Two players play a game on the complete graph with n vertices. Each move of the first player consists of claiming k previously unclaimed edges, each move of the second player consists of claiming one previously unclaimed edge. The second player's goal is to claim all the edges of some tree on the n vertices, the first player's goal is to prevent the second from doing that. If k is sufficiently large (resp. small) with respect to n then the first (resp. second) player has a win. We prove that… Expand