  The AlphaZero algorithm for the learning of strategy games via self-play,
which has produced superhuman ability in the games of Go, chess, and shogi,
uses a quantitative reward function for game outcomes, requiring the users of
the algorithm to explicitly balance different components of the reward against
each other, such as the game winner and margin of victory. We present a
modification to the AlphaZero algorithm that requires only a total ordering
over game outcomes, obviating the need to perform any quantitative balancing of
reward components. We demonstrate that this system learns optimal play in a
comparable amount of time to AlphaZero on a sample game.
