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by Nick Benjaminsz
According to widespread beliefs a so-called law of averages should ensure that in a long coin-tossing game each player will be on the winning side for about half the time, and that the lead will pass not infrequently from one player to the other & [but] intuition leads to an erroneous picture of the probable effects of chance fluctuations (p.78).
One should expect naively that in a prolonged coin-tossing game the observed number of changes of lead should increase roughly in proportion to the duration of the game ?c this intuitive reasoning is false. (p. 84). [The number of changes of lead in n trials is, in fact, on the order of the square root of n.]
Feller, William (1968), An Introduction to Probability Theory and Its Applications, Volume 1, Third Edition (revised printing), John Wiley & Sons, New York.
