"Anything that can happen will" -- Steve Goodman, from ''The Dying Cubs Fan's Last Request''

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The law of averages makes a suggestion about all reiterated prbabilistic events.  If we take a specific example, like a 
repeated coin toss, it implies that prior tosses should make us expect something from future tosses.  Like if I throw heads 19 times, though I should still think that the probability of another heads is 50%, I should be somewhat relieved to finally see my coin land on tails.