Gambling – Sometimes the Law of Averages Works

There is a well known myth that has become known as “the gambler’s folly”, or alternatively “the law of averages”. This goes “if something hasn’t happened for a long time and statistically it should have; then it is more likely to happen in the future”. In other words, if in a lottery a specific number hasn’t come up anywhere near as many times as it should have on average, then it is more likely to come up in the next and in subsequent draws.

The arguments against this are that as each draw (or spin of a coin, spin of a roulette wheel and so forth) is an independent event, it is not influenced by what has happened previously and does not have a bearing on what might happen in the future; a lottery ball does not have a memory and it does not know that it has not been selected enough times, after all it has not been deliberately avoiding being picked.

However, there is anecdotal evidence that the law of averages does pay off, and what follows is a true story concerning the author’s father who was very keen on the football pools.

It was in the days before home computers, so all his efforts were painstakingly recorded in many hard backed notebooks. Every week he would record detailed information on all the football results, ignoring Scotland because he thought Scottish football results to be too random. He did not concern himself with the actual football (though he was interested in the sport and had at one time played for Notts. County reserves); he was simply interested in the numbers.

He would plot the number of score and no-score draws and the home and away wins associated with each number and he would calculate what he called each number’s expectation of a specific result. He would then rank the numbers in terms of draw expectation and he would use these to calculate complex permutations that he believed would increase his chances of winning. Simply put, he firmly believed that if say number 15 on the football pools had received only two drawn games whilst say number 24 might have received nine drawn games, then 15 would be more likely than 24 to be a draw in subsequent weeks and that the likelihood depended on the draw difference between the numbers.

Of course, mathematically that is nonsense, and as a science teacher he should have known it, but it worked for him. He regularly won the pools, not large amounts but enough to make a profit, which he did every year for a decade or so. And of course there was always the chance of a big win. The law of averages shouldn’t work, except that sometimes in some cases it does.