I am not an authority on this, but my impression was that Chess algorithms use a combination of techniques:
- Openings database - the algorithm will keep a database of known good opening moves that get it to a certain point
- Brute force - try to predict all possible combinations of moves up until some future point (only do this for the next, say, 10, moves); keep track of the path that maximizes your chances for victory
Here is an interesting read from StackExchange.