Friday, April 3, 2015

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It’s Friday, so of course our players are giving me extra work tonight.

Later in the post, I’ll discuss Tom’s Antepenultimate Wager – I didn’t like it all that much.

Here’s how things stand heading into Final:

Kerry Greene	Tom Imler	Pat Kavanaugh
11,600	20,800	8,000

We’ve got this category to decide today’s game:

EUROPEAN HISTORY

This is a two-horse race. Pat has less than the difference between Tom and Kerry, so she is effectively eliminated.

First-order calculations

Second doubles up

If Kerry doubles her score, she’ll have 23,200.

To cover this all-in wager, Tom will need to wager 2,400.

Kerry		Tom		Pat
11,600		20,800		8,000
11,600		2,400
23,200		23,200
min	max	min	max	min	max
		2,400

An incorrect response with that wager will leave Tom with 18,400.

To get above his total, Kerry must wager at least 6,800. Might as well go for broke.

Kerry		Tom		Pat
11,600		20,800		8,000
6,800		2,400
18,400		18,400
min	max	min	max	min	max
6,800*		2,400

A successful doubling will put Pat at 16,000.

To cover this, Kerry should wager at least 4,400.

Tom could wager at most 4,800.

Kerry		Tom		Pat
11,600		20,800		8,000
4,400		4,800		8,000
16,000		16,000		16,000
min	max	min	max	min	max
6,800*		2,400	4,800

That’s pretty much it! And yet…

What actually happened

Kerry		Tom		Pat
11,600		20,800		8,000
11,598		9,300		5,000
23,198		11,500		13,000
		min	max
11,600		2,401	4,799

…Tom leaves the door open for Pat for no reason at all. (I’m less concerned about falling below a zero wager by Kerry – she’s shown herself to be a smart wagerer, and won’t be doing anything stupid.)

I can understand a desire to rake in some extra cash on a strong category but it should never – ever – come at the cost of allowing an eliminated player back into the game. In short, this is a bit of a Clavin.

The Antepenultimate Wager

How do you feel about BIG BUSINESS? That’s the question Tom faced when he found the last Daily Double under the $1200 clue in that category. All that remained was an $800 clue.

He had a sizable lead over Kerry – enough that he could put it away immediately. Alex even made a comment to this effect.

Kerry	Tom	Pat
11,600	16,800	8,000

Let’s start by assuming he loves the category. So let’s put it away now!

Worst-case scenario is that Kerry gets the remaining $800 clue, putting her at 12,400. So Tom would need to have 24,801.

Kerry		Tom		Pat
11,600		16,800		8,000
800		8,001
12,400		24,801

If he’s wrong with that wager, he’ll have $8,799 – still very much alive.

Now, if he doesn’t like this category, I suggest he wager to get above 1.5 times Kerry’s score. This means she would have to get it right in Final to have a chance.

To find the target number, take one-half of Kerry’s worst-case score and add it to her present score. One half of 12,400 is 6,200; together, those equal 18,600.

(For more on this math, see my discussion of break points.)

Kerry		Tom		Pat
11,600		16,800		8,000
800		1,801
12,400		18,601

As it was, Tom’s wager of 3,200 eliminated Pat from contention for the time being, although she could have gotten back in had she (or Kerry) nabbed that final clue. (Except that whole thing didn’t matter!)

Beware the siren’s call of round numbers.

The Final Jeopardy! clue

EUROPEAN HISTORY

A 3-LETTER 9th CENTURY TRIBE IS IN THE NAMES OF 2 21st CENTURY COUNTRIES: THE WORLD’S MOST VAST, & THIS ONE

[spoiler]What is Belarus? (For the Rus tribe)[/spoiler]

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