## Welcoming our new computer overlords!

on February 17th, 2011 at 3:19 pmIBM’s Watson pulled off a resounding victory in the computer vs. Jeopardy champions! The computer did make some strange answers (e.g., “What is Toronto?????????” to a question about American cities), but was much faster than the humans on the easy questions (not so surprising) and did get many tricky questions right.

Here’s the New York Times article: *Computer Wins on ‘Jeopardy!’: Trivial, It’s Not*.

The research definitely focused mostly on the question understanding and information retrieval aspects, but it seems to have had a very curious game theory strategy also, with its bet sizes and question choices. At the end of a Jeopardy game, there is a “Final Jeopardy” question where each player (there are 3 players) secretly writes down the amount she wants to wager (up to their current total). So, the leading player could guarantee a victory by betting the maximum amount and getting the answer correct. If a player answers incorrectly, they lose the amount they bet.

**Challenge Problem!** What is the optimal Final Jeopardy betting strategy? I think this is quite a difficult game theory question, especially since there are 3 players involved, and there is a likelihood that the probability of opponents answering the question incorrectly is correlated with the probability I will answer incorrectly (e.g., if the question is very difficult, it is likely all players will get it wrong; but if it is easy, everyone will answer correctly). An obvious first order strategy would be for the leading player to bet enough so her total would be 2b+1 where b is the total for the second highest player (call this bet x), player 2 should bet an amount y that is small enough so that (b – y) > (a – x), to win when all players are incorrect, but also worry about exceeding 2c+1 where c is the total for the third highest player. This is definitely not optimal, though, since the other players should adjust their strategies accordingly. Note that there is an extensive database of Jeopardy! games here, *http://www.j-archive.com/*, so you can analyze how poor most players betting strategies are, as well as the probabilities of different correctness outcomes for the final Jeopardy! question. (e.g., how often do all 3 get the answer correct or incorrect). They also have a Wagering Calculator, which seems to follow a strategy similar to the obvious strategy above.

## Recent Comments