I think this link botches the explanation for 51%. 51% is because of precession, as explained in the paper[1]. With enough precession the coin will <i>always</i> come up heads if it starts out heads. That's how magicians control coin tosses.<p>He tries to describe it in terms of HTHTHT. Coins do not have memory. They don't know if they've previously flipped 3 times, 4 times, or 1e308 times. If you draw from [HTHTHT..HT] randomly, you'll get 50% heads and 50% tails. Change that to [THTHTH..TH] and the answer is the same.<p><i>With</i> precession the answer changes because it stays in the initial state longer. As the paper points our "Keller showed that in the limit of large initial velocity and largerate of spin, a vigorous flip, caught in the hand without bouncing, lands heads half the time." Keller assumed no precession.<p>[1] <a href="http://statweb.stanford.edu/~susan/papers/headswithJ.pdf" rel="nofollow">http://statweb.stanford.edu/~susan/papers/headswithJ.pdf</a><p>edit: I just saw that in the comments they point this flaw out. It gets hand waved away by the author as a "oversimplification" that he made. My opinion is that it is okay to simplify, but not to the point of being wrong. The explanation is not how probability works, at all.