Reversi

There is one rule. Place a disc so that it traps a line of your opponent's between it and another of your own, and every disc you trapped turns over to your colour. People have been finding new things in that sentence since the 1880s.

Eight squares by eight, four discs in the middle to start with, and dark moves first. Every square you are allowed to play is ringed for you. Working out which of the sixty empty squares happens to bracket something is arithmetic, and it is not the interesting part of the game. Choosing between the four or five moves you actually have is.

Three strengths of opponent. Easy is the greedy one: it takes whichever move flips the most discs, which is the mistake every beginner makes and the one the tips below will cure. Medium looks three moves ahead. Hard looks six, values the corners properly, and plays the last dozen moves out exactly. It will take a corner you leave open, and it will not hand you one.