Go

By all appearances, Go is just two players taking turns laying stones on a 19×19 (or smaller) grid of intersections. But once its basic rules are understood,Go shows its staggering depth. One can see why many people say it's one of the most elegant brain-burning abstract games in history.

Players place one stone at a time on the board at an empty intersection. The goal of the game is to try to claim the most territory by walling off sections of the board and surrounding or capturing each other's stones. The game doesn't end until the board fills up, or, more often, when both players agree to end it, at which time whoever controls the most territory wins.