Question on proof of coin-tossing in "how to simulate it"
Actually, a probabilistic adversary $A$ can be viewed as a deterministic adversary with a random tape: $A$ just picks a random string in the beginning and then run deterministically according to that fixed string. In the proof, the simulator $S$ uses the real-world adversary $A$ as a black box but can control its random tape (because a random tape always contains fair random strings that can be generated by anyone). So, $S$ can simulate the output of a probabilistic adversary $A$ by first choosing a random string $r$ then dealing with the resulting deterministic adversary $A'=A(r)$.