Nim

In choose-your-own-pile-nim, each player starts with a pile of coins of size n. Depending on the group preference, n can be limited to a range {0, b}. Players will then take turns, and on each turn they can remove up to b coins from any other players pile, or their own. If a pile is empty, the player owning that pile must report so, and the individual who is attempting to take a coin form that pile may choose another one. The player who takes the last coin from the last pile wins.