experiments approaches the expected value as the number of experiments goes to infinity it is worth noting that the law of large numbers does not implyas too many seem to thinkthat if deviations from expected behavior occurthese deviations are likely to be evened out by opposite deviations in the future this misapplication of the law of large numbers is known as the gambler' fallacy note that "largeis relative concept for exampleif we were to flip fair coin on the order of , , timeswe should expect to encounter several sequences of at least million consecutive heads if we looked only at the subset of flips containing these headswe would inevitably jump to the wrong conclusion about the fairness of the coin in factif every subsequence of large sequence of events appears to be randomit is highly likely that the sequence itself is not truly random if your itunes shuffle mode doesn' play the same song first once in whileyou can assume that the shuffle is not really random finallynotice that in the case of coin flips the law of large numbers does not imply that the absolute difference between the number of heads and the number of tails decreases as the number of flips increases in factwe can expect that number to increase what decreases is the ratio of the absolute difference to the number of flips figure contains functionflipplotthat produces some plots intended to show the law of large numbers at work the line random seed( near the bottom ensures that the pseudo-random number generator used by random random will generate the same sequence of pseudorandom numbers each time this code is executed this is convenient for debugging "on august at the casino in monte carloblack came up record twenty-six times in succession [in roulette[therewas near-panicky rush to bet on redbeginning about the time black had come up phenomenal fifteen times in application of the maturity [of the chancesdoctrineplayers doubled and tripled their stakesthis doctrine leading them to believe after black came up the twentieth time that there was not chance in million of another repeat in the end the unusual run enriched the casino by some millions of francs huff and geishow to take chancepp -