What formula can be used to always win at nim?

Answer 1

In the game of Nim, a winning strategy involves calculating the "Nim-sum," which is the bitwise XOR of the sizes of all piles. To ensure a win, a player should aim to leave their opponent in a position where the Nim-sum equals zero after their turn. Specifically, if the Nim-sum is not zero at the start of a player's turn, they can make a move that forces it to zero, thereby maximizing their chances of winning.