from Amazon
Friday, February 05, 2010
Baseball Jeopardy
Great question being asked:
“Let’s say you’re on ‘Jeopardy!’ and you’re absolutely routing your two opponents. You have $40,000 going into the final round, while one of your opponents has, let’s say, $15,000. You’re guaranteed to move onto the next day, but the final category comes up and it has something to do with baseball, which is your favorite sport. How much — if anything — do you risk?”
He then proceeds to show us 10 real Final Jeopardy baseball questions. Remember, you have 30 seconds to answer. I count 4 as gimmes, and the other 6 depend on deep history or geography knowledge, or can recall things that you normally would get in a minute or two, but you need to do it in 30 seconds. Let’s say you have a 75% success rate because you really know your sh!t.
Here’s how it works. You bet 9,999$, which is the maximum you can bet, and be guaranteed to win the game, even if you lose on this question. And you get to come back tomorrow to play.
Let’s say the average winner makes 30,000$ for each game, and you have a 1 in 3 shot of winning. And if you win, you get to come back the next game. So, one shot in 3, you pocket 30K and come back again. Two times in 3, you are left empty-handed. Your overall expectation therefor is 45,000$. That’s what playing in a 30,000$ game in Jeopardy is worth, if the winner gets to keep coming back.
Back to where you are in the decision making:
1a. You bet 9,999$, you lose on the question (happens 25% of the time), but win on the game (happens 100% of the time), pocket 30,001$, plus the 45,000$ in future dollars: total earnings = 75,001$
1b. You bet 9,999$, you win on the question (happens 75% of the time), but win on the game (happens 100% of the time), pocket 49,999$, plus the 45,000$ in future dollars: total earnings = 94,999$
Total expected earnings if you bet 9,999$ = 89,999.50$
2a You bet 40,000$, you lose on the question (happens 25% of the time), are out of this game and future games: earnings = 0$
2b. You bet 40,000$, you win on the question (happens 75% of the time), win on the game (happens 100% of the time), pocket 80,000$ dollar, plus the 45,000$ in future dollars: total earnings = 125,000$
Total expected earnings if you bet 40,000$ = 93,750$
Indeed, the breakeven point is 71.4%. That is, if you are 71.4% sure of your ability to answer the question, then you can go either way. If you are more sure, you should go for the bigger bet. And if you DON’T, then you are being risk averse. And the more sure you are above that 71.4% and that you don’t make the bigger bet, the more risk averse you are.
It seems to me that, given the setup (30 seconds to answer), you should not risk the big payoff today.
(I’m also ignoring a tie if everyone bets all their money and they all lose. Presumably, the 2nd place guy isn’t as knowledgeable as you are in baseball and will lose. And, you would think, the 3rd place guy would bet almost nothing, just to make sure that if two guys bet it all and lose can come out the winner.)