So far I have mentioned two very general methods to play better in most games and to grow playing skills like a science.
The first one is heuristics — and heuristics to find them and improve on them — so that you develop a well-structured theory about how to augment your view of the playing field with useful concepts abstractly derived from the game specifications and constraint relaxations. Its efficiency relies on your general past experience with games and combinatorial searches, on your meta-thinking abilities, and more generally on your scientific intelligence before and while playing.
The second general method is deepening combinatorial minimax, so that you explore most pertinent moves and their counter-responses farther and farther in the branching-off immediate future. Its efficiency relies on your awareness and brute-force thinking while playing, and on specialized experience with the game coupled with general or specialized heuristics and time-saving algorithms.
It is time to introduce Monte Carlo — a third general method that has recently emerged and has proved to be surprisingly powerful, especially with the game of Go. It consists in randomly playing out many games up to their end and counting how many you have won, starting from a few board states you wish to compare. You may think sampling tons of games may only yield a dull average. But something unexpected may as well come out. Think of how our unexpected physical world comes out of tons of games...