WordNet (r) 3.0 (2006):

law of averages
    n 1: a law affirming that in the long run probabilities will
         determine performance

Moby Thesaurus II by Grady Ward, 1.0:

39 Moby Thesaurus words for "law of averages":
   accidentality, actuarial calculation, adventitiousness, break,
   casualness, chance, destiny, fate, flukiness, fortuitousness,
   fortuity, fortune, gamble, good fortune, good luck, hap,
   happenstance, happy chance, heedless hap, how they fall,
   indeterminacy, indeterminateness, lot, luck, moira, opportunity,
   principle of indeterminacy, probability, problematicness,
   random sample, risk, run of luck, serendipity,
   statistical probability, the breaks, theory of probability,
   uncertainty, uncertainty principle, whatever comes