There is a very nice construction by Conway of surreal numbers. They are "numbers" that contain both real numbers and ordinals, are totally ordered, and have all the properties of a field (except they do not form a set but a class).
They can be even more generalized to so-called "games", which are originally introduced to study combinatorial games. The original motivation of Conway was to analyze the game of Go, in particular the endgame is especially suited to be modeled with "surreal games".
My question is: do you know if anybody has implemented this approach in an AI (i.e. computer player) to improve its level at a game? I am especially interested in the case of Go, but others as well. If not, is there an obstacle or a reason why it would not be a good idea?