There is a fascinating (and charming) paper by Alan Turing that describes his "Turochamp" chess 'engine'. Apparently, it was the first program capable of playing a complete game of chess, and the first program that could be described as a computer game (although it sadly only ever existed on paper). The general pattern he outlines (a heuristic evaluation function with hand-tuned weights, along with minimax game tree search--i.e. backwards induction) has formed the basis of most chess engines, both ancient and modern. Here's the original copy: https://docs.google.com/file/d/0B0xb4crOvCgTNmEtRXFBQUIxQWs/...

Intriguingly, Turing posed the question, "Could one make a machine to play chess, and to improve its play, game by game, profiting from its experience?" This reinforcement learning approach to chess did not enjoy much success--until AlphaZero. That story that has been well-told in many places, but perhaps best so by David Silver in this recently released lecture by DeepMind: https://www.youtube.com/watch?v=ld28AU7DDB4. The first ~40 mins are a lucid explanation of the classical methods, and the rest covers RL/MCTS/AlphaZero.