Law of averages
The law of averages is the commonly held belief that a particular outcome or event will, over certain periods of time, occur at a frequency that is similar to its probability. Depending on context or application it can be considered a valid common-sense observation or a misunderstanding of probability. This notion can lead to the gambler's fallacy when one becomes convinced that a particular outcome must come soon simply because it has not occurred recently.
As invoked in everyday life, the "law" usually reflects wishful thinking or a poor understanding of statistics rather than any mathematical principle. While there is a real theorem, the law of large numbers, that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that an unnatural short-term "balance" must occur. Typical applications also generally assume no bias in the underlying probability distribution, which is frequently at odds with the empirical evidence.
Examples
Gambler's fallacy
The gambler's fallacy is a particular misapplication of the law of averages in which the gambler believes that a particular outcome is more likely because it has not happened recently, or that because a particular outcome has recently occurred, it will be less likely in the immediate future.As an example, consider a roulette wheel that has landed on red in three consecutive spins. An onlooker might apply the law of averages to conclude that on its next spin it is guaranteed to land on black. Of course, the wheel has no memory and its probabilities do not change according to past results. So even if the wheel has landed on red in ten or a hundred consecutive spins, the probability that the next spin will be black is still no more than 48.6%. Similarly, there is no statistical basis for the belief that lottery numbers which haven't appeared recently are due to appear soon.