I'd like to see if I could find a way to win go comprehensively - if by searching the complete game space you can say "actually, this is how you should approach a game".

Work-wise, I'd like to have a crack at a problem that bugs me about simulations - how do we know when we've done enough simulations?

I'd make my money by devising a good weather forecasting system, and bringing back enough good enough predictions to bet on white Christmasses and the like :)

Go can just be brute-forced in order to determine for sure that "Black Wins". Then, find the lines as played by White which result in the smallest point difference in the final position. There you have your exemplar game; detailed study once you come home should reveal the most important approaches to the game.