Casino Guide to ‘The Law of Averages'

The Law of Averages is something that many gamblers hold close to their heart. It is something that comes up in every gambling game that involves pure chance, and it is particularly applicable to games such as roulette.

The Law of Averages states that the results of any random event will even out in the short term. For instance, using an example of the game of roulette, the law states that if there have been a number of successive blacks, then there is a higher probability that the next spin will result in the ball landing in a red pocket than a black one.

The Law of Averages is closely related to another law that is known as ‘The Law of Large Numbers'. Using a similar example, this law states that with increasing numbers of spins of the wheel, the number of reds (and of blacks) will approach and remain close to fifty percent.

It is easy to see why people get these two laws mixed up. The Law of Large Numbers (LoLL) is real and an easily derived and proven law. The Law of Averages (LoA) is a nonsense by which the human mind is readily deceived.

The differences between the LoA and the LoLL are perfectly illustrated by another concept that is termed the Gambler's fallacy which again is based on the expected outcome of a random event being influenced by history. We shall again use roulette to illustrate it.

If the roulette wheel is spun 21 times, then the chance of getting 21 reds is around 1 in 2,000,000. But, if there have already been 20 reds, the chance of the 21st spin being red is 50%. The probability of 20 reds and one black is thus identical to the probability of getting 21 reds, both about one in two million.

Terry Pratchet, the author of an excellent modern fantasy set in what he calls Discworld, has invented characters who believe that if the chances of something happening are exactly a million to one, its outcome is guaranteed.

In a spin of the roulette wheel, every possible outcome has the same possibility of happening as any other no matter what has happened before.

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