July 10, 2015

Friday, July 10, 2015

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This week: Four games, four champs… will Kathy stem the tide?

She might need a bit of help.

Kathy

Riley

Rob

Seidenwurm

H.B.

Taylor

11,600

7,700

12,600

Good work by H.B. heading to the $400 clue at the end instead of the $2,000 – kept his lead securely in his grasp.

Tonight’s Final Jeopardy! category is:

19th CENTURY BRITISH LITERATURE

Everyone’s very much alive!

First-order calculations

Second doubles up

If Kathy doubles her score, she’ll have 23,200.

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

Kathy		Rob		H.B.
11,600		7,700		12,600
11,600				10,600
23,200				23,200

min	max	min	max	min	max
				10,600

An incorrect response with that wager will leave H.B. with 2,000.

To stay above his total, Kathy can wager up to 9,600.

Rob can wager up to 5,700.

Kathy		Rob		H.B.
11,600		7,700		12,600
9,600		5,700		10,600
2,000		2,000		2,000

min	max	min	max	min	max
	9,600		5,700	10,600

Third doubles up

A successful doubling will put Rob at 15,400.

To cover this, Kathy should wager at least 3,800.

(H.B. would need to wager at least 2,800, but this is somewhat questionable.)

Kathy		Rob		H.B.
11,600		7,700		12,600
3,800		7,700		2,800
15,400		15,400		15,400

min	max	min	max	min	max
3,800	9,600		5,700	10,600

				2,800

Rob would need to wager at least 100 against Kathy.

Kathy		Rob		H.B.
11,600		7,700		12,600
3,800		100
7,800		7,800

min	max	min	max	min	max
3,800	9,600	100	5,700	10,600

				2,800

Just in case, we’ll also say he needs to wager 2,100 against H.B.

Here’s where things stand after the first order:

Kathy		Rob		H.B.
11,600		7,700		12,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
3,800	9,600	2,100	5,700	10,600
		100
				2,800

Second-order calculations

Second’s max vs. first

If Kathy makes the rational maximum wager of 9,600, H.B. will need to wager 8,600 to cover her. They’re too close to make this a feasible play, though, but we can tighten up the others’ ranges.

He’ll be left with 4,000. To stay above him, Kathy can wager up to 7,600, and Rob may risk up to 3,700.

Kathy		Rob		H.B.
11,600		7,700		12,600
7,600		3,700		8,600
4,000		4,000		4,000

min	max	min	max	min	max
3,800	7,600	2,100	3,700	10,600
	9,600	100
			5,700	2,800

Third’s max vs. first

If Rob goes for 5,700, Kathy could cover him with 1,800. If H.B.’s 2,800 was questionable, 800 is even more so.

Kathy		Rob		H.B.
11,600		7,700		12,600
1,800		5,700		800
13,400		13,400		13,400

min	max	min	max	min	max
3,800	7,600	2,100	3,700	10,600
1,800	9,600	100
			5,700	2,800

An incorrect response with that wager will leave Kathy with 9,800. Again, I’m unconcerned about H.B. wagering 800.

Kathy		Rob		H.B.
11,600		7,700		12,600
1,800		2,100		800
9,800		9,800		11,800

min	max	min	max	min	max
3,800	7,600	2,100	3,700	10,600
1,800	9,600	100
			5,700	2,800

Now, after two orders of analysis:

Kathy		Rob		H.B.
11,600		7,700		12,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
3,800	7,600	2,100	3,700	10,600
1,800	9,600	100
			5,700	2,800

Zero wagers

Score differences:
H.B. and Kathy: 1,000
H.B. and Rob: 4,900
Kathy and Rob: 3,900

Kathy		Rob		H.B.
11,600		7,700		12,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
3,800	3,900	2,100	3,700	10,600
	7,600	100
1,800		4,900	5,700	2,800	4,900

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

What actually happened

Kathy		Rob		H.B.
11,600		7,700		12,600
3,801		2,371		10,601
7,799		5,329		23,201

min	max	min	max	min	max
3,801	3,899	4,901	5,699	10,601
	7,599	2,101	3,699
1,801				2,801	4,899

Great job, everyone! I can head into this weekend with a smile on my face.

The Final Jeopardy! clue