Biased coin toss probability of a sequence before other sequence
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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" H or "tails" T) with equal probability. A coin is therefore a two-sided die. Despite slight differences between the sides and nonzero thickness of actual coins, the distribution of their tosses makes a good approximation to a  Bernoulli distribution.
There are, however, some rather counterintuitive properties of coin tossing. For example, it is twice as likely that the triple TTH will be encountered before THTthan after it, and three times as likely that THH will precede HHT. Furthermore, it is six times as likely that HTT will be the first of HTT, TTH, and TTT to occur than either of the others (Honsberger 1979). There are also strings  of Hs and Ts that have the property that the expected wait  to see string  is less than the expected wait  to see , but the probability of seeing  before seeing  is less than 1/2
There are, however, some rather counterintuitive properties of coin tossing. For example, it is twice as likely that the triple TTH will be encountered before THTthan after it, and three times as likely that THH will precede HHT. Furthermore, it is six times as likely that HTT will be the first of HTT, TTH, and TTT to occur than either of the others (Honsberger 1979). There are also strings  of Hs and Ts that have the property that the expected wait  to see string  is less than the expected wait  to see , but the probability of seeing  before seeing  is less than 1/2
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