We develop a new model that can be applied to any perfect information two-player zero-sum game to target a high score, and thus a perfect play. We integrate this model into the Monte Carlo tree search-policy iteration learning pipeline introduced by Google DeepMind with AlphaGo. Training this model on 9×9 Go produces a superhuman Go player, thus proving that it is stable and robust. We show that this model can be used to effectively play with both positional and score handicap. We develop a family of agents that can target high scores against any opponent, and recover from very severe disadvantage against weak opponents. To the best of our knowledge, these are the first effective achievements in this direction.