Page "Gambler's fallacy" Paragraph 4

Now suppose that we have just tossed four heads in a row, so that if the next coin toss were also to come up heads, it would complete a run of five successive heads.

Since the probability of a run of five successive heads is only ( one in thirty-two ), a believer in the gambler's fallacy might believe that this next flip is less likely to be heads than to be tails.

However, this is not correct, and is a manifestation of the gambler's fallacy ; the event of 5 heads in a row and the event of " first 4 heads, then a tails " are equally likely, each having probability.

Given the first four rolls turn up heads, the probability that the next toss is a head is in fact,