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  • This is the fallacious step in the argument. If the coin is fair, then by definition the probability of tails must always be .5, never more (or less), and the probability of heads must always be .5, never less (or more). While a run of five heads is only 1 in 32 (0.03125), it is 1 in 32 before the coin is first tossed. After the first four tosses the results are no longer unknown, so they don't count. The probability of five consecutive heads is the same as four successive heads followed by one tails. Tails is no more likely. Each of the two possible outcomes has equal probability no matter how many times the coin has been flipped previously and no matter what the result. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses is the fallacy. The fallacy is the idea that a run of luck in the past somehow influences the odds of a bet in the future. Blackjack
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  • 2006-03-05, 20:39

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