Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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The idea that  past results of a random event influence 
future results. For example, if in a sequence of tossings of a coin (assuming
the coin to be perfectly symmetric), we have had 20 tails in a row, that's doesn't make any more probable that the next result
will be head, the probability of head or tail remains 50/50.