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July 10, 2015

Friday, July 10, 2015

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This week: Four games, four champs… will Kathy stem the tide?The Final Wager – July 10, 2015

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

19th CENTURY BRITISH LITERATURE
“I OUGHT TO BE THY ADAM, BUT I AM RATHER THE FALLEN ANGEL” IS SPOKEN TO THIS TITLE CHARACTER BY HIS CREATION
Correct response: Show
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