@alexkontorovich never gonna be all heads, so must be the other one.
here is a great problem. you toss a  and e(x) is the expected number of tosses before hhh comes up, and e(y) is the expected number of tosses before hth comes up. is e(x)&gt;e(y), e(x) = ey or e(x)&lt;e(y)