Conditions to find the attractor

Question

The rules for understanding the attractor in Zielonka algorithm is confusing.

Please help me understand what rules needs to followed in the cases:

1) when the current player is 1 (i=1) , Qh belongs to player 1

2) when the current player is 1 (i=0) , Qh belongs to player 1

3) when the current player is 1 (i=1) , Qh belongs to player 0

4) when the current player is 1 (i=0) , Qh belongs to player 0

Answer 1

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.