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!

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