Wednesday, April 15, 2015

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For an overall analysis of Alex’s strategies, check out this post.

Happy tax day to my fellow Americans. We’ll have to see how pleased the IRS is with tonight’s winnings…

Well, it took four games and a $100 Daily Double, but Alex is finally within reach. And not only within reach – barring a terrible wager out of Becky, he’ll have to get it right to win.

Alex Jacob	Doug Butler	Becky Hammer
20,700	1,600	18,600

Tonight’s Final Jeopardy! category is:

THE GREEK ALPHABET

Now, Alex is officially 0/3 on Final Jeopardy!, but I’m guessing he’d really be 2/3 if someone had stuck his feet in the fire. We’ll see what he does here.

First-order calculations

Second doubles up

If Becky doubles her score, she’ll have 37,200.

To cover this all-in wager, Alex will need to wager 16,500.

Alex		Doug		Becky
20,700		1,600		18,600
16,500				18,600
37,200				37,200
min	max	min	max	min	max
16,500

An incorrect response with that wager will leave Alex with 4,200.

To stay above his total, Becky can wager up to 14,400.

Alex		Doug		Becky
20,700		1,600		18,600
16,500				14,400
4,200				4,200
min	max	min	max	min	max
16,500					14,400

Third doubles up

A successful doubling will put Doug at 3,200.

To stay above him, Becky can wager at most 15,400, but that’s too much, so we’ll ignore it.

Alex could wager at most 17,500.

Alex		Doug		Becky
20,700		1,600		18,600
17,500		1,600		15,400
3,200		3,200		3,200
min	max	min	max	min	max
16,500	17,500				14,400

Here’s where things stand after the first order:

Alex		Doug		Becky
20,700		1,600		18,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
16,500	17,500				14,400

Second-order calculations

Second’s max vs. first

Alex and Becky are too close for Alex to play any mind games.

Unless he can predict to within a reasonable range what Becky is going to wager, Alex should either play for the lockout or go for the Colbyesque wager.

Becky might want to restrict her maximum wager, however, just in case Alex gets tricky.

On the upside, Alex might wager 12,300…

Alex		Doug		Becky
20,700		1,600		18,600
12,300				14,400
33,000				33,000

…which means Becky might want to top off at 10,200.

Alex		Doug		Becky
20,700		1,600		18,600
12,300				10,200
8,400				8,400
min	max	min	max	min	max
16,500	17,500				10,200
					14,400

For

Zero wagers

Score differences:
Alex and Becky: 2,100

Alex		Doug		Becky
20,700		1,600		18,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
16,500	17,500			4,200	10,200
	2,100				14,400

Becky should wager at least twice their difference (4,200) to account for the possibility that Alex will go small.

What actually happened

Alex		Doug		Becky
20,700		1,600		18,600
16,501		1,500		2,101
37,201		100		16,499
min	max			min	max
16,501	17,499			4,201	10,199
	2,099				14,399

Not noticing this, apparently, Becky wagered to cover a zero from Alex. It didn’t matter, because Alex went for the outright win and nailed it.

This was a weird game, with all three players hunting for the Daily Doubles. I was hoping Becky might continue the theme of “copy Alex’s strategy” on that final DD with a $12,000 all-in bet, but she wagered just $3,000. It’s a good thing she got Final wrong, because she probably would be kicking herself in hindsight.

A few items of note.

First, Alex’s poker face is amusing:

Second, I can’t be the only one who was reminded of a certain music video thanks to the Neil deGrasse Tyson clues:

Third, the last two categories in the Jeopardy! round were NEW ENGLAND PATRIOTS and DIE FLEDERMAUS. Or, if you prefer, DEFLATOR-MAUS. (Very funny, writers.)

Fourth, and finally, all three clues so far this week have been two-parters.

The Final Jeopardy! clue

THE GREEK ALPHABET

WHEN SPELLED OUT AS WORDS IN ENGLISH, 2 OF THE 3 LONGEST GREEK LETTERS

[spoiler]What are (2 of) epsilon, upsilon, and omicron?[/spoiler]

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