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March 4, 2015

Wednesday, March 4, 2015

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There’s something in the water this week at Sony Pictures Studios – and I want whatever it is.The Final Wager – March 4, 2015

On average, around 8.5 players each week enter Final Jeopardy! with five-digit scores.

So far this week, we’ve had eight – and the lone holdout, Leslie from Monday’s game, was just 300 short.

Alvin

Chin

Dave

Perkins

Laura

Lorson

13,200 16,200 11,400

A nice historical category to decide tonight’s winner (and possibly a big payday):

PRESIDENTS AND THE WHITE HOUSE

This one’s trickier than it looks at first.

First-order calculations

Second doubles up

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

To cover this all-in wager, Dave will need to wager 10,200.

Alvin Dave Laura
13,200 16,200 11,400
13,200 10,200
26,400 26,400

An incorrect response with that wager will leave Dave with 6,000.

To stay above his total, Alvin can wager up to 7,200. Laura can wager up to 5,400.

Alvin Dave Laura
13,200 16,200 11,400
7,200 10,200 5,400
6,000 6,000 6,000

Third doubles up

A successful doubling will put Laura at 22,800.

To cover this, Alvin should wager at least 9,600. Dave would need to wager at least 6,600.

Alvin Dave Laura
13,200 16,200 11,400
9,600 6,600 11,400
22,800 22,800 22,800

Alvin is in Stratton’s Dilemma: if he covers Laura and gets it wrong, he’ll lose to Dave. If he chooses this route, therefore, he should go all-in.

Here’s where things stand after the first order:

Second-order calculations

Second’s max vs. first

If Alvin makes the rational maximum wager of 7,200, Dave will need to wager 4,200 to cover him.

Alvin Dave Laura
13,200 16,200 11,400
7,200 4,200
20,400 20,400

But at that rate, he might as well cover Laura, too.

Third’s max vs. first

Maybe Laura goes for her 5,400 maximum. In that case, Alvin should wager 3,600, and Dave, 600.

Alvin Dave Laura
13,200 16,200 11,400
3,600 600 5,400
16,800 16,800 16,800

If Alvin’s wrong, Laura can wager up to 1,800 to stay above him.

Alvin Dave Laura
13,200 16,200 11,400
3,600 1,800
9,600 9,600

And now, after the second order:

Zero wagers

What happens when each player wagers against potential zero and Colbyesque wagers from their opponents? We run into a problem.

Laura is almost forced to wager 1,800 in that lower range, which has knock-on effect to the other players. If she adds a dollar, she covers a zero wager by Alvin (unlikely); if she withholds a dollar, she can stay above a wager to tie by Dave if he aims to cover her all-in (even more unlikely).

In her shoes, I would be more aggressive, and max out at 5,399.

What actually happened

Laura’s wager is fine, of course, but I need to judge based on the math. Either way, she’s got the money, and a second date with the signaling devices tomorrow.

The Final Jeopardy! clue

PRESIDENTS AND THE WHITE HOUSE
WHEN THE CURRENT PRESIDENTIAL OCCUPANT OF THE WHITE HOUSE WAS BORN, THIS PRESIDENT WAS LIVING THERE
Correct response: Show
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One Comment
  1. Perfect wager by Laura. She needs a triple stumper. Chance that 1st and 2nd don’t bet big enough to drop below her current score is essentially 0. Probability that they both don’t wager enough to cover Laura’s double is also pretty low, so she really needs them both to miss to have any realistic shot. Triple stumper occurs twice as likely as a single get by Laura (19% vs 9%), so by far her most likely winning scenario is a triple stumper, therefore betting 0 is the best play.

What do you think?