Probabilistic Thinking

By now, I hope you’re beginning to accept that how you see the world, and a lot of how you think, is influenced by your cognitive biases. These aren’t occasional quirks. They’re running constantly in the background, affecting every decision you make, every interpretation you create, every judgement you form.

Most of what you do day in, day out, is automatic. You’ve done those things thousands of times before. You’re a creature of habit, and you spend huge chunks of your life running on autopilot, doing the same things and getting the same results. This isn’t necessarily bad. Habits are efficient. Your brain would be exhausted if it had to consciously process every single decision.

In a moment, I’m going to tell you about probabilistic thinking, which is quite a complicated concept. I’m putting it here in this course at this stage of your journey rather than further on because it’s really important to underline just how much probabilistic thinking can cause you problems by preventing you from making the changes you need to make in your life.

We spend most of our lives doing what we’ve always done, relying on habits, doing what feels right, using instinctual behaviour to handle situations. I see some people where patterns in their lives seem to repeat themselves time and again. They go from one bad situation to the next, from one failed relationship to another, from one dead-end job to the next dead-end job. Either these people are spectacularly unlucky (which they’re not), or they’re somehow influencing these patterns to happen. This gets us onto the concept of probabilistic thinking, or more specifically, how badly most people understand probability.

Perhaps the easiest way to discuss probabilistic thinking is to use the Gambler’s Fallacy to explain the concept with an example. Years ago, I remember watching a roulette wheel in a casino, and the ball landed on black eight times in a row. Eight times. During this run of blacks, there were people literally throwing money on the table, convinced that due to the number of times it had landed on black, the ball was far more likely to land on red with the next spin.

This false assumption is known as the Gambler’s Fallacy. The mistaken belief that if something happens more frequently than normal during a given period, it will then happen less frequently in the future, or vice versa. It’s one of the most common thinking errors people make, and it costs them dearly.

This is probabilistic thinking. Or rather, it’s getting probabilistic thinking catastrophically wrong. The past doesn’t predict the future in independent events. In this case, it’s still roughly fifty-fifty (or to be more precise, 48.65% if it’s a European roulette wheel with only a single green zero) that the next spin will land on red or black. What happens in the spin before in no way predicts the next spin of the wheel. The ball has no memory. The wheel doesn’t care what happened before. Each spin is independent.

The most famous example of the Gambler’s Fallacy happened in a casino in Monte Carlo on the 18th of August 1913. Here, a ball was said to have fallen on black twenty-six times in a row. Twenty-six times. As you’d expect, millions of francs were lost as people gambled away their money, falling victim to the Gambler’s Fallacy and to catastrophically bad probabilistic thinking.

If something happens a lot, it doesn’t mean it’s less likely to happen again in the future. Reach into your pocket and toss a coin. It’s fifty-fifty, heads or tails. It’s always going to be fifty-fifty because the last throw in no way influences the next. The coin doesn’t remember. It doesn’t balance out. It doesn’t owe you anything.

So what’s the Gambler’s Fallacy and probabilistic thinking got to do with you, I hear you saying. Life, I’ll give you, is certainly a bit more complicated than a roulette wheel. But the basic principles still apply in ways that might surprise you.

Your life isn’t going to change unless you change. However bad the stuff you’ve gone through in the past, it doesn’t mean that now your life is any more likely to get better in the future. Not unless you start stacking the odds in your favour by doing something about it. The universe doesn’t owe you a good turn just because you’ve had a string of bad ones.

People often say to me that they think their luck must be changing soon, or that they’re due some better luck in their life. There’s a famous saying that “the only cure for hard luck is hard work.” There are many other quotes with the same message. My favourite is the golfer Gary Player’s quote: “The harder I practice, the luckier I get.”

Probabilistic thinking means that if your life is really terrible for a really long time, it doesn’t mean that statistically it’s likely to get any better soon. The universe isn’t keeping score. Life isn’t a roulette wheel that’s going to balance itself out. You’re not “due” for something good to happen just because bad things have been happening.

Yet here’s the good thing. The past does not dictate the future either. A different result in your life is no more likely or less likely because of how long you’ve spent feeling bad or stuck in a bad situation. You’re starting fresh every single day, whether you realise it or not. What happened yesterday doesn’t determine what happens today unless you let it.

Things only change when you change the odds. To do this, you may really have to change the way you play the game. The game of life isn’t going to change unless you do. Do the same thing, repeat the same patterns, and you’ll probably get the same results. Because things really only change for a reason. They change because you make them change.

Let me give you a patient example. Sarah came to see me convinced that she was cursed in relationships. Every man she’d been with had turned out to be emotionally unavailable. Every single one. Five relationships, five emotionally unavailable men. She was absolutely certain that her luck was about to change, that the next one would be different. After all, what were the odds that she’d find yet another emotionally unavailable man?

Pretty high, actually. Because Sarah wasn’t randomly selecting men from the entire male population. She had a type. She was attracted to a specific set of characteristics that, unfortunately for her, correlated strongly with emotional unavailability. She was going to the same places, looking for the same qualities, making the same choices. The universe wasn’t conspiring against her. She was creating the pattern herself.

Until Sarah changed what she was attracted to, where she was looking, and what she was choosing, the next relationship was going to be exactly like the last five. The probability wasn’t changing. She was just spinning the same weighted roulette wheel over and over, expecting different results.

This is where most people get probabilistic thinking wrong in their lives. They think that because they’ve had a string of failures, they’re due for a success. Because they’ve been stuck for years, surely something has to give. Because they’ve tried and failed multiple times, the next attempt must be the one that works.

No. Not unless you change something fundamental. Not unless you alter the probability itself by changing your approach, your mindset, your actions, your choices. Otherwise, you’re just the person in the casino betting on red because black has come up eight times in a row, convinced that the odds are now in your favour when really they’re exactly the same as they’ve always been.

Here’s another way to think about it. Imagine you’ve applied for ten jobs and been rejected for all ten. Does that mean you’re more likely to get the eleventh job? Only if you’ve changed something. Only if you’ve improved your CV, practised your interview technique, applied for more suitable positions, developed new skills. Otherwise, the probability of success remains exactly as it was for jobs one through ten.

The past is not working in your favour just because you’ve had a tough time. The universe is not storing up good fortune to bestow upon you later. Probability doesn’t care about your history. It only cares about the current conditions, the current odds, the current setup.

So if you want different results, you need different odds. You need to change the game you’re playing. You need to load the dice in your favour instead of hoping they’ll magically land on six just because they’ve landed on one the past five times.

Do the same thing, repeat the same patterns, make the same choices, and you’ll get the same results. Not because the universe is against you. Not because you’re unlucky. But because that’s how probability works. The outcome matches the conditions. Change the conditions, change the outcome. Keep the conditions the same, keep getting what you’ve always got.

This isn’t pessimistic. This is empowering. Because it means you’re not at the mercy of random chance waiting for your luck to turn. You’re in control of the odds. You can change the game. You can load the dice. You can stack the deck in your favour.

But you have to do it deliberately. You have to recognise that repeating the same actions and expecting different results isn’t hope, it’s delusion. You have to accept that your past struggles don’t entitle you to future success. They just prove that what you’ve been doing isn’t working.

So what are you going to do differently? What odds are you going to change? What game are you going to stop playing? What new approach are you going to try? Because things really only change for a reason, and that reason is you.

Ready?

Further reading

• Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124-1131.
• Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.
• Croson, R., & Sundali, J. (2005). The gambler’s fallacy and the hot hand: Empirical data from casinos. Journal of Risk and Uncertainty, 30(3), 195-209.
• Ayton, P., & Fischer, I. (2004). The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness? Memory & Cognition, 32(8), 1369-1378.
• Langer, E. J. (1975). The illusion of control. Journal of Personality and Social Psychology, 32(2), 311-328.