I recently came across a video making the rather extraordinary claim that stupid people get rich while intelligent people stay poor. The argument, conveniently attributed to Machiavelli, is that intelligent people overthink everything. They see risks, question their assumptions, and wait for the perfect opportunity. Less intelligent people simply act. They borrow money, start businesses, make mistakes, and eventually succeed because they were willing to do what everyone else was afraid of.
It is an appealing explanation, partly because we can all think of examples that seem to support it. We know successful people who have made spectacularly reckless decisions, and intelligent people who never seem to turn their abilities into financial success. But there is something fundamentally wrong with drawing conclusions from those observations. We are looking at the people who made it, without considering everyone who behaved in exactly the same way and failed.
Consider a simple experiment. Imagine flipping a fair coin with $100 in your pocket. Heads increases your money by 50 percent, tails reduces it by 40 percent. Mathematically, this is a favourable bet. Your expected return is 5 percent per flip, so it seems reasonable to keep playing. But suppose you bet your entire balance on every flip, one hundred times. If you get fifty heads and fifty tails, a perfectly ordinary outcome, your original $100 becomes approximately 52 cents.
The explanation is straightforward. A 50 percent gain followed by a 40 percent loss leaves you 10 percent poorer. Gains and losses compound rather than cancel each other out. Repeat that process enough times and the difference becomes enormous. What makes this particularly fascinating is that the expected wealth after a hundred flips is more than $13,000. The average outcome is extraordinarily positive, while the typical person loses almost everything. A tiny number of exceptionally lucky sequences account for an enormous share of the expected wealth.
This distinction between the average across many possible outcomes and what happens to one individual over time is closely related to the concept of ergodicity. In an ergodic system, averaging across the population tells you something meaningful about what happens to an individual over time. But wealth exposed to repeated multiplicative risks does not generally behave that way. The population can become wealthier on average while most individuals become poorer. You cannot plan your life around an average that is sustained by a handful of extraordinary winners.
In 1956, John Kelly, a researcher at Bell Labs, developed a mathematical approach to this problem. Instead of asking how to maximise expected wealth, he asked how to maximise the rate at which wealth compounds over time. His answer was to bet only a fraction of your capital, determined by the probabilities and payouts involved. For our particular coin, that fraction is 25 percent. With fifty heads and fifty tails over a hundred flips, the person repeatedly betting everything ends with 52 cents. The person following Kelly’s rule ends with approximately $185. Same coin, same luck, same starting capital. The difference is how much risk they accepted on each turn.
I find this particularly interesting as an entrepreneur because the startup world is full of people taking concentrated risks. We admire founders who abandon comfortable careers, invest their savings, and dedicate years to building something that may never work. And I think we should admire them. Creating something genuinely new requires acting under uncertainty. But the economics look very different depending on where you sit. A venture capital investor might own stakes in thirty companies, expecting most to fail and a few to generate exceptional returns. The investor can benefit from the average across an entire portfolio. The founder, meanwhile, has one company, one career, and a finite number of years to spend.
That difference is more important than we tend to acknowledge. Research into venture-backed entrepreneurship has found that although the average founder payout can reach millions of dollars, the typical founder receives nothing. This is not necessarily evidence that starting a company is a bad decision. There are many reasons to become an entrepreneur beyond maximising expected financial returns. But it does mean that founders and investors are often playing fundamentally different games, even when they appear to share the same objectives.
Now imagine a room containing thousands of people playing our coin game. Some bet everything, while others follow Kelly’s more conservative approach. At the end, the people who bet everything dominate both extremes of the wealth distribution. They occupy the very top, but they also fill the bottom. The cautious players tend to finish somewhere in the middle, often with substantially more than they started with.
Take a photograph of the richest fifty people in that room and you have what looks like convincing evidence that boldness creates wealth. The photograph is perfectly accurate. What is missing is everyone outside the frame.
This is survivorship bias, and social media has become remarkably efficient at exploiting it. We study billionaires, successful founders, and exceptional investors, then work backwards to identify the behaviours that supposedly made them successful. Perhaps they were unusually intelligent, disciplined, courageous, or persistent. Often they were. But unless we compare them with people who displayed similar characteristics and failed, we cannot know which qualities actually explain the outcome. We confuse the characteristics of winners with the causes of winning.
Of course, the real world is more complicated than a coin toss. Intelligence, competence, and effort matter. Studies using cognitive tests and subsequent earnings data in Nordic countries generally find that higher cognitive ability is associated with higher income. But luck also matters, sometimes enormously, particularly in environments where outcomes are highly unequal. We should be careful about interpreting wealth as a direct measure of someone’s ability, just as we should avoid interpreting failure as proof of incompetence.
Which brings me back to Machiavelli. He never wrote that stupid people get rich. What he actually wrote in The Prince is considerably more interesting. He compared fortune to a river that, when it floods, destroys everything in its path. Human beings cannot control the river, but during calmer times they can build embankments and channels to reduce the destruction when the waters rise. Machiavelli admired boldness, but he also understood how dependent success could be on circumstances. A strategy that brings extraordinary victories in one period can lead to disaster when conditions change.
I think there is something profound in that image. We cannot eliminate uncertainty, and we probably should not try. Risk is inseparable from progress, particularly when attempting to build something that does not yet exist. But there is a difference between accepting uncertainty and exposing yourself to ruin. Financial runway, the ability to change direction, and the discipline to avoid betting everything on a single assumption are all forms of those embankments Machiavelli described five centuries ago.
The most interesting result of the coin experiment is not that the conservative player becomes wealthy. Turning $100 into $185 is hardly the material of a motivational documentary. It is that this player retains the ability to continue. They can take another opportunity, survive another setback, and participate in whatever comes next. The player who bet everything might have become extraordinarily rich, but the typical player has practically nothing left.
Perhaps that is what bothers me most about the original video. It suggests that success is primarily a matter of being brave enough to act, while overlooking how much of success depends on surviving long enough for your decisions to matter. I have enormous respect for people who take risks, and I would hardly be building a company myself if I believed caution was always the answer. But I am increasingly convinced that understanding risk is not the opposite of ambition. It is one of the things that makes sustained ambition possible.
We each get one sequence of events, not the average of ten thousand lives. And while we cannot decide how every coin will land, we have considerably more control over how much we put on the table.
The people at the top of the room are real. So are the people at the bottom. Many of them made exactly the same bets.
And the ones in the middle? They rarely make the headlines. They simply go home, get up the next morning, and play again.
In this episode of Coordinated with Fredrik, Lily and I explore the mathematics of luck, the Kelly criterion, survivorship bias, and what Machiavelli actually understood about fortune.
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