Tuesday, April 7, 2015

previous week					same week					following week
30	31	1	2	3	6	7	8	9	10	13	14	15	16	17

Two games in a row now, Kerry Greene has won from behind in Final. How will she enter the last round in her fifth game?

Same deal. Another exciting game.

Kerry Greene	Jan Schwartzberg	Evan Bick
18,500	7,400	22,600

Kerry’s streak might depend on this Final Jeopardy! category:

CELEBRITY FATHERS & DAUGHTERS

It also might depend on the wagering.

Remember, we save the dollar changes until the end.

First-order calculations

Second doubles up

If Kerry doubles her score, she’ll have 37,000.

To cover this all-in wager, Evan will need to wager 14,400.

Kerry		Jan		Evan
18,500		7,400		22,600
18,500				14,400
37,000				37,000
min	max	min	max	min	max
				14,400

An incorrect response with that wager will leave Evan with 8,200.

To stay above his total, Kerry can wager up to 10,300.

Jan must respond correctly to have a shot, so all-in is the way to go.

Kerry		Jan		Evan
18,500		7,400		22,600
10,300		800		14,400
8,200		8,200		8,200
min	max	min	max	min	max
	10,300	800*		14,400

Third doubles up

A successful doubling will put Jan at 14,800.

To stay above her, Kerry can wager at most 3,700.

Evan could wager at most 7,800.

Kerry		Jan		Evan
18,500		7,400		22,600
3,700		7,400		7,800
14,800		14,800		14,800
min	max	min	max	min	max
	10,300	800*		14,400
	3,700
					7,800

Here’s where things stand after the first order:

Kerry		Jan		Evan
18,500		7,400		22,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
	10,300	800*		14,400
	3,700
					7,800

Second-order calculations

Quasi-Shoretegic wagers

If Kerry chooses to stay above a double-up by Jan, she will have at most 22,200.

Evan can stay above that total by wagering no more than 400.

Kerry		Jan		Evan
18,500		7,400		22,600
3,700				400
22,200				22,200
min	max	min	max	min	max
	10,300	800*		14,400	400
	3,700
					7,800

Not quite a Shore’s situation because Kerry can’t cover a zero wager by Evan.

If she’s afraid he’ll get cute, Kerry must wager 4,500.

Kerry		Jan		Evan
18,500		7,400		22,600
4,500				400
23,000				22,200
min	max	min	max	min	max
4,500	10,300	800*		14,400	400
	3,700
					7,800

Second’s max vs. first

If Kerry makes the rational maximum wager of 10,300, Evan will need to wager 6,200 to cover her.

Kerry		Jan		Evan
18,500		7,400		22,600
10,300				6,200
28,800				28,800
min	max	min	max	min	max
4,500	10,300	800*		14,400	400
	3,700
				6,200	7,800

If he’s wrong with that wager, he’ll be left with 16,400.

To stay above him, Kerry can wager up to 2,100.

Kerry		Jan		Evan
18,500		7,400		22,600
2,100				6,200
16,400				16,400
min	max	min	max	min	max
4,500	10,300	800*		14,400	400
	2,100
	3,700			6,200	7,800

Now, after two orders of analysis:

Kerry		Jan		Evan
18,500		7,400		22,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
4,500	10,300	800*		14,400	400
	2,100
	3,700			6,200	7,800

Zero wagers

Score differences:
Evan and Kerry: 4,100
Evan and Jan: 15,200
Kerry and Jan: 11,100

Kerry		Jan		Evan
18,500		7,400		22,600
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
8,200	10,300	800*		14,400	15,200
	2,100				400
	3,700			6,200	7,800

Now that we’ve paired off the tightest possible ranges, we add a dollar to the minimum wagers, and subtract a dollar from the maximum wagers.

What actually happened

Kerry		Jan		Evan
18,500		7,400		22,600
18,498		7,398		14,500
36,998		14,798		8,100
min	max			min	max
8,201	10,299	7,400		14,401	15,199
	2,099			6,201	7,799
					399

Lack of wagering skills – or straight-up confidence in her own ability? Either way, Kerry has over $125,000 and no need to apologize to me or to anyone saying she’s boring. (Hey, was that a smile she cracked at the end?)

That’s three in a row coming from behind for Kerry – in the next By the Numbers, I’m going to investigate how frequently this happens. I’m guessing twice a season, tops.

Not to beat a dead horse, but Julia Collins was the last six-game winner…

The Final Jeopardy! clue

CELEBRITY FATHERS & DAUGHTERS

HE WON A GRAMMY IN 1959, SHE WON 3 IN THE 1970s & A SONG BY BOTH WAS 1991’s SONG & RECORD OF THE YEAR

[spoiler]Who are Nat King Cole and Natalie Cole?

Eat your heart out, Tupac:

[/spoiler]

previous week					same week					following week
30	31	1	2	3	6	7	8	9	10	13	14	15	16	17