The three contestants on the venerable game show all finished with $16,000 after each answering the final question correctly in the category, "Women of the 1930s," on Friday's show. They identified Bonnie Parker, of the famed Bonnie and Clyde crime duo, as a woman who, as a waitress, once served one of the men who shot her…The show contacted a mathematician who calculated the odds of such a three-way tie happening — one in 25 million.In that final round contestants choose how much of their winnings to risk, so it is impossible to give a probability in such a setting. It's more an issue of simple game theory.
Before the Final Jeopardy round the totals were $13,400, $8000 and $8000. Both of the $8000 decided to risk all of their money so they wouldn't be overtaken by the other one.
The $13,400 belonged to Scott Weiss, a computer science professor at Mount St. Mary's University in Maryland. Since $13,400 is between 1.5 and 2 times $8000, the standard strategy is to bet enough so that if you win you have more than $16,000 and if you lose you have more than $8000, for example betting $3000. Had Scott done so, he would have taken home all his winnings and come back for the next show.
Instead Scott bet $2600, leading to the $16,000 tie. By doing this, Scott gets to take home all his winnings and comes back for the next show.
It takes a computer scientist to make the most conservative bet, knowing that the rules of the game give no particular advantage to winning over tying and leading to the first three-way tie ever.