Good point. I am going off of the original algo by von Neumann, which throws away both flips if you get HH or TT. There are many others, and I don't see any reason against your optimization, if the flips are truly independent.
yeah, indeed -- but i think the optimization is actually broken. if you are just waiting for an HT or a TH in a sequence of flips, then you will just wind up with H..HT or T..TH, so that the very first flip decides the outcome. this is how i first (much too hastily) read the algorithm, but, somewhat surprisingly, found that the expectation matched exactly.