Of optimism and the odds at the casino of chaos
We are optimistic animals, we human beings, and that gives us an evolutionary advantage. Yet, in other respects, it is no advantage at all – especially at the roulette wheel, the one-armed bandit or when fervently flaying away those silvery-grey blocks on a scratch card.
Why is explained by probability and chaos theory, and Frank Burnet will be at the Sofia Science Festival to explain chaos theory. Among his principal props will be a roulette table.
Though, really, chaos theory is constantly being proven at casinos and gaming houses everywhere around the world.
What of the punter who goes to the table, believing in a win that will result if playing all the odd red numbers?
“People do believe, sometimes, that they have systems that can make them more likely to win,” Frank says.
“But the only people that really win are the casinos, because the odds are tipped in their favour, not by cheating but by the setup of the game. In fact, in America, the game is tipped more strongly in favour of the casino than in Europe, because in America, roulette wheels have two zeros – a double zero and a zero. A European roulette wheel has only a single zero slot.”
That, by the way, changes the amount that over time a casino in the United States will rake in from 5.5 per cent, compared with just about 2.9 per cent in Europe.
“So if you are going to play roulette, play it in Europe or demand that they use a European roulette wheel,” Frank says – not that he is one to believe anyone should be confident of predicting that they can break the bank at any casino. In casinos, chaos and probability reign.
In a game of roulette, the croupier spins the wheel and drops the ball, and as the wheel slows, the ball begins to fall towards the numbers – encountering on the way diamond-shaped objects embedded in the wall of the wheel, objects that are designed to increase the chaotic nature of the balls behaviour. Even if you could predict when the ball is going to fall down from the rim, you could not predict which number it is headed towards.
“Basically, things like roulette wheels contain elements which increase the chaotic nature of the process that you are dealing with, and therefore increase its unpredictability.”
The same is true of dice games such as craps.
“Some people claim that you can actually learn to throw dice in a way which allows you to beat the odds, by increasing the chance of them throwing particular numbers. But this is, I think, very unlikely.
“It’s claimed by some professional craps players that they can do this, but actually, the craps table itself has two ways in which it creates a chaotic system built into it.” The first is that throwing dice on to a hard surface changes their orientation, and it is changed again when the dice hit the back wall of the craps table.
Gaming tables contain elements that increase the level of chaos. And chaos, in the sense of chaos theory, posits that small differences in initial conditions, yield widely diverging possible outcomes, making – as a general rule – long-term prediction impossible. The same principle applies to, for instance, long-term weather forecasts, stock market fluctuations and for that matter, elections.
But what of those punters counting on “luck”. Does luck exist?
Frank cites the book by his British compatriot, mathematician Ian Stewart, Does God Play Dice? (the title is a reference to the saying by Einstein, “God does not play dice with the universe”).
As Frank explains it, it is not difficult to demonstrate the absence of an element of luck by taking two keys and dropping them repeatedly from the same height.
“Every time I drop them, they will end up in different places on the floor, and the reason for that is although they start in the same place, the moment I release them different forces are acting on the keys, that is why they end up in different places. You can’t predict that, so you can’t predict what will happen, you only know that they won’t produce the same outcome more than once. So basically there isn’t really an element of luck.”
Gamblers, though, are drawn into believing that they are getting lucky by deliberate near-misses being built into the game.
For example, many scratch cards put you in the position of coming close, but not quite close enough, to winning. A card using crowns as symbols may require four to win. Many will be made with three crowns on them.
“The idea is that the gambler will think they getting lucky. And they will buy another card, thinking, ‘ah, well, it’s my lucky day’. Unfortunately, of course, it isn’t. The same odds apply on the next card.”
Things are not really different with one-armed bandits, programmed similarly to produce periodic series of small payouts – and occasionally, of course, big ones – to give those using them a sense that they are getting close to winning.
All of this adds up to much more than an issue of mathematical abstractions. A gambling addiction has been classified as just that, an addiction, not a compulsion. It is rather like an addiction to opiates.
The most effective treatments for gambling addicts are very similar to those used to wean people off opiates.
Inevitably, this has much to do with the working of the human brain. The treatment of Parkinson’s Disease can involve giving the patient a precursor of Dopamine to compensate for the malfunction that leads to a specific group of brain cells dying. A side-effect observed in a small number of patients is that people thus treated for Parkinson’s become prone to gambling addiction because the brain areas involved in addictive behaviours are Dopamine rich.
Aside from outright gambling addiction, there is a factor that drives people to continue “trying their luck” – an optimism intrinsic within us.
“One of the most fascinating things about us as animals is that we are unreasonably optimistic. We are way more optimistic than circumstances would normally suggest we should be. And that is something that really comes into play with gambling,” Frank says.
He explains that people understand that the chances of winning the lottery, for example in the UK, are approximately equivalent to knowing that a friend lives in London, but not knowing their home telephone number – and then guessing correctly, first time, their nine-digit phone number.
“That’s roughly the odds that you’re working on. People know that, and it’s really not hard to explain, but they’ll go on buying the lottery ticket, go on entering the lottery; it is just that they are very optimistic. They retain optimism in the face of all the evidence.”
In any chaotic system, the point is that you cannot measure all the variables that you need to in order to predict the outcome. This applies to the stock exchange, that the fact of so many people buying and selling at the same time makes it a fairly classic chaotic system.
Similarly again, politics and elections. There are innumerable variables, unknown in advance, that can change the outcome.
One should be careful, however, of extending this to imagine that every task of working towards a conclusion about an outcome is bedevilled by the intrinsic problem explained by chaos theory.
Take the profession of the actuary.
“Actuarial science is actually based on statistics, on numbers, and the measurements are there,” Frank says, cautioning that while actuaries have access to a great deal of information, it is information about statistics, not individuals.
“They calculate a level of risk, they are not coming up with an absolute,” he says, giving the example that informed of the profile of a person of a certain age and habits, an actuary can give the odds of that person reaching a certain age – but solely in regard to the statistics about those factors.
“So it is not based on a chaotic system, there are lots of knowns, and so it’s a science, and always described as such.”
Then there are weather forecasts. One of the most notable chapters in the history of chaos theory emerged as Edward Lorenz, in 1961, began attempting to use a digital computer to produce more accurate long term weather forecasts. His experience confirmed the principle that small changes in the initial conditions produced such large variations that the outcome was unpredictable even with access to enormous amounts of computing that remains the case today.
Frank says that the enormously interesting thing about chaotic systems is that outcomes are more predictable the nearer to the beginning of the process you are.
“So, one-day weather forecasts around the world are actually brilliant,” but those longer than that period fall prey to the syndrome.
“The further you are from the point at which you begin the process, the more and more unpredictable it becomes. That’s a chaotic system. So that it’s not that we are bad at predicting the weather. We actually have got very good at it. But only in the short term.”
There is, however, a theoretical possibility of overcoming the problem – but that would require the measurement absolutely of every single factor, leaving none out, at which point – again, theoretically – accurate long-term prediction should become possible.
And yet, to return to the gaming table, the craps table, the one-armed bandit and the scratch card, we remain optimistic?
“We remain optimistic. We are quite pessimistic in groups. As individuals, we are very optimistic – in general terms, not every day, of course – so, when it comes to, should we do that again, we go, yeah, why not?”
Frank Burnet’s presentation at the Sofia Science Festival is on May 14 at 8.30pm on the main stage at Theatre Sofia in Zaimov (Oborishte) Park. It is for 18+ audiences only. He is something of a veteran of the festival, having appeared previously, in 2011 and 2013.
A Scot who read biochemistry at the University of St Andrews, Frank Burnet spent a year in the 1970s working as an actor on Sudan’s English-language television channel. At Oxford, he took up the dual pursuits of acting and neuroendocrinology. Deciding on a career in science, in the mid-1990s he became a science communicator and in 2002, the first professor of science communication in the UK at the University of West England in Bristol.
The Sofia Science Festival is organised by the British Council Bulgaria and is under the patronage of the Bulgarian Ministry of Education and Science. The Sofia Globe is a media partner of The Sofia Science Festival 2016.
(Photo: Daniel Altherr/freeimages.com)
