Let us suppose there is no element of what finance types call "counter-party risk" here. Your counter-party is the emcee. We'll assume he is entirely trustworthy and that there is nothing tricky about the coin flip itself.
The expected value of the coin flip, in simple arithmetical terms, is ($200 + 0) ÷ 2 = $100. The value of the payoff if you reject the coin flip is, again, $100. So you should on one quite abstract level be indifferent which course the emcee takes. You might even want to flip a coin to decide whether to tell him to flip the coin.
Except that you won't. Unless you are an extraordinary specimen you, dear reader, will be risk averse. One of the choices involves just taking what has been offered you, the other involves the risk that you'll end up with nothing. You'll opt for the former.
Let me stop there. If any of my readers is NOT risk averse in the sense I've just described, let me hear from you in the comments.