# Luk Arbuckle

## Debunking the “law” of averages

In probability on 12 June 2008 at 2:40 am

One example of the “law of averages”—not to be confused with the law of large numbers—describes the belief that a particular event becomes more or less likely to occur in order to move a series of random events closer to the long-run average.  A coin toss, for example, is believed more likely to come up tails if ten heads have been successively thrown beforehand.  The belief is that the long-run average of 50/50 must be made up for, and therefore the probability of the single event must change to suit that long-run average.

It’s not surprising that anyone would believe the law of averages, even if it is misguided.  Although the coin isn’t aware of what was thrown beforehand, there is the notion of a long-run average to contend with.  The binomial distribution, used to consider success and failure experiments like coin tosses, can be used to show why this law is false.  But we’ll skip the math and only discuss results.