Alice and Bob have a fair coin with sides labeled C and M, and they flip the coin repeatedly while recording the outcomes; for example, if they flip two C's then an M, they have C C M recorded. They play the following game: Alice chooses a four-character string \mathcal{A}, then Bob chooses two distinct three-character strings \mathcal{B}_{1} and \mathcal{B}_{2} such that neither is a substring of \mathcal{A}. Bob wins if \mathcal{A} shows up in the running record before either \mathcal{B}_{1} or \mathcal{B}_{2} do, and otherwise Alice wins. Given that Alice chooses \mathcal{A}=C M M C and Bob plays optimally, compute the probability that Bob wins.