The rare-win bias

Every week, millions of people buy a lottery ticket. They know the chance is tiny. They play anyway.

That is not stupidity. It is a very human bias, and it doesn't only touch the lottery.

Our brain handles very small probabilities badly. It blows them up. One chance in a million feels much bigger than it is.

Two psychologists, Daniel Kahneman and Amos Tversky, described this bias in the late seventies.

Faced with a huge and very unlikely win, we overrate our chances. And we happily pay to dream.

In the French Loto, hitting the winning combination is one chance in nineteen million, sixty-eight thousand, eight hundred and forty.

With one ticket a week, it would take on average more than three hundred and sixty thousand years to hit it.

Second idea: negative expectation. The average payout of a gambling game is below the stake. Always.

That is how the organizer pays its costs, the state its taxes, and keeps the rest as profit.

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Take an imaginary game that pays out sixty per cent of stakes to winners. That is called the payout rate.

For every hundred euros staked over time, you get back sixty on average. The other forty stay with the house.

Say a million players stake two euros each. Two million euros are wagered.

One million two hundred thousand euros are paid back. Eight hundred thousand stay with the organizer, whatever happens.

The twist: the house doesn't bet. It can't lose overall. Only the players take a risk.

Third idea: the winner's story. On television, you see the one who won. Never the millions who lost.

Losers don't give interviews. Nobody makes a report about a losing ticket. So winning looks more frequent than it is.

That is survivorship bias. We judge by those who remain visible, and forget those who disappeared.

This bias exists in the stock market too. The story of the one who put everything on a single stock and won is everywhere.

Those who made the same bet and lost everything don't make a video.

A very speculative stock, a long-odds bet, a trendy token: all play on the same spring, the rare win.

To protect yourself, ask one question: out of a hundred people doing exactly the same thing, how many win, and how much do they win?

If the answer is "one in a million, and a lot", you are buying a dream. It has a price. It is not an investment.

Dreaming isn't forbidden. But a dream that costs you every week counts as spending, not as a chance.