The unfair coin that can't be more likely to give two different results than two the same assumes that each flip has the same probabilities (so k doesn't depend

The unfair coin that can't be more likely to give two different results than two the same assumes that each flip has the same probabilities (so k doesn't depend on how many times you flipped it or what you got). Which is fair, but maybe a coin could be built that tends to toggle between outcomes. If it was half full of honey, and you flipped it over once in your hand after catching to read it, it might be more likely to give the other result the next time. Anyway, this is a bit outside the box; the point was that within a set of rules there was a problem that was impossible to solve.