Tuesday, May 19, 2015

Andrew Haringer has won three games, all from behind. What will happen in his fourth?

He’s gonna need to do it again.

Andrew Haringer	Todd Grabarsky	Liz Rapelye
13,200	13,600	7,400

Tonight’s Final Jeopardy! category is:

EUROPEAN CITIES

Remember that yesterday, Andrew played it safe and won by a dollar.

First-order calculations

Second doubles up

If Andrew doubles his score, he’ll have 26,400.

To cover this all-in wager, Todd will need to wager 12,800.

Andrew		Todd		Liz
13,200		13,600		7,400
13,200		12,800
26,400		26,400
min	max	min	max	min	max
		12,800

An incorrect response with that wager will leave Todd with 800.

To stay above his total, Andrew can wager up to 12,400.

Liz can wager up to 6,600.

Andrew		Todd		Liz
13,200		13,600		7,400
12,400		12,800		6,600
800		800		800
min	max	min	max	min	max
	12,400	12,800			6,600

Third doubles up

A successful doubling will put Liz at 14,800.

To cover this, Andrew should wager at least 1,600.

Todd would need to wager at least 1,200.

Andrew		Todd		Liz
13,200		13,600		7,400
1,600		1,200		7,400
14,800		14,800		14,800
min	max	min	max	min	max
1,600	12,400	12,800			6,600
		1,200

Liz would need to wager at least 5,000 to get above Todd if he makes that play.

Andrew		Todd		Liz
13,200		13,600		7,400
1,600		1,200		5,000
11,600		12,400		12,400
min	max	min	max	min	max
1,600	12,400	12,800		5,000	6,600
		1,200

Here’s where things stand after the first order:

Andrew		Todd		Liz
13,200		13,600		7,400
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,600	12,400	12,800		5,000	6,600
		1,200

Second-order calculations

Mind games don’t make a ton of sense here. Todd and Andrew are too close in score for Todd to go for less than the lockout wager; there’s also no downside to Andrew covering a double-up by Liz rather than, say, wager 800 to cover her maximum against Todd.

Zero wagers

Score differences:
Todd and Andrew: 400
Todd and Liz: 6,200
Andrew and Liz: 5,800

Andrew		Todd		Liz
13,200		13,600		7,400
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
1,600	5,800	12,800		6,200	6,600
	11,600
	12,400	1,200	6,200	5,000

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

What actually happened

Andrew		Todd		Liz
13,200		13,600		7,400
13,200		12,801		1,600
26,400		799		5,800
min	max	min	max	min	max
1,601	5,799	12,801		6,201	6,599
	11,599	1,201	6,199

A few questions about Andrew:

Why? That’s such a completely reckless wager, when holding back even $800 would be far better.

How? He’s picked his spots perfectly: all-in both times he got Final right, and conservatively both times he got Final wrong.

What? … the hell is going on? (Note that this question is distinct from WHAAAAAT?)

Andrew has now won 4 games and $72,399 – all from second, the first time that’s happened to my knowledge. Using the same baseline assumptions that I did for Kerry Greene’s run, the odds of him pulling this off given the actual wagers are:

Game 1: 3/8 (WRx, WWW)
Game 2: 1/4 (WRx)
Game 3: 1/2 (Wxx)
Game 4: 1/4 (WRx)

Overall: 3/256 = 1.17%

The Final Jeopardy! clue

EUROPEAN CITIES

THE EUROPEAN CENTRAL BANK IS BASED IN THIS CITY SOMETIMES CALLED “MAINHATTAN”

[spoiler]What is Frankfurt?[/spoiler]

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