# Question on proof of coin-tossing in “how to simulate it”

I am reading Professor Lindell's "How To Simulate It - A Tutorial on the Simulation Proof Technique" paper, which is very enlightening.

I am trying to follow through the proof of the security of Blum's coin-tossing protocol and have some questions: in the end of page 41 it says ": Let $$b_1$$ be the value committed in the commitment $$c$$ sent by $$A$$ (since $$A$$ is deterministic and this is the first message, this is a fixed value)."

1. I don't understand why we can assume $$A$$ is deterministic?
2. In general, should the security proof work for probabilistic adversaries?

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 $$A'=A(r)$$.