The need for control

We seem to be hard-wired to seek causality – finding correlations where there are none – and struggle to see events as independent. Early man had a very limited understanding of the mechanics of a harsh environment so desperately sought to infer cause or consequence of actions for events that were either random, or simply too complex to understand. Superstition and ritual emerged as ways to somehow gain a sense of control, and these are still very evident today.

Fascinating experiments illustrate this behaviour right across the animal kingdom, one of the most famous being that of Harvard psychologist B. F. Skinner.

In 1948 Skinner introduced food hoppers at timed intervals into a pigeon’s cage. The pigeon had no influence over the frequency of the feeding, but whatever behaviour they happened to be displaying as food was introduced – nodding head, turning – became conditioned as responsible for the appearance of the food. Each pigeon developed a unique ritual that it thought triggered the reward.

The same is true for humans, who have associated a sense of control with various rituals (e.g. avoiding black cats, never walking under ladders). These still occur today in less obvious places. Studies of city traders, for example, have shown that they perceive a sense of control over random systems.

Skinner’s findings led him to define what he called Operant Conditioning – responses that reinforced, punished or had a neutral impact on behaviour. Personal choice plays a big part in reinforcement and casino games provide great examples of this.

The influence of personal choice

The majority of casino games are entirely random, yet bettors display an irrational belief in their ability to control outcomes where they can assert personal choice.

“We seem to be hard-wired to seek causality – finding correlations where there are none – and struggle to see events as independent”

This tendency is illustrated by gamblers betting more when they are the ones throwing the dice in Craps, or spinning the ball into the roulette wheel. In both examples bettors demonstrate an irrational belief in their ability to control what is a random outcome because they exercise personal choice in the process of the game. This is also true by proxy, such as when bettors piggyback on the bets of someone on a lucky streak – someone perceived to be especially in control.

Lotteries provide another illustration of the illusion of control as players place greater confidence in potential success when playing their own numbers, rather than machine-generated entries. Given the outcome is entirely random, the chances of success are the same.

In fact, random lottery selections often increase potential winnings because of the common use of birth dates for numbers. The chances of winning are the same, but the likelihood of sharing the prize increases as selections are skewed towards numbers from 1 to 31, decreasing the potential payout.

In the casino examples, the behaviours that produced success – how the ball was thrown, the ritual involved – will be reinforced, whereas those producing failure are likely to generate a punishment response, decreasing our propensity to repeat them.

However, because life and betting cannot simply be reduced to narrow definitions of success and failure, and the causes thereof, the potential for irrationally reinforcing behaviour is enormous.

Dangerous information and near misses

You may have heard the expression ‘a little information is a dangerous thing’. This is particularly true in betting, where the sense of empowerment that a degree of knowledge about a team, sports or event, gives rise to an exaggerated sense of understanding and predictive ability.

Where success follows, but not necessarily as expected, bettors often back-fit the logic of their choices to match what happened, producing the reinforcement described above, and the illusion of control.

This is equally true of near misses, where bettors take enough encouragement from almost getting things right, to reinforce the behaviour. As a result they persevere with what they think is a valid approach, when in fact in all probability there is no valid correlation.

Some things to bear in mind to mitigate this effect would be to accept that you have no control where outcomes are random, test narrow, clearly defined hypotheses, one at a time, and don’t take betting tips simply at face value. You should also try and differentiate between signal and noise when you can.

As with superstition, the pathological association of betting outcomes and particular behaviours is unfortunately hard to resist, because these are hard-wired behaviours. The key for bettors is to be as disciplined as possible when drawing conclusions from their betting history, and keep the “lucky pants” for clubbing.

The law of large numbers

Using a fair coin toss as an example (where the chance of hitting heads and tails has an equal 50% chance), Bernoulli calculated that as the number of coin tosses gets larger, the percentage of heads or tails results gets closer to 50%, while the difference between the actual number of heads or tails thrown also gets larger.

“As the number of tosses get larger the distribution of heads or tails evens out to 50%”

It’s the second part of Bernoulli’s theorem that people have a problem understanding – which has led to it being coined the “Gambler’s Fallacy”. If you tell someone that a coin has been flipped nine times, landing on heads each time, their prediction for the next flip tends to be tails.

This is incorrect, however, as a coin has no memory, so each time it is tossed the probability of heads or tails is the same: 0.5 (a 50% chance).

Bernoulli’s discovery showed that as a sample of fair coin-tosses gets really big – e.g. a million – the distribution of heads or tails would even out to around 50%. Because the sample is so large, however, the expected deviation from an equal 50/50 split can be as large as 500.

This equation for calculating the statistical standard deviation gives us an idea what we should expect:

While the expected deviation is observable for this many tosses, the nine-toss example mentioned earlier isn’t a large enough sample for this to apply.

Therefore the nine tosses are like an extract from the million-toss sequence – the sample is too small to even-out like Bernoulli suggests will happen over a sample of a million tosses, and instead can form a sequence by pure chance.

Applying distribution in betting

There are some clear applications for expected deviation in relation to betting. The most obvious application is for casino games like Roulette, where a misplaced belief that sequences of red or black or odd or even will even out during a single session of play can leave you out of pocket. That’s why the Gambler’s Fallacy is also known as the Monte Carlo fallacy.

In 1913, a roulette table in a Monte Carlo casino saw black come up 26 times in a row. After the 15th black, bettors were piling onto red, assuming the chances of yet another black number were becoming astronomical, thereby illustrating an irrational belief that one spin somehow influences the next.

“In 1913, a roulette table in a Monte Carlo casino saw black come up 26 times in a row. For that reason, gambler’s fallacy is also known as Monte Carlo fallacy”

Another example could be a slot machine, which is in effect a random number generator with a set RTP (Return to Player). You can often witness players who have pumped considerable sums into a machine without success embargoing other players from their machine, convinced that a big win must logically follow their losing run.

Of course, for this tactic to be viable, the bettor would have to have played an impractically large number of times to reach the RTP.

When he established his law, Jacob Bernouilli asserted that even the stupidest man understands that the larger the sample, the more likely it is to represent the true probability of the observed event. He may have been a little harsh in his assessment by once you have an understanding of the Law of Large Numbers, and the law (or flaw) of averages is consigned to the rubbish bin, you won’t be one of Bernouilli’s ‘stupid men’.