Game Theory problem with n piles and 2 players, one player selects 2 piles, the other takes from one of them

Question

Player 'A' and player 'B' play with n piles of stones. 'A' starts the game. He chooses 2 piles, the 'B' takes an arbitrary (but nonzero) number of stones from one of them. Then 'B' selects two piles and 'A' takes some stones from one of them. The player that removed the last stone wins. Who has a winning strategy and what is it?

I tried using nim sums but not sure how to go on

Answer 1

Let W1 be the set of positions where you can take the last stone. Let L1 be the set of positions where you are forced to enter a state in W1. Let W2 be the set of positions where you can enter a state in L1, and so on.

Then find a pattern.