How can you find the best strategy to win any game?
It has been proven that for two-player zero-sum games of perfect information - where you know all possible future moves and positions, and where there is only a winner and loser, there is an optimal strategy.
This is known as Zermelo's Theorem, named for Ernst Zermelo, one of the first mathematicians to seriously looking at a mathematical method of winning chess. It works like this:
Start with what you know is a winning position, and 'work backwards' from every known winning position. Eventually, since you know all winning positions, you will be able to backwards induce an optimal strategy since you know all possible paths to victory or at least draws.
Essentially, Zermelo's Theorem proves that an optimal strategy exists for any such game.
This does not guarantee a winning strategy, only the optimal one.
Many games have no winning strategy. Some can only hope for a draw against another player playing optimally (Checkers, for instance). But if you have enough time, you can solve any games by backwards induction.
But solving a game in this manner takes a lot of time. Solving chess by backwards induction would take thousands of years with the most powerful computers working on it, there are so many possible variations.