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Daily analysis, September 25: In the driver’s seat, but out of gas

September 25, 2013

Wednesday’s game looks tight at first glance, but Kamal is in the driver’s seat. If she responds incorrectly and wagers properly, she’ll still have more than the other two players, which means one of them will have to get it right for her to lose.

Compare this with yesterday’s game, where with proper wagering, Neal, the leader, had to get it right or he was toast.

This is because in this case, Kamal has more than 1.5 times the other players’ scores. This is what is known in Jeopardy! parlance as a crush, and is a huge advantage for the leader. The simple math will bear this out.

The Final Jeopardy! clue for September 25, 2013:

20th CENTURY NAMES
SINCE HIS 1988 DEATH, HE’S BEEN INDUCTED INTO THE U.S. HOCKEY, WORLD FIGURE SKATING & NATIONAL INVENTORS HALLS OF FAME

Correct response: Who is Frank Zamboni?

If you haven’t watched them yet, check out Part One and Part Two of my tutorial.Cover 20130925

From → Daily analysis

2 Comments
  1. Kelly permalink

    Like I suggested yesterday and you briefly touched in the case of a “crush” game like this one where the trailers fall if they miss is of significance for only 2nd vs. 3rd place (unless the leader does something really strange). Thus I don’t think Eric made a bad move by betting more than what your formula suggested. In any crush game both trailers should bet enough to get within the range of winning (unless 3rd is too distant*) and 2nd should bet enough to cover 3rd (which Neal did here).

    *In any game, if 3rd’s score is less than the difference between 1st’s and 2nd’s, he/she has an insufficient amount to get into the winning range and thus has no hope of winning (barring an overbet by the leader). If 3rd’s score is at least the difference but less than twice the difference (such as in this game), he/she must get it right to move into range. When 3rd’s score is at least twice the difference betting to win on a “Triple Stumper” becomes a possibility (note this is impossible in a crush scenario). (Also note that the two breakpoints of 1st=2nd+3rd and 1st = 2nd+(1/2)3rd are cases where it becomes prudent for the leader to bet for a tie since he/she has the strong possibility of losing by a dollar to 3rd if that contestant bets it all and is the only one right in the former case, or if 3rd bets nothing in the latter case.)

    • Hi Kelly – I agree, Eric’s bet was fine in terms of winning, since he needs to get it right to have a shot. The reason he got yellow, and not green, is that his aggressive wager puts him at risk for falling to third should both he and Neal get it wrong (although thanks to Neal’s near-all-in, it wouldn’t have made a difference here). He has less of a reason than Neal does to risk more, since the odds of him winning are remote (he needs a solo-get).

      As for your second paragraph, did I mention that most discussion of FJ! game theory makes my head spin? 🙂 Parts Three and Four will show how to figure out those three-player bet-to-tie scenarios without involving explicit formulas.

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