user vs computer:On each turn a player can pick up between 1 to 3 sticks. Who has to pick the last one loses.The computer first plays randomly(it should be truly random). But the computer should learn from the games, it should be able to develop a strategy with the number of games played. As more games are played the Computer should be able to play well and beat you.
You could just start by writing a program and don't factor in the program learning. that'll be a good start.
Then you'll need to learn about optimisation algorithms probably.