Many people mistakenly believe that luck “evens itself out in the end” – that somehow if you experience a run of good fortune, a dip is just around the corner. To give a more tangible example, say you throw a dice 100 times. The following totals are recorded for each face of the dice:
1 – 15
2 – 16
3 – 17
4 – 17
5 – 9
6 – 26
The chances of rolling a six on any throw of the dice will always be 16.7%, which over 100 times means that it is likely to be rolled an average of 16.7 times.
Someone who believes in the law of averages would be likely to bet that a six is going to occur somewhere considerably below 16.7 times on the next hundred throws, to compensate for the high number thrown in the first 100. Whilst this may happen, the belief that underpins the bet is absolute nonsense: the odds are the same on every single throw of the dice, regardless of what has gone before. In this sense, the law of averages most definitely does not exist. In a nutshell, in a series of independent events, outcomes are not affected by antecedent events.
However, there is such a thing as the law of large numbers, which can be described as the tendency for the proportions of different outcomes to more closely approximate probabilities the further towards infinity a series of repeating events is extended.
The belief that independent events are somehow related is also known as gambler’s fallacy. If a coin lands heads up 10 times on the run, there is no greater chance of it landing on tails on the eleventh toss. The coin has no memory, and unless the mechanical construction of it is abnormal, there is an even chance again on the next, and all subsequent repetitions.
Gambler’s fallacy can often be seen with things like the National Lottery, where people mistakenly think that a number is more likely to come up if it hasn’t appeared for a while.