What is the optimal strategy for Euclid's game?

As Douglas Zare explains, there is an analytical solution. Here is a simple way to solve it with an algorithm, which also suggests the best move to play at each stage. read more

Euclid's game (also known as the Game of Euclid) is played as follows: 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. read more

My guess is that, for large enough $n$, picking the number that nets the most points on each individual turn is optimal. For example, if $n = 49$, then the first player would pick $47$ (to net $46$) and their opponent would respond with $49$ (to net $42$). read more