In order to give the computer the ability to play against human opponents, one could utilize the Alpha-Beta algorithm. However, this algorithm has several limitations restricting its playing capabilities. Over the years, many variants of this algorithm were developed, among them a couple that make use of neural networks: a neural network to focus the search in the game tree, and a neural network trained without expert knowledge that substitutes the heuristic function in the Alpha-Beta algorithm. In this paper the weaknesses of the Alpha-Beta algorithm are reviewed alongside its variants that use neural networks. It is explained how each approach overcomes different limitations of the Alpha-Beta algorithm, and an attempt to overcome its weaknesses by the use of a combination of the neural network algorithms is presented. The proposed hybrid algorithm, which was developed using Evolutionary Strategies, still keeps the advantages of each of the individual neural algorithms, and shows a significant improvement in play against them.