Two players compete in the following game: There is a pile containing n chips; the first player removes any number of chips except that he cannot take the whole pile. From then on, the players alternate moves, each person removing one or more chips but not more than twice as many chips as the preceding player has taken. The player who removes the last chip wins. (For example, suppose that n = 11; player A removes 3 chips; player B may remove up to 6 chips, and he takes 1. There remain 7 chips; player A may take 1 or 2 chips, and he takes 2; player B may remove up to 4, and he picks up 1. There remain 4 chips; player A now takes 1; player B must take at least one chip and player A wins in the his next chance.
What is the best move for the first player to ensure his win if possible if there are initially n chips?