Assuming you have a board, and you attempt to play with your opponent such as that you try to avoid taking each other's pieces. Is there going to be a limit in the number of moves after which you can't avoid taking over another piece?
(Assuming of course that at least one player doesn't use a repetitive pattern movement that avoids contact from the enemy)
I was trying to find a solution myself but didn't know how to approach this problem.
You say that one player is not allowed to use a repetitive pattern.
In that case, since there are a finite number of moves to be made and a finite number of board configurations to achieve, if the board configuration must be new after each move (since otherwise, that would mean a repeat of a move the player already did), at some point, one player will have to lose a piece.