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May 19, 2015

Tuesday, May 19, 2015

Andrew Haringer has won three games, all from behind. What will happen in his fourth?The Final Wager – May 19, 2015

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”
Correct response: Show
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3 Comments
  1. Tom permalink

    Andrew seems to be one of those players who wager based on category rather than game theory, even though he can wager pretty well from second when he wants to (game 3).

  2. Dont know if I’d go Red for Liz here, 2nd over wagers a big enough percent of the time to make it a viable wager (note I’m not arguing its good game theory, but ignoring observed betting patterns isnt wise either). Maybe a light pink :)

    • Kelly permalink

      Since Liz can both get into range if Andrew wagers the minimum to cover her while at the same time remaining above Todd’s MSBIW that’s probably her best range (and since she can additionally cover both opponents’ zero wagers that narrows it further). If the two ranges were mutually exclusive then her choice would have more justification, but since she doesn’t have to choose her wager gets the “bad but not terrible” grade IMO.

What do you think?