Make better decisions

Some people are appalled by the idea of gambling – while ignoring the fact that everyone makes ‘bets’ every day, from guessing the quickest route to work to deciding whether or not to take a job offer. They’re all choices made in the face of uncertainty. Fortunately, there’s a branch of probability theory that helps cut through the complexity. Called Decision Theory, it’s a powerful way of identifying the choice most likely to give the best result.


To use it, we need to consider not only the chances of the various outcomes happening, but also the consequences in each case. Imagine you’ve heard rumours that a road may be built near your house. Should you move or stay? First, consider the consequences of moving or staying. As these will also depend on whether the rumours prove true or false, there will be four such consequences; you can rate each on a scale of, say, +10 (ideal) to -10 (awful).

Now multiply each consequence by the chances of it coming to pass – remember that if there’s a 20 per cent chance of the rumour being true, there must be an 80 per cent chance of it being false.

The results are the consequences you can expect in each of the four scenarios. Finally, add together the two consequences expected from staying put, and see if the result is bigger than the total expected from moving. If it is, the optimal decision is to stay. Otherwise, it’s time to move.


Play the financial markets

Back in the 1950s, economists developed Nobel Prize-winning theories for how best to invest money in financial markets. And to do it, they drew on the theory of probability. The result was Modern Portfolio Theory (MPT), which shows how to create a mix of stocks, bonds and other assets to get the best possible return for the lowest risk. By feeding in past performance data for each asset, the formulas of MPT reveal the relative proportions of each needed to achieve this optimal performance.

To pull off this miracle, MPT involves some fearsome equations that only rocket scientists might be expected to solve. But – like any attempt to model reality with mathematics – MPT makes assumptions, and the bad news is they’re not very realistic. A wealth of data now suggests that MPT simply cannot capture the real complexity of markets, making its conclusions dubious at best.

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Even Harry Markowitz, the US economist who won the economics Nobel Prize in 1990 for developing MPT, admitted he ignored his own theory and simply split his investments equally between stocks and bonds.

The lesson of the laws of chance this time is: don’t get too clever. When it comes to investment, history suggests most of us may do best by simply dividing our money among so-called index trackers that just follow entire sectors of the market – and then forget about them until we retire.


Have more fun in casinos

With global revenues in excess of $150bn a year, casinos provide compelling proof of the benefits of turning a theorem about chance into a business model.

That theorem is the Law of Large Numbers, and it achieves the remarkable feat of allowing punters to believe they can win big, while guaranteeing the casinos a profit margin.

Take roulette, with its famous wheel of 36 alternating red and black number ‘pockets’. As there are 18 of each colour, it seems obvious the chances of the ball landing in red or black and getting double your money back is 50:50. But look again: there’s a green ‘0’ pocket on the wheel (and a second marked ‘00’ in US casinos). So the chances of landing on red or black are actually 18 in 37 (or 38 in the US) – slightly less than 50 per cent.

The prize on offer therefore doesn’t quite compensate for the chances of losing. But the Law of Large Numbers does guarantee that over thousands of spins that tiny difference – the ‘house edge’ – becomes ever more reliable as a source of profit. On the way, however, there’ll also be a few punters who have some luck and win a bit of that profit.

You can still make your own luck in a casino. Just choose games where the house edge is tiny, as in blackjack or single-zero roulette. Decide how much you are prepared to lose, and then avoid making lots of small bets – as these give the Law of Large Numbers the biggest chance of eating your money.

Though your best bet of keeping hold of your cash at a casino is to avoid going there in the first place.


Turn guesses into breakthroughs

When Alan Turing arrived at Bletchley Park in 1939 to break enemy codes, his boss thought the task was hopeless. The Nazis were using Enigma machines that scrambled messages in 15 billion billion different ways. Without an astonishing stroke of luck, what hope was there of hitting the right combination and revealing the messages? But Turing knew of an obscure formula that was up to the job – and used it to help win WWII.

Known as Bayes’ Theorem, it had emerged from attempts by mathematicians in the 18th Century to solve probability problems. Turing used Bayes’ Theorem to take low-probability guesses about how Enigma messages had been encoded, combine them with evidence from intercepted messages, and produce slightly better guesses. Repeated over and over, the process homed in on the Enigma settings with the highest chance of being right, thus ‘breaking’ the code.

Bayes’ Theorem proved incredibly effective. By the end of the war, the codebreakers were routinely reading not only Enigma messages but also Hitler’s personal communications, encrypted using far more complex machines. Turing’s application of the theorem was deemed so powerful that it was only declassified in 2012.

Today, Bayes’ Theorem is used to turn guesses into insight in fields ranging from medicine to cosmology. And it’s now helping Turing’s successors at the UK Government Communication Headquarters (GCHQ) to win the cyberwar against hackers and terrorists.


Predict coincidences

We are all aware of the Titanic disaster of 1912, when the ‘unsinkable’ liner struck an iceberg and sank with huge loss of life because there weren’t enough lifeboats. Spookily, a fictional story about an ‘unsinkable’ liner that suffered the same fate had been published 14 years earlier. And the name of that ship? SS Titan.

Coincidences are intriguing, but they’re also demonstrations of our shaky understanding of how chance works.

When the SS Titan story appeared, there were already concerns about icebergs, and about inadequate provision of lifeboats on big liners. As for the name, someone penning a story about a huge liner is unlikely to name it SS Midget. In short, all these ‘coincidences’ aren’t independent of each other, and are more likely to occur together than we’d expect.

But genuinely independent events can also coincide more often than you’d think. For example, probability theory shows that almost 90 per cent of football matches will include players with birthdays within a day of each other. The chances are so high because the birthdays of 22 players can be paired off in 231 different ways. Add in the fact we’re not demanding an exact match either, and the chances of coincidences rocket upwards.

You can make your own luck out of that. Chances are your mates don’t know it – so turn it into a bet while you’re waiting for the kick-off.


Beat the odds

From the winner of the Grand National to the member of One Direction most likely to go to rehab first, it’s possible to bet on virtually anything these days. Millions of us do, but even those who think they know what they’re doing actually don’t. Studies suggest 95 per cent of gamblers fail to make consistent profits.

So what are one in 20 people doing right? Put simply, they understand a theorem first proved over 300 years ago that shows when a bet makes sense.

The good news is that this ‘Golden Rule of Gambling’ is amazingly simple: only bet on events whose chances of happening are significantly greater than the bookmakers’ odds suggest. For example, if a bookmaker is offering even odds on an event, don’t make a bet simply because you agree that there’s a 50:50 chance of winning.

Bookmakers’ odds are specifically designed to give an optimistic view. As a result, if the event does come to pass, they’ll pay out less than the fair amount – and then pocket the difference as profit.

The Golden Rule of Gambling reveals that the only way to beat the bookies is to carry out in-depth research and find factors the bookmakers have overlooked. If this suggests the bookies have blundered and offered overly pessimistic odds, the Rule says the bet makes sense.

Now the bad news: simply checking past ‘form’ isn’t enough, as the bookmakers do all that, and much more. Your research must be better than theirs – a big challenge. But it’s not impossible: one top tip is to focus on ‘novelty bets’ like how many shots a team has on target. Bookmakers aren’t so focused on nailing down the odds on these.

The lesson is simple: if you don’t do the research, don’t place the bet.

GamCare is a registered charity that provides confidential telephone and online support and counselling to anyone affected directly or indirectly by problem gambling. See www.gamcare.org.uk or freephone: 0808 8020 133 (free calls from all UK landlines and most major mobile networks) every day from 8am to midnight.


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Robert is a science writer and visiting professor of science at Aston University.