This might be easy, but I've enjoyed thinking about it so I thought I would share.
You and your opponent are playing a variant of Dominion in which instead of starting with the usual 7 Coppers and 3 Estates you will each choose a Kingdom card and gain 10 of it to start. You cannot choose any VP cards. Since you each will have all of a Kingdom card in your deck you are considering the game to be 2 piles depleted at the start. Aside from this setup the Kingdom will have no cards in it except all basic cards, including Alchemy and Prosperity basic cards (though you may not need them for this puzzle). Estates, Duchies, Provinces, Coppers, Silvers, Golds, Curses, Potion, Colony and Platinum.
Your opponent is first player and chooses his deck to be all Expands. You then choose your deck.
Your opponent opens by Expanding one of his Expands into a Province. He states that he intends to run out the Province pile to win. His first priority for the rest of the game will be to Expand one of his Expands into a Province if possible. If he is unable to do that and he is ahead he will Expand one of his Provinces into a Province. If he is unable to Expand an Expand into a Province and he is behind or taking the last Province would end the game with him losing he will Expand one of his Provinces into a Colony. If he can do none of those things he will do nothing.
I can think of four strategies that will beat this strategy. How do you win? And for bonus points: How do you win in a single turn? (there are two ways I can think of)
Followup puzzle: if you were first player instead of second player, what strategies could you choose that would be impossible for your opponent to beat?