Wednesday, July 29, 2015

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Hey! Look what I found! I won’t go thirsty tonight!

It’s the dregs of a bottle of Gosling’s Black Rum! I’ll need it after this – seriously, what was everyone thinking here? (Calculations are below the post.)

Jonathan		Jennifer		Colby
18,100		10,800		15,200
18,100		10,786		15,000
0		14		200
min	max	min	max	min	max
12,301	14,599	801	1,999	6,401	8,799
6,501	7,299	4,401	4,999	2,901	3,599
3,501	5,799

I joked about this last week, but due to popular demand, I’ve opened a fundraiser for my liquor cabinet.

Now if you’ll excuse me, I’m off to the bar.

The Final Jeopardy! clue

WOMEN AUTHORS

THIS WOMAN WHO PASSED AWAY IN 2015 WROTE WHAT IS BILLED AS AUSTRALIA’S “GONE WITH THE WIND”

[spoiler]Who was Colleen McCullough? (the novel in question was The Thorn Birds)[/spoiler]

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First-order calculations

Second doubles up

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

To cover this all-in wager, Jonathan will need to wager 12,300.

Jonathan		Jennifer		Colby
18,100		10,800		15,200
12,300				15,200
30,400				30,400
min	max	min	max	min	max
12,300

An incorrect response with that wager will leave Jonathan with 5,800.

To stay above his total, Colby can wager up to 9,400.

Jennifer can wager up to 5,000.

Jonathan		Jennifer		Colby
18,100		10,800		15,200
12,300		5,000		9,400
5,800		5,800		5,800
min	max	min	max	min	max
12,300			5,000		9,400

Third doubles up

A successful doubling will put Jennifer at 21,600.

To cover this, Colby should wager at least 6,400.

(Jonathan would need to wager at least 3,500, but this is somewhat questionable.)

Jonathan		Jennifer		Colby
18,100		10,800		15,200
3,500		10,800		6,400
21,600		21,600		21,600
min	max	min	max	min	max
12,300			5,000	6,400	9,400
3,500

If Colby is incorrect with that wager, Jennifer can wager up to 2,000 to stay above his total.

Jonathan		Jennifer		Colby
18,100		10,800		15,200
		2,000		6,400
		8,800		8,800
min	max	min	max	min	max
12,300			2,000	6,400	9,400
			5,000
3,500

We’ll throw in the 3,800 minimum for Jennifer to cover Jonathan’s small range.

Jonathan		Jennifer		Colby
18,100		10,800		15,200
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
12,300			2,000	6,400	9,400
		3,800	5,000
3,500

Second-order calculations

Second’s max vs. first

If Colby makes the rational maximum wager of 9,400, Jonathan will need to wager 6,500 to cover him.

Jonathan		Jennifer		Colby
18,100		10,800		15,200
6,500				9,400
24,600				24,600
min	max	min	max	min	max
12,300			2,000	6,400	9,400
6,500		3,800	5,000
3,500

If he’s wrong with that wager, he’ll be left with 11,600.

To stay above him, Colby can wager up to 3,600.

Jennifer might consider risking at least 800.

Jonathan		Jennifer		Colby
18,100		10,800		15,200
6,500		800		3,600
11,600		11,600		11,600
min	max	min	max	min	max
12,300		800	2,000	6,400	9,400
6,500		3,800	5,000		3,600
3,500

That should be enough of a range for our players.

Zero wagers

Score differences:
Jonathan and Colby: 2,900
Jonathan and Jennifer: 7,300
Colby and Jennifer: 4,400

Jonathan		Jennifer		Colby
18,100		10,800		15,200
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
12,300	14,600	800	2,000	6,400	8,800
6,500	7,300	4,400	5,000	2,900	3,600
3,500	5,800