This study investigates the evolutionary training of neural networks (NNs) with binary, ternary, and real-valued connection weights using Evolution Strategy (ES). The NNs are trained to control the Atari Galaxian game, with the objective of maximizing the game score. A three-layer feedforward neural network is employed, in which both connection weights and unit biases are represented using one of three parameter domains: {-1, 1}, {-1, 0, 1}, or the continuous interval [-1.0, 1.0]. The experiments examine the effects of ES hyperparameter configurations, connection-weight representations, and the number of hidden units on game-playing performance. Two ES configurations with the same total number of fitness evaluations are compared. The results show that the configuration using a larger offspring population and fewer generations significantly outperforms the configuration using a smaller offspring population and more generations for all three weight representations. Under the better-performing configuration, NNs with binary and ternary weights generally achieve higher game scores than those with real-valued weights, although the differences are not statistically significant. Furthermore, for ternary-weight NNs, a network with four hidden units significantly outperforms one with a single hidden unit and achieves performance comparable to networks with 8, 16, and 32 hidden units, providing a favorable trade-off between model size and game-playing performance.