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The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of ''balancing'' nature). In situations where what is being observed is truly random (i.e., independent trials of a random process), this belief, though appealing to the human mind, is false. This fallacy can arise in many practical situations although it is most strongly associated with gambling where such mistakes are common among players. The use of the term ''Monte Carlo fallacy'' originates from the most famous example of this phenomenon, which occurred in a Monte Carlo Casino in 1913.〔(Blog - "Fallacy Files" ) What happened at Monte Carlo in 1913.〕 ==An example: coin-tossing== The gambler's fallacy can be illustrated by considering the repeated toss of a fair coin. With a fair coin, the outcomes in different tosses are statistically independent and the probability of getting heads on a single toss is exactly (one in two). It follows that the probability of getting two heads in two tosses is (one in four) and the probability of getting three heads in three tosses is (one in eight). In general, if we let ''Ai'' be the event that toss ''i'' of a fair coin comes up heads, then we have, :. 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 person subject to the gambler's fallacy might believe that this next flip was 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 that the first four tosses turn up heads, the probability that the next toss is a head is in fact, :. While a run of five heads is only = 0.03125, it is only that ''before'' the coin is first tossed. ''After'' the first four tosses the results are no longer unknown, so their probabilities are 1. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses, that a run of luck in the past somehow influences the odds in the future, is the fallacy. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「gambler's fallacy」の詳細全文を読む スポンサード リンク
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