This is tangential to your question, but interesting, I think.
Your Young Witch cursed your opponent on turns 3, 4, 7, 11, 17, 23.
Your opponent's cursed you on turns: 13, 14, 19, and 26.
There's a huge snowballing disparity there. By the time you drew your first Curse, you had already bought Platinum. If one looks to see what purchasing difference might have contributed to that, the only relevant difference is that ended up buying a Wishing Well instead of a Young Witch on turn 4. (This pretty much agrees with other comments that the YW is weak here, with proper defense.) You also got some good luck with the curse/bane ratio, I think.
Another side note from reviewing: as played, you should wish for Copper much more.
Like some other commenters, I would have bought Lighthouse early instead of Hamlet. I would also go for Lookout early; you're going to want to trash a lot of stuff in this game (even if you don't have Curses).