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February 28, 2014

Daily analysis, Friday, February 28

For the first game in five, someone’s got a hold of Arthur’s toe. Could this be the end of a spectacular run?The Final Wager - February 28, 2014

In the video, I take a seat to explain this whole situation.

Arthur Chu: 22,400
Semret Lemma: 11,400
Dawn Volmert: 7,400

The Final Jeopardy! category: MODERN DAY SUFFIXES

The wagering here is straightforward.

Arthur should wager 400. Since Semret must answer correctly, Arthur could wager up to 7,600 so as not to fall below a doubled-up Dawn – but only if he feels really confident in the category.

Semret must get it right, so he might as well go all in. At a bare minimum he must wager 10,600.

Dawn should aim to preserve second if Semret misses, with a maximum wager of 6,599. (Technically, she should also wager at least 4,001, but I’ll overlook that since Semret will be going large.)

All bare minimums – and poor Semret. Since all four previous games were locks, Semret had no idea Arthur wagers for the tie. Had he known, would Semret have wagered an extra dollar? Why not two? So, then, why not all 800 remaining?

In this case, being cheeky costs him $20,800 and the opportunity to challenge King Arthur once more. And for what? The remote possibility of making an extra thou for second over third? Note that Dawn rendered this a moot point.

So we move on to Corollary #2: If you must get it right to be in contention, wager everything.

Note that with proper wagering by Arthur, Dawn can’t win, so this corollary does not apply to her. She can only get to second place at best, which depends entirely on Semret’s response.

One other thing this covers: an underwager by Arthur. This has happened before.

The Final Jeopardy! clue for February 28, 2014 (MODERN DAY SUFFIXES):

DATING FROM 1973, THIS 4-LETTER SUFFIX INDICATES A PERSON OR THING THAT HAS BECOME ASSOCIATED WITH PUBLIC SCANDAL

Correct response: What is -gate?

5 Comments
  1. Hans Weidig permalink

    I’m reading/watching the archives, and I think I’m picking up some new thoughts that you haven’t been directly expressive about before. For one, Arthur could have Wagered For the Tie on Wednesday, at 1,000 instead of 600. It wouldn’t have affected that game, but if Semret saw that, he might’ve wagered better.

    All-In and Zero wagering could be considered a “Level 0” wager, the instinctual rational wager. Which can be proven to be the best choice, even at “higher level” rational wagering. This game is an excellent case of why it can be the best choice: In order to get high enough to meet or beat Arthur’s Zero wager, Semret would have to wager enough for Dawn to beat him if he got it wrong. If Arthur wagers based on Semret’s All-In wager, and gets it wrong, in order to beat that new score, Semret would STILL have to wager high enough for Dawn to beat him.

    Since his rational wagers are all so high, he had a choice between guaranteeing himself $2,000 (by wagering $0) or taking a risk between $1,000 and becoming a co-champion. He accidentally chose to take a risk between $1,000 and $2,000.

  2. Kelly permalink

    I agree you with the corollary that if you need to be right to win, go ahead and bet it all. (I’d also extend that to say if you use a strategy that requires you to be right, like if you’re in Stratton’s Dilemma and choose to cover third or you’re worried about the leader making an unsafe wager with less than 3/4 and want to bet big, the same thing applies – you ought to bet it all.)

    There is another corollary I think is worthy: As a leader, to maximize your chances of winning, don’t bet more than what is necessary to either tie or beat by a dollar a double-up by second (depending on the game type and your philosophy on tying vs. outright winning). Like you and I have said this is very important in tournament quarterfinals where what you have left over if wrong is crucial for the wildcards, and probably so in other tournament games where your score has no cash value. Even in regular games, where an extra total means more $, since coming back to play is generally more important than your winnings on that day, it’s generally best not to pad on extra unless you’re very confident.

  3. Another big reason to bet it all in this situation: you win more money! Every dollar you leave off is a dollar less in your pocket. There’s also the (admittedly small) chance that this extra money could get you into the TOC if you end up a 3-game or 4-game winner.

  4. I completely agree with the analysis. However, in terms of Nash equilibriums I think there is an oddity in this situation.

    Of course, Arthur betting Big (400) and Semret betting Big (All – 11,400) is a Nash equilibrium. But, I think so too is Arthur betting Small (0) and Semret betting Small, but slightly larger than he actually did (11,000 instead of 10,600).

    What is really strange is for Semret, this alternate equilibrium has the same expected value for him (he wins if and only if he gets the Final correct in both cases) but for Arthur the alternate equilibrium is better (Arthur always wins in the alternate case but can lose in the original case). So, even though Semret’s dominant strategy is to bet it All (11,400), with cooperation the two could land on the alternate equilibrium without hurting anyone.

    • Technically, yes, it’s a Nash equilibrium … but it’s still dominated by Semret’s all-in wager. There are strict rules against collusion.

What do you think?