“A Proof That HT Is More Likely to Outnumber HH Than vice Versa in a Sequence of n Coin Flips”, 2024-05-26 (; backlinks):
Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point.
Who is more likely to win? We provide a proof that Bob wins more often for every n ≥ 3.
As a byproduct, we derive the asymptotic form of the difference in win probabilities, and obtain an efficient algorithms for their calculation.