The last player in the circle
Players are numbered clockwise. Player 1 holds a token, removes the next player, and passes to the next remaining player. So 1 removes 2 and passes to 3; 3 removes 4 and passes to 5.
Hint & mathematical explanation
Try 4, 8 and 16 players first. For this exact remove-every-second rule, write n = 2ᵐ + L, using the largest power of 2 not exceeding n. The winner is 2L + 1. With 100 players: 100 = 64 + 36, so player 73 remains. Changing who starts or how the token passes changes the result.