Mis(appeal) to Mathematics
On Friday's (3/16) Jeopardy show, the three contestants ended in a tie. This made headlines the next day, but it should not have done so..at least for the reasons stated.
I watched the show; my feeling was that something interesting had happened, nothing more. But, the show claims that they "contacted a mathematician who calculated the odds of such a three-way tie happening: one in 25 million." Balderdash!
Going into the finals, the current Champion (a computer science professor) was ahead by about $6000, the other two were tied at $8000. On the finals, the first two men were correct and bet double their money, giving them $16000. Then, the current Champion also was correct, but he bet only enough (something weird like $2041) to end up equal to $16000. Usually, the Champion (or person ahead) will bet enough to win by at least $1 (which he could easily do, since he had won more than $40000 the night before (and bet more than $20,000 on the final question). Thus, I think he purposly controlled the outcome (i.e. the three-way tie), which to me destroys any sense of calculating "odds."
Again, in Final Jeopardy, the "leader" knows the amounts of the others, and knows that they have little to lose by betting double their existing amounts (as they get nothing unless they win). Plus, the leader has little to lose by betting an amount that would tie with them (if they are successful in doubling their money) as it means he would still get to return the next week (as if he had won, and face two "known" opponents rather than two new ones). So, I claim that probability has little to do with this situation (as the events are not random but are subject to someone's control). However, it may be an interesting example as part of game theory, where one makes bets subject to full knowledge about the other player's positions and constraints.
Finally, the mathematician contacted by Jeopardy needs to rethink things...or at least watch the show to understand the situation!