Chris and Michael play a game on a board which is a rhombus of side length n (a
positive integer) consisting of two equilateral triangles, each of which has been divided into equilateral triangles of side length 1. Each has a single token, initially on the leftmost and rightmost squares of the board, called the “home” squares.
A move consists of moving your token to an adjacent triangle (two triangles are adjacent only if they share a side). To win the game, you must either capture your opponent’s token (by moving to the triangle it occupies), or move on to your opponent’s home square. Supposing that Chris moves first, which, if any, player has a winning strategy?
Wouldnt it effectively come down to probability? I don't quite know how to approach this bizarre question. I realise beginning with n=1 would be a good idea, and proving that he will indeed have an advantage, as he will with n=2. Help as to what to do would be great.