In 1969, Cole and Davie developed a two-player game based on the Euclidean algorithm, called "The Game of Euclid", which has an optimal strategy. The players begin with two piles of "a" and "b" stones. The players take turns removing "m" multiples of the smaller pile from the larger. Thus, if the two piles consist of "x" and "y" stones, where "x" is larger than "y", the next player can reduce the larger pile from "x" stones to "x" − "my" stones, as long as the latter is a nonnegative integer. The winner is the first player to reduce one pile to zero stones.