Toss a coin: heads or tails, impossible to know. Toss it ten times: you might get 7 heads, or 3. Toss it a thousand times: you'll get almost exactly half and half. This little miracle has a name: the law of large numbers.
A Swiss discovery
It was a mathematician from Basel, Jacob Bernoulli, who proved it. His book was published in 1713, after his death. His idea: a single event is unpredictable, but many events together become predictable.
The numbers are striking. With 10 tosses, there's about a 66% chance of getting between 4 and 6 heads. With 100 tosses, about a 96% chance of landing between 40% and 60% heads. With 1,000 tosses, it's practically certain.
What this means for your money
Imagine companies that each have a 5% risk of going bust over the next few years.
- Buddy puts his CHF 1,000 into a single company. He has a 5% risk of losing everything. One chance in twenty is a lot.
- Mangosteen spreads his CHF 1,000 across 20 different companies, CHF 50 each. It's actually likely that one of them goes bust (about a 64% chance). But then he only loses CHF 50. To lose a quarter of his money, 5 companies out of 20 would have to fail: about 1 chance in 400.
The same risk for each company, but a much calmer result. That's the meaning of the old proverb: don't put all your eggs in one basket. Investments that buy hundreds of companies in one go (the index funds we've talked about) use exactly this law.
Two limits worth knowing
First limit: this calculation assumes companies fail independently of one another. In a big crisis, many fall at the same time. "A bit of everything" reduces risk, but doesn't remove it.
Second limit: in 1963, the economist Paul Samuelson told the story of a colleague who turned down a risky bet once, but would accept it if he could repeat it a hundred times, thinking "it would all even out". Samuelson showed this was a mistake: repeating the same bet doesn't make it safe; the amount you could lose grows too. What protects you is sharing out the same sum across many different things, not betting more often.
Try this tonight with your child
Take a die. Your child rolls it once and writes down the result: it could be a 1 or a 6. Then they roll 10 dice (or the same die 10 times) and work out the average. Repeat each experiment three times. They'll see that the single roll jumps all over the place, while the average of 10 dice stays close to 3.5. Ask: "Which would you prefer for your money?"
Read also: Shares, gold, property, savings account: the big family of investments
Further reading
- Bernoulli, J. (1713). Ars Conjectandi. Basel: Thurneysen.
- Samuelson, P. A. (1963). Risk and Uncertainty: A Fallacy of Large Numbers. Scientia, 98, 108–113.
Teach them to fill lots of baskets. Join the Mangosteen Buddy waitlist: Book 1 of the comic is free, and the first 500 families get their first year of Premium on us (worth CHF 150). Save my place
Educational content, not investment advice. The probabilities shown come from a simplified model (independent companies, each with a 5% risk of failure).