Monday, November 9, 2015 – ToC2015 QF #1

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We’re off and running in the 2015 Tournament of Champions! Will Dan, Vaughn, or Catherine earn the first semifinal berth?

Are you in the #Vaughntourage!?…

…or are you a #FanofDan?

What a rush this episode was! My model had Catherine in the lead heading into Final – but not with scores like this.

Dan Feitel	Vaughn Winchell	Catherine Hardee
7,800	17,200	17,800

Everyone’s in decent position with this Final Jeopardy! category:

AMERICAN AUTHORS

I built a calculator to derive optimal wagers depending on a player’s confidence level in the category. It uses all past non-winning scores from ToCs.

I’ll write about it in more depth later this week, but here’s what it says:

	Dan	Vaughn	Catherine
	7,800	17,200	17,800
Current percentile	54%	95%	96%
20% confidence	0	400	0
30% confidence	0	400	0
40% confidence	5,300	400	0
50% confidence	5,300	400	0
60% confidence	5,300	400	800
70% confidence	7,300	400	800
80% confidence	7,300	2,900	2,300

Now, one thing the calculator does not take into account is winning outright – to see what everyone should do there, we’ll do some old-school math.

First-order calculations

My first assumption is that Vaughn will wager Shoretegically – that is, he’ll keep Dan locked out no matter what. He can max out at 1,600, and Catherine can cover him with a wager of 1,000.

Dan		Vaughn		Catherine
7,800		17,200		17,800
FIRST-ORDER		SECOND-ORDER		COVER ZERO
min	max	min	max	min	max
			1,600	1,000

Second-order calculations

Now, as you’ll see in my video, I think maybe Vaughn will take Catherine’s potential 1,000 wager into account and cap his bet at 399, but that’s probably going too far, right?

Right?

What actually happened

Dan		Vaughn		Catherine
7,800		17,200		17,800
6,200		601		200
14,000		16,599		17,600
		min	max	min	max
		601	1,599	1,001	1,199
			399		199

…and then Catherine comes out of nowhere with a fourth-level wager of 200. Note that if Vaughn had indeed wagered 399 and gotten it right, Catherine would have won by a dollar!

Seriously – someone’s been doing her homework when it comes to wagering! Huge gold star for Catherine, and my sincere gratitude to all three players for a spectacular start to the tournament.

Quarterfinal winners:

1. Catherine Hardee

Wild-card race:

1. Vaughn Winchell – 16,599 (98%)
2. Dan Feitel – 14,000 (84%)

Percentage represents probability of advancing based on past ToC data. Although it’s not a Gaussian distribution, the average non-winning score is 8,290 with standard deviation 6,306.

The Final Jeopardy! clue

AMERICAN AUTHORS

HE WAS THE FIRST TO HAVE BOTH FICTION AND NONFICTION NUMBER ONE NEW YORK TIMES BEST SELLERS; THE LATTER FEATURED HIS BELOVED POODLE

[spoiler]Who was John Steinbeck?[/spoiler]

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