Three-way tie on Jeopardy - Why doesn't this happen more often?

On March 16, three players all finished with $16,000 on Jeopardy. The Associated press released a story claiming a 1 in 25 million chance of this happening (http://www.msnbc.msn.com/id/17653609/).

My question is: Why doesn't this happen more? My prediction: It will now.

First off, the 1 in 25 million number is not correct. Odds cannot be calculated for a three-way tie on Jeopardy since a tie relies on one or more contestants choosing to tie. Final Jeopardy is not a game of chance. The contestants have free will to bet to win, or to tie unless all three contestants enter final Jeopardy with the same amount. In this case, Scott Weiss chose to tie the game.

Friday's game played out like this: Mr. Weiss entered final Jeopardy with $13,600. The other two contestants each had $8,000. The rational bet for the two players with $8,000 was to bet all of their money hoping for a two way tie should Mr. Weiss get the question wrong. They would have assumed (incorrectly in this case) that Mr. Weiss would bet $2,599 assuring a win should he get the question correct. But that is not what happened. Mr. Weiss bet $2,600 (http://www.youtube.com/watch?v=ZV9vuKfVO04), and all three tied. There is a lot of talk now about why someone would do this. Mr. Weiss says he was being generous. But what if he was following his own self interest?


Under the rules of Jeopardy, in a first place tie all tied players get the money, and all are crowned Jeopardy champions, and all tied players return the following week. So Mr. Weiss gets the payout AND he gets to face the same two people he just beat by 60% instead of drawing random players the following week who might turn out to be much stronger. Mr. Weiss gave up $1 to pick his competition. In game theory we would look at this as a sequential game. Mr. Weiss's two day payout is likely to be bigger with a tie than a win. As other contestants catch on to this, expect to see more ties for first place on Jeopardy.