January 29, 2014

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Yesterday, our champion wagered for the tie. Will history repeat itself today?

If this analysis interests you, perhaps you’d like to check out my wagering tutorial?

Before we begin, I’m going to talk about why exactly one should wager for the tie. There are two reasons.

The first is based strictly on game theory. The whole point of Jeopardy! (see my Rule #0) is to come back the next day; you have a higher chance of doing so if you withhold that extra dollar.

Whether you’re playing a proven challenger or a random player from the pool in your next game is irrelevant. Thinking about your next game is like looking down the field for the end zone before you’ve caught the ball. You need to BE in that next game for it to matter!

The second is a mind-game tactic. If your opponent knows you’re going to wager for the tie, he might disregard a rational wager and go for broke in an attempt to tie you. There’s no downside for you if you’re right; you’ll come back the next day, with or without the challenger.

The advantage comes when you’re both wrong. With a “proper” wager, he might beat you, but with his all-in, he’ll have zero, and you’ll increase your chances of winning.

Arthur Chu: 18,200

Erik Post: 8,400

Carolyn Collins: 13,400

The Final Jeopardy! category: CAPITAL CITIES

Here’s what each player should do.

Arthur should wager 8,600 to ensure his return if he’s right.

Carolyn should wager at least 3,400 to cover a double-up by Erik, and no more than 3,800 so as not to fall below Arthur if they’re both incorrect.

Erik needs to get it right to have a shot, and wager at least 1,200 against Arthur, and 1,600 to cover a rational incorrect wager by Carolyn. At that rate, he should wager everything to maximize his chances of winning.

Now, since she’s seen Arthur wager for the tie already, Carolyn is fully justified in wagering everything – not a dollar less! And that’s what she did, and she’s rewarded with $26,800 and an invitation to Thursday’s match.

To demonstrate my second point above, let’s look at what would have happened had the question turned out to be a head-scratcher. Arthur would have won by virtue of being the only player with money.

Now, had Carolyn wagered “rationally” and the clue stumped all three participants, she would have emerged victorious. Yet, Arthur still would have won had he gotten it right.

In other words, no difference if he’s right; but, perhaps, a world of difference if he’s wrong.

The Final Jeopardy! clue for January 29, 2014 (CAPITAL CITIES):

ONE OF THE 2 WORLD CAPITALS THAT END IN THE LETTER “Z”; ONE IS IN EUROPE & ONE IN THE AMERICAS

Correct response: What is Vaduz or La Paz?