You know next turn you have tournament, province and $8, and opponent has <$2 (because you cutpursed him this turn, and he revealed his hand of no coppers). If you buy the duchy now, you get 3pts + 6 next turn=9pts, if you buy estate now, you get 1pt+9 next turn=10pts, allowing you to win by 1 point.
I'm thinking there's simpler solutions though.