Comment by cokernel

Yes. Diaconis, Holmes, and Montgomery demonstrate (but do not provide a full specification for) a coin-flipping machine which will yield heads 100%* of the time (as long as it starts on heads).

"Dynamical bias in the coin toss". https://statweb.stanford.edu/~susan/papers/headswithJ.pdf

* Or at least every time the experiment is performed.