The game is as follows: There are heaps consisting of stones and two players. In a move, a player may take the entire heap if it consists of 1 or 2 stones, but if not, must remove two stones and split the rest of the heap into two (non-empty) heaps. A player loses if he is unable to make a move.
My questions are: How does adding a heap of 3 stones affect the outcome
What is the law for an arbitrary $n$? I am guessing that $n$s of the form $3^k$ are losing positions for the first player.