A discussion is given of what it means for a coin toss to be random. To aid in that discussion, we produce and solve numerically a physically realistic model of such a toss. The ideas we develop should apply in a general way to other commonly used mechanical randomizers. The coin's randomness is determined by the nature of the basins of attraction of heads and tails. Although mechanical systems are known which are intrinsically random, we conclude that the coin flip is not among them. Rather, the effective randomness in practice is based on the magnitude of the scale of the variation of the basins of attraction relative to the precision of the flipping mechanism.