It could be done. Endgame positions (which will probably result in a win in three moves or less) can easily be analysed completely using basic game theory - I could probably write you a program that plays tic-tac-toe, or Nine Man's Morris. More complex positions are the real problem, but a lot of human-playable games have basic strategies like "try to keep as many of your pieces on the board as you can (Chess, drafts, Go, and so on)", "try to get your pieces to form rows (Connect-4, Nine Man's Morris)", or even "bet higher than you should to bluff your opponent (Poker and gambling games)". Perhaps it could learn from past mistakes too.

Not saying it would be easy to make, that it could beat a human at an arbitrary game, or even that it could beat a specialised AI designed for that particular task. But making AIs adaptable makes them much more human-like, if that is what you want.

PS: Toss might actually be able to do this. The description isn't very clear; I'll check for you.