I'm not sure how that is relevant. The price of the option will decay to zero or to its intrinsic value and if it ends in the money one side will give $X to the

I'm not sure how that is relevant. The price of the option will decay to zero or to its intrinsic value and if it ends in the money one side will give $X to the other at the end. Someone also paid a premium to the other (ignoring the bid-ask spread and transaction costs). Peter's gain is Paul's loss. You have 50/50 probability of being Peter or Paul.