An example of the Wikipedias brilliance: over the last years Ive read several explanations of the Gambler’s Fallacy (including, I think, SEP and a book on (informal) logic), and from the wording it never made sense to me why wouldnt it be reasonable to anticipate a heads when a coin turned up tails many times beforehand; it seemed that disputing this anticipation is a direct contradiction of the law of large numbers. But here, in the Wikipedia article, a crucial bit of information finally let me understand the problem: “While a run of five heads is only 1⁄32 = 0.03125 [chance], 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.”
Posted on: Wed, 12 Mar 2014 00:47:40 +0000
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