June 15, 2015

Monday, June 15, 2015

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Dark Lord is back for his fourth game – and a crack at solidifying his TOC potential.

Wow – a really tight game up until the end, when Brennan nabbed a couple of big clues. In any event, all three players could win despite an incorrect answer in Final:

Dark Lord

Harris-Fain

Amy

Merrick

Brennan

Bushee

13,000

13,600

19,000

Tonight’s Final Jeopardy! category is:

19th CENTURY POETRY

Given that, I’m guessing Dark Lord will push all his chips to the middle. The other players should follow suit to cover him. We’ll go through the calculations anyway.

First-order calculations

Second doubles up

If Amy doubles her score, she’ll have 27,200.

To cover this all-in wager, Brennan will need to wager 8,200.

Dark Lord		Amy		Brennan
13,000		13,600		19,000
		13,600		8,200
		27,200		27,200

min	max	min	max	min	max
				8,200

An incorrect response with that wager will leave Brennan with 10,800.

To stay above his total, Amy can wager up to 2,800.

Dark Lord can wager up to 2,200.

Dark Lord		Amy		Brennan
13,000		13,600		19,000
2,200		2,800		8,200
10,800		10,800		10,800

min	max	min	max	min	max
	2,200		2,800	8,200

Third doubles up

A successful doubling will put Dark Lord at 26,000.

To cover this, Amy should wager at least 12,400. In this case, though, she will lose on an incorrect response, so she might as well wager everything.

Dark Lord		Amy		Brennan
13,000		13,600		19,000
13,000		12,400		7,000
26,000		26,000		26,000

min	max	min	max	min	max
	2,200	12,400*		8,200
			2,800

Here’s where things stand after the first order:

Dark Lord		Amy		Brennan
13,000		13,600		19,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	2,200	12,400*		8,200
			2,800

Second-order calculations

Second’s max vs. first

If Amy makes the rational maximum wager of 2,800, Brennan will need to wager 2,600 to stay above her. Probably not a good move here.

Dark Lord		Amy		Brennan
13,000		13,600		19,000
		2,800		2,600
		16,400		16,400

min	max	min	max	min	max
	2,200	12,400*		8,200
			2,800
					2,600

In that case, Amy would have to wager 8,000 and respond correctly, but she’s already got a logical all-in range.

Dark Lord might consider risking at least 8,600 (read: everything).

Dark Lord		Amy		Brennan
13,000		13,600		19,000
8,600		8,000		2,600
21,600		21,600		21,600

min	max	min	max	min	max
	2,200	12,400*		8,200
8,600*			2,800
					2,600

Third’s max vs. first

Amy could cover Dark Lord with a smaller range, if she’s willing to take the risk.

Dark Lord		Amy		Brennan
13,000		13,600		19,000
2,200		1,600
15,200		15,200

min	max	min	max	min	max
	2,200	12,400*		8,200
8,600*		1,600	2,800
					2,600

Dark Lord should cap his wager at 1,000.

Dark Lord		Amy		Brennan
13,000		13,600		19,000
1,000		1,600
12,000		12,000

min	max	min	max	min	max
	1,000	12,400*		8,200
8,600*		1,600	2,800
	2,200				2,600

Now, after two orders of analysis:

Dark Lord		Amy		Brennan
13,000		13,600		19,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	1,000	12,400*		8,200
8,600*		1,600	2,800
	2,200				2,600

Zero wagers

Score differences:
Brennan and Amy: 5,400
Brennan and Dark Lord: 6,000
Amy and Dark Lord: 600

Dark Lord		Amy		Brennan
13,000		13,600		19,000
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
600	1,000	12,400*		8,200	10,800
1,200	2,200	1,600	2,800
8,600*					2,600

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

What actually happened

Dark Lord		Amy		Brennan
13,000		13,600		19,000
12,500		12,401		8,201
25,500		26,001		27,201

min	max	min	max	min	max
601	999	13,600		8,201	10,799
1,201	2,199	1,601	2,799
13,000					2,599

Dark Lord’s reign comes to an end, but not before he takes home $63,000. Great work!

Brennan came to play, though, amassing that total without the benefit of a Daily Double. We’ll see how he does tomorrow!

The Final Jeopardy! clue