It is conjectured that as becomes large, the average number of The numbers of distinct minimal toss sequences for, 2. The minimal sequences for are HT and TH,Īnd for are HHTTH, HTTHH, THHTT, and TTHHT. The minimum number of tosses is (Havil 2003, Length occur as subsequences of the tosses. Toss a fair coin over and over, record the sequence of heads and tails, and consider the number of tosses needed such that all possible sequences of heads and tails of Similarly, the probability that no consecutive tails

For example, the probability that no two consecutive tails will The study of runs of two or more identical tosses is well-developed, but a detailed treatment is surprisingly complicated given the simple nature of the The probability of a coin of finite thickness landing on edge has been computed by Hernández-Navarro and Piñero (2022) as Only about 30% of the time (Paulos 1995). More amazingly still, spinning a penny instead of tossing it results in heads Occurs before HTHH is 9/14 (Gardner 1988, p. 64),įor which the probability that TTHH occurs before HHH is 7/12, andįor which the probability that THHH occurs before HHH is 7/8 (Penney , but for which the probability that THTH Is less than 1/2 (Gardner 1988, Berlekamp et Is less than the expected wait to see, but the probability of seeing before seeing Ts that have the property that the expected wait to see string

Of HTT, TTH, and TTT to occur than either of the others (Honsberger Furthermore, it is six times as likely that HTT will be the first THT than after it, and three times as likely that THH will precede For example, it is twice as likely that the triple TTH will be encountered before There are, however, some rather counterintuitive properties of coin tossing. Tosses makes a good approximation to a Bernoulli Despite slight differences between the sides and nonzero thickness of actual coins, the distribution of their An idealized coin consists of a circular disk of zero thickness which, when thrown in the air and allowed to fall, will rest with either side face up ('heads'

Digital coin flip