Friday, March 6, 2009

Jeopardy: Strategery, or: Don't hate the player, hate the game

Part of an ongoing series.

In tandem with studying potential Jeopardy content, I familiarized myself in Jeopardy strategy in December and January. The J! Archive was particularly helpful for this, as it has every clue and their outcomes from almost all of the show's seasons available for browsing. It also has a long glossary full of game theory and strategy, including guidelines on how you should bet in Final Jeopardy! under a variety of conditions. Head-spinning.

I eventually came across a description of the game pictured above, which was the first and thus far only three-way tie in the history of the show. You can watch their FJ! on YouTube (WaMu Files For ChapLev). I wondered what the game-leader (Scott Weiss, left, a computer scientist) had been thinking with his wager. Typically, if you're leading enough to potentially outpace the other contestants, you bet enough to get to 2x(their current score)+1 so you win. My first thought was that he'd done it for the sake of the uniqueness of the tie. It's neat to be a part of something like that.

But then I realized that the rules of the game, and by extension the nature of competition, might incentivize going for the tie. Here's how prizes work on the show:
  • First-place player gets to keep the money in their score, and gets to play again in the next day's show.
  • Second-place player gets $2000 regardless of winnings.
  • Third-place player gets $1000 regardless of winnings, which only partially defrays the cost of traveling to the show if you got on a plane to get there.
  • If there is a tie for first place, both or all three players keep the money and get to play again.
So if you're in Weiss' position, and you bet the whatever+1, all you're doing is screwing the other players out of $14,000 and $15,000. You jerk. But, if you play for the tie and everybody gets the question right, then you've just made two new best friends AND you get to play your next game against two players you've already been able to beat once. The benefit of this is hard to estimate. Reading Prisoner of Trebekistan left me with the impression that any known quantity with regards to who your opponents will be is greatly beneficial, both psychologically and strategically. Otherwise, you might end up with what Bob Harris calls an "Ivy League Serial Killer," who can get all the really obscure crap regardless of who might beat him or her on the buzzer (excuse me, Signalling Device).

(Of course, in the later rounds of a Tournament of Champions game, this rule does not hold, as the poor guy on the left in this video learned all too well. I would've been in the same boat here, incidentally, answering the FJ! handily but being useless on this particular tiebreaker.)

Now, skipping ahead somewhat in the narrative, I learned when I was actually at the show that The Powers That Be actively discourage ties. They were certainly excited about the three-way tie due to its novelty, and if you go into FJ as the leader with exactly twice the score of the person in second, it doesn't make sense to endanger your lock-tie with a non-zero wager. But, they screen thousands of contestants a year, and turn away most of them. They want to move as many people through the show as they can, and any game with two winners cuts in half the new players in the next game. So they encourage playing for the tie+1.

Back to me approaching my tape date... I watched the show daily in the weeks leading to my tape date. The week before I went out to California, there was a five-day winner named Matt Kohlstedt (a graduate student originally from La Grange, IL, pictured, borrowed from PioneerLocal). Kohlstedt had two very interesting FJ situations wherein (1) he was not in the lead going in, (2) everybody got it wrong (triple-stumpers), and (3) he won by $1 or $2 with wagers that were not obvious choices to me. I decided that it would behoove me to understand them before I appeared on the show, so the day I left, I copied down the FJ scenarios of these two games in my book, and on the flight westward, I reasoned my way through them.

I believe Matt's logic was roughly this:
  • I'm not in the lead
  • The people ahead of me are most likely going to make rational wagers to cover their nearest opponent doubling their score
  • If they get the question right, I will lose
  • I can't guarantee that I will get the question right
  • Therefore, the only way to win is to assume that the people ahead of me will get it wrong, and base my wager on what their wager is likely to be
Look at the January 20th game. Matt's in 2nd going in, with 10,000 to Rebecca's 11,800. Matt figures Rebecca will bet 8200 to tie him if he doubles. So he assumes she'll lose 8200, and bets just enough that if he loses too, they'll tie at 3600. This almost happened, except she played for the win+1, and lost by $1.

He did it again, two days later. Here Matt is in third with 6400 to Luis' 12,200 and Chris' 15,000. He figures Chris will bet 9400 to cover Luis doubling up. So he bets enough that if everybody's wrong, he'll cover Chris by a dollar. It ended up being $2 in this case, because Chris also played for the win+1. (Note that in this case, if Luis hadn't overbid 8800, and instead bet between 2801 and 5600, he'd have won. Matt's gambit is less likely to be successful, it seems to me, from third place.)

(Matt Kohlstedt will be in this year's Tournament of Champions, which begins airing on Wednesday's broadcast. Watch for him, as well as for Deborah Fitzgerald, right, a retired government employee from McLean, VA, who is a friend of my Aunt's.)

This is crafty stuff. On the flight, prime ministers and countries on the Equator competed for headspace, along with Matt's strategy, the crush, and the 2/3, 3/4, and 4/5 rules. But mostly I tried to stay frosty.

Next Jeopardy Blog: To The Studio!


John said...

Geez, Fred. My head hurts.

Fred said...

Mine did too, John. Mine did too.

Allison Foley said...

Fred, if I ever get on that show, can I hire you as a coach? Because trivia I know, strategy I do not.

Harrumph said...

The fellow who instigated the three way tie was very much an "Aspie" - a person with Asperger's syndrome. This is not a disparaging remark, and many of the better Jeopardy players have touches of it (note how many rock back and forth while they play). Sometimes Aspies are motivated more by statistics than by the considerations that "normal" minded people have. Strategically it was a poor decision, as he was playing against two very tough competitors, and having them back for a second game led to his defeat.