200
			1,000	2,800	3,600
5,200		8,200	8,200		6,400

Also, in the video, I suggest that you could calculate a range for Jami between 9,600 (cover a first-order max from Pete) to 10,000 (stay a first-order Max from Jacob).

What actually happened

Jacob		Pete		Jami
5,200		15,000		16,800
0		4,500		5,800
5,200		10,500		11,000

min	max	min	max	min	max
	1,599	3,601	4,599	13,201
			999	2,801	3,599
5,200		8,200		9,601	9,999

Yikes. I wonder if Pete is kicking himself over not wagering $3,600 or $3,601 – the minimum to cover a Colbyesque wager out of Jami.

Or $4,000. That wager would have given us our first tiebreaker under the new rules.

Well, Jami has continued my string of red grades. Will she continue it tomorrow? Tune in and find out.

The Final Jeopardy! clue