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April 20, 2015

Monday, April 20, 2015

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

Alex Jacob became the first player since Julia Collins to sweep an entire week. Will he win a seventh tonight?The Final Wager – April 20, 2015

What a thrilling game this was, with both Alex and Todd making big True Daily Double wagers in the second round.

Alex

Jacob

Monica

Lott

Todd

Lovell

26,400 9,600 18,400

Speaking of Julia, we’re just a few thousand short of the total amassed by her, Ben Ingram, and Arthur Chu in the first game of the last Tournament of Champions.

All three contestants are alive with this category:

BUSINESS

Here we go.

First-order calculations

Second doubles up

If Todd doubles his score, he’ll have 36,800.

To cover this all-in wager, Alex will need to wager 10,400.

Alex
Monica
Todd
26,400 9,600 18,400
10,400 18,400
36,800 36,800
min max min max min max
10,400

An incorrect response with that wager will leave Alex with 16,000.

To stay above his total, Todd can wager up to 2,400.

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

Alex
Monica
Todd
26,400 9,600 18,400
10,400 6,400 2,400
16,000 16,000 16,000
min max min max min max
10,400 6,400* 2,400

Third doubles up

A successful doubling will put Monica at 19,200.

To cover this, Todd should wager at least 800.

Alex could wager at most 7,200.

Alex
Monica
Todd
26,400 9,600 18,400
7,200 9,600 800
19,200 19,200 19,200
min max min max min max
10,400 6,400* 800 2,400
7,200

Just in case Todd goes for the 800 wager, Monica needs to go for at least 8,000 – still, all-in.

Alex
Monica
Todd
26,400 9,600 18,400
8,000 800
17,600 17,600
min max min max min max
10,400 8,000* 800 2,400
7,200

Here’s where things stand after the first order:

Alex
Monica
Todd
26,400 9,600 18,400
FIRST-ORDER SECOND-ORDER COVER ZERO
min max min max min max
10,400 8,000* 800 2,400
7,200

Second-order calculations

Second’s max vs. first

If Todd makes the rational maximum wager of 2,400, Alex will need to wager 5,600 to stay above him.

Alex
Monica
Todd
26,400 9,600 18,400
5,600 2,400
20,800 20,800
min max min max min max
10,400 8,000* 800 2,400
5,600

In that case, Todd would have to wager 13,600 and respond correctly. That’s another all-in wager if he’s scared that Alex isn’t playing to win.

Alex
Monica
Todd
26,400 9,600 18,400
5,600 13,600
32,000 32,000
min max min max min max
10,400 8,000* 800 2,400
5,600 13,600*

Zero wagers

Score differences:
Alex and Todd: 8,000
Alex and Monica: 16,800
Todd and Monica: 8,800

Alex
Monica
Todd
26,400 9,600 18,400
FIRST-ORDER SECOND-ORDER COVER ZERO
min max min max min max
10,400 16,000 8,000* 800 2,400
5,600 16,000*

Then we add a dollar to the minimum wagers, and subtract a dollar from the maximum wagers.

What actually happened

Alex Monica Todd
26,400 9,600 18,400
10,401 5,000 8,001
15,999 4,600 26,401
min max min max
10,401 15,999 9,600 801 2,399
5,599 18,400

Monica’s wager makes no sense – she doesn’t even give herself a chance to win! The ol’ black wager for her.

Todd gets a red because he’s not covering the small range out of Alex – plus, he left a whopping $10,399 on the table. Shame. I hear Sony Pictures Studios could use the money after its recent email issue.

More analysis of Alex’s play coming up tomorrow.

The Final Jeopardy! clue

BUSINESS
THIS SOCIAL MEDIA COMPANY LAUNCHED IN OCTOBER 2010; IN 2012, WITH ABOUT A DOZEN EMPLOYEES & NO REVENUE, IT SOLD FOR $1 BILLION
Correct response: Show
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