Build a program to analyze coin flip sequence choices
Python 3 (139 136 134 132 126 115 143)

Uses Conway's Algorithm as described at here. Handles all sequence pairs as long as the first is not a terminating subsequence of the second (as per instructions).

def f(a,b):c=lambda x,y=a:sum((x[~i:]==y[:i+1])&lt;&lt;i for i in range(len(x)));return 0 if b in a else(1/(1+(c(a)-c(a,b))/(c(b,b)-c(b))),1)[a in b]


Thanks xnor for shaving 6 bytes off. Thanks Zgarb for spotting a bug with subsequences.