Take turns removing stones from several piles. On your turn, you can take as many as you like, but only from a single pile. Whoever takes the last stone wins. Can you beat the computer?
Nim is one of the most thoroughly studied strategy games in the world. The rules look simple, but the mathematician Charles Bouton mathematically proved a complete winning strategy for it back in 1901 — more than a century ago.
The secret lies in converting each pile's stone count to binary, then taking the XOR (0 if the two digits match, 1 if they differ) across every digit position. If this value is 0, whoever's turn it is right now is at a disadvantage; if it's not 0, they have the advantage. Whoever's holding the advantage can always win in the end, by always removing however many stones brings that value back to 0.
How to play: In whichever pile you want to take from, click the stone right after the point you want to leave behind, and every stone from there to the far end gets taken. For example, in a pile of 5, clicking the 3rd stone takes the 3rd, 4th, and 5th stones (3 stones).