"A ply is a half move and a move is equivalent to 2 ply or a turn by each player. For example, 1. e4 is one ply and 1…e5 would be the 2nd ply, together these two plys make one move." source: http://beginchess.com/2010/05/09/the-sixth-ply/ So essentially, what the sentence is saying is that when they look ahead by 5 ply: their turn (1 ply) other player's turn (2 ply) their turn (3 ply) other player's turn (4 ply) their turn (5 ply) they would pick differently than if they waited longer :)