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July 6, 2015

Monday, July 6, 2015

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To me, nothing says America like bad math – something we’ve seen all too often lately!The Final Wager – July 6, 2015

We had a good game tonight – will we keep it up in Final?

Hilary

Carney

Shu-Ping

Shen

Jess

Lindoerfer

17,800 11,400 15,400

Here’s our category:

THE OSCARS

First-order calculations

Second doubles up

If Jess doubles her score, she’ll have 30,800.

To cover this all-in wager, Hilary will need to wager 13,000.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
13,000 15,400
30,800 30,800
min max min max min max
13,000

An incorrect response with that wager will leave Hilary with 4,800.

To stay above her total, Jess can wager up to 10,600.

Shu-Ping can wager up to 6,600.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
13,000 6,600 10,600
4,800 4,800 4,800
min max min max min max
13,000 6,600 10,600

Third doubles up

A successful doubling will put Shu-Ping at 22,800.

To cover this, Jess should wager at least 7,400.

Hilary would need to wager at least 5,000, but leaves herself prone to getting overtaken by Jess.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
5,000 11,400 7,400
22,800 22,800 22,800
min max min max min max
13,000 6,600 10,600
7,400
5,000

If Jess is incorrect with that wager, Shu-Ping can wager up to 3,400 to stay above her total. He’d also want to wager 1,400 to cover an incorrect Hilary response.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
3,400 7,400
8,000 8,000
min max min max min max
13,000 6,600 10,600
1,400 3,400 7,400
5,000

Here’s where things stand after the first order:

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
FIRST-ORDER SECOND-ORDER COVER ZERO
min max min max min max
13,000 6,600 10,600
1,400 3,400 7,400
5,000

Second-order calculations

Second’s max vs. first

If Jess makes the rational maximum wager of 10,600, Hilary will need to wager 8,200 to cover her.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
8,200 10,600
26,000 26,000
min max min max min max
13,000 6,600 10,600
5,000 1,400 3,400 7,400
8,200

If she’s wrong with that wager, she’ll be left with 9,600.

To stay above her, Jess can wager up to 5,800.

Shu-Ping may risk up to 1,800.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
8,200 1,800 5,800
9,600 9,600 9,600
min max min max min max
13,000 6,600 7,400 10,600
5,000 1,400 1,800 5,800
8,200 3,400

Third’s max vs. second

Against Jess, Shu-Ping can wager at most 3,400. With a correct response, he’ll have 14,800.

To stay above this, Jess can wager at most 600.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
3,400 600
14,800 14,800
min max min max min max
13,000 6,600 7,400 10,600
5,000 1,400 1,800 5,800
8,200 3,400 600

If she is correct, Jess will have 16,000.

To account for this, Shu-Ping will need to wager at least 4,600.

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
4,600 600
16,000 16,000
min max min max min max
13,000 4,600 6,600 7,400 10,600
5,000 1,400 1,800 5,800
8,200 3,400 600

Now, after two orders of analysis:

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
FIRST-ORDER SECOND-ORDER COVER ZERO
min max min max min max

Zero wagers

Score differences:
Hilary and Jess: 2,400
Hilary and Shu-Ping: 6,400
Jess and Shu-Ping: 4,000

Hilary
Shu-Ping
Jess
17,800 11,400 15,400
FIRST-ORDER SECOND-ORDER COVER ZERO
min max min max min max
13,000 6,400 6,600 7,400 8,000
5,000 6,400 1,400 1,800 4,800 5,800
8,200 3,400 2,400 4,000

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

What actually happened

Hilary Shu-Ping Jess
17,800 11,400 15,400
12,400 1,601 2,401
5,400 13,001 17,801
min max min max min max
13,001 6,401 6,599 7,401 7,999
5,001 6,399 1,401 1,799 4,801 5,799
8,201 3,399 2,401 3,999

Looks like Shu-Ping was thinking ahead, and predicting that 2,401 wager out of Jess. I’m guessing Hilary made a mistake with the math. Check! Double-check! Triple-check!

At first I gave Jess a pink, but I upgraded her to an orange – although the 4,801 wager is probably better in most circumstances, I just don’t see Hilary wagering less than 5,001, particularly against two knowledgeable opponents. Plus that larger range would make Jess fall below Shu-Ping’s pre-Final total.

Maybe the 599 wager makes more sense for Jess if she doesn’t want to cover Shu-Ping. Tough call.

Another new champ!

The Final Jeopardy! clue

THE OSCARS
“GLADIATOR” IS CLOSE, BUT THIS FILM HAS THE EARLIEST HISTORICAL SETTING OF ANY BEST PICTURE OSCAR WINNER
Correct response: Show
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