Two learning methods for acquiring position evaluation for small Go boards are studied and compared. In each case the function to be learned is a position-weighted piece counter and only the learning method differs. The methods studied are temporal difference learning (TDL) using the self-play gradient-descent method and coevolutionary learning, using an evolution strategy. The two approaches are compared with the hope of gaining a greater insight into the problem of searching for "optimal" zero-sum game strategies. Using tuned standard setups for each algorithm, it was found that the temporal-difference method learned faster, and in most cases also achieved a higher level of play than coevolution, providing that the gradient descent step size was chosen suitably. The performance of the coevolution method was found to be sensitive to the design of the evolutionary algorithm in several respects. Given the right configuration, however, coevolution achieved a higher level of play than TDL. Self-play results in optimal play against a copy of itself. A self-play player will prefer moves from which it is unlikely to lose even when it occasionally makes random exploratory moves. An evolutionary player forced to perform exploratory moves in the same way can achieve superior strategies to those acquired through self-play alone. The reason for this is that the evolutionary player is exposed to more varied game-play, because it plays against a diverse population of players.