Simply consider the Zielonka algorithm on page 152: First, we determine the highest rank h that we find on some state of the game, and then we compute player i as i := h mod 2, so i is 1 if h is an odd number, and i is 0 if h is an even number.

The thought behind this is that we try to find a strategy to infinitely often visit states with highest rank h, which would give the player i a winning strategy.