Jeopardy Probability and Human Nature

Interesting analysis of Jeopardy and ties from the Numbers Guy (Carl Bialik) at the Wall Street Journal. To simplify the article, once in the year 2000 the contestants went into a three way tie with $5,200 apiece. One contestant wagered only $5000. All three got the correct answer, but she lost as was the only one who didn't bet $5200. She missed the first clear opportunity to create a three way tie.

Flash forward seven years and the contestants go into the final round. Two are tied at $8,000 and the leader has $13,600. The leader bets exactly $2400 and they all get the question correct. As expected the other two contestants bet their whole amount, the final score was $16K apiece. Their story is featured in all the newspapers and are asked to appear on CNN.

What is the likelihood of this happening? Sony Pictures Television released a probability of such a three-way tie which (typically was carried by all the networks without question). Make your own estimate, and see if you are in the same ballpark as the news release. Answer the poll, then read the article and see what number was released.


I'll Take 'Probability' For $2,400, Alex: Odds of Three-Way Tie

Quote: pacomartin

What is the likelihood of this happening? Sony Pictures Television released a probability of such a three-way tie which (typically was carried by all the networks without question). Make your own estimate, and see if you are in the same ballpark as the news release. Answer the poll, then read the article and see what number was released.

My estimate was much lower than the number in the article. Note: It's not possible to answer the poll (meaningfully) and then read the article. The poll is structured around the info in the article.

Back then the five-game limit was in effect (any contestant winning five games was through, and got a luxury car on top of the money), very few contestants with the upper hand bet for a tie. I ahven't watched the show regularly for many years, but I believe that rule no longer exists.

The answer is definitely not a straight forward calculation, and I'm convinced it cannot be calculated at all.

I argue that if all three players were perfect logicians, a tie could only ever occur if all players have the same amount of money. However, players are not perfect logicians - just look at how virtually all players misplay their daily doubles.

Another question to ask yourself: how much is it worth to be a "returning champion?" If it's not worth much, then maybe you are better off (expected value-wise) trying to maximize your winnings by betting everything on the final jeopardy question rather than trying to just win the game so you can come back tomorrow.

How about 3 iterations of Watson playing against himselves? ;P