Complex sentence: Games with forbidden positions, University of Gdansk, Tech. Report 78 (1991), so that if a player has a winning strategy then she has a winning strategy which depends only on the board position, and not on the history of the play.
Split into simpler sentences: Games with forbidden positions, University of Gdansk, Tech. Report 78 (1991). This means that if a player has a winning strategy then she has a winning strategy that depends only on the current board position, and not on the history of the play.