Suppose we have i.i.d random variables $X_1,X_2,...$ s.t $P(X_i=1)=\frac{1}{2}=P(X_i=0)$. Let $$\Omega=\inf\{n\geq 5|(X_{n-4},X_{n-3},X_{n-2},X_{n-1},X_{n})=(1,0,1,0,1)\}.$$
I would like to use optional stopping theorem to try to calculate $E[\Omega]$ but I can't seem to find the right martingale to do so. Any ideas or suggestions?