Lottery: your real odds of winning (and how to calculate them)
Every Wednesday and Saturday evening, a French family kisses a ticket. A few minutes later, six numbers come up on television and, in 99.999995% of cases, that ticket ends up in the kitchen bin. The picture that circulates afterwards — an anonymous winner, hooded, holding an oversized cheque — is not the story of the Loto. It is its exception. The story of the Loto is the ticket in the bin, nineteen million times out of nineteen million and one.
This article does not tell you to stop playing. It simply offers you a calm look at what a Loto grid is worth in numbers: how many combinations exist, how many you would have to play to win statistically, and what the cognitive sciences say about the gap between those numbers and our intuition. Once those orders of magnitude are laid out, playing or not remains your choice — but it becomes an informed one.
The grid and its dizzying number of combinations
The French Loto operated by Française des jeux has, since 2008, run on a mechanic that is simple to describe: you tick 5 numbers out of 49, plus 1 ‘lucky number’ out of 10. The number of possible combinations is calculated by multiplying the number of ways to pick 5 numbers among 49 (a binomial coefficient that gives 1,906,884) by the 10 possible lucky numbers. Result: 19,068,840 combinations. Only one wins the top prize.
The probability of winning the jackpot with one validated grid is therefore 1 in 19,068,840 — roughly 0.0000052%. That is the figure FDJ itself publishes in its official rules, and that you’ll find in every reference source, including the Wikipedia entry and the educational pages of France’s Institute for Public Financial Education.
EuroMillions, its pan-European big sibling, plays in a different league. You have to tick 5 numbers out of 50 plus 2 stars out of 12: 2,118,760 number combinations multiplied by 66 star combinations, that is 139,838,160 combinations. One chance in one hundred and forty million. To put that in perspective: if every inhabitant of mainland France played a different grid, with two draws a week, it would take more than two years before a winning grid was randomly played.
These figures are not exotic — they are public, calculable on the back of a napkin by a high-school student. What is exotic is the gap between these counts and the mental image you form of your grid as you tick it.
Three scales to find your footing
A number like ‘19 million’ rolls off the tongue but doesn’t really land. Here are three concrete, sourced comparisons to make the order of magnitude tangible.
Being born an identical twin. According to INED and France’s National Museum of Natural History, the rate of monozygotic twin births is remarkably stable worldwide: about 4 deliveries per 1,000, that is 1 chance in 250. Being born an identical twin is therefore around 76,000 times more likely than winning the Loto top prize with one grid.
Being struck by lightning. Per the lightning-accident analysis published in the journal La Météorologie using Météorage data, about 100 people are struck by lightning each year in mainland France. Adjusted for population, that gives an annual probability close to 1 in 700,000. In a single year you are 27 times more likely to be hit by a lightning bolt than to win the Loto top prize with one grid.
Dying in a road accident. The lifetime cumulative risk, calculated by the American National Safety Council (French figures are of the same order), sits around 1 in 100. Across a whole life. Compared with 1 in 19 million, the ratio is 190,000.
None of these comparisons claims to discourage you. They simply serve as a calibration point: your brain needs a concrete reference frame to process a number like 19,068,840.
Probability versus expected value: the distinction that changes everything
Most players reason in terms of probability of winning: ‘I’ve got a chance’. The right tool to evaluate a gambling product is not that one. It is the expected value: the average return per grid, calculated by multiplying every possible payout by its probability and then subtracting the stake. It is what you win on average per grid if you played to infinity.
For lottery games, expected value is almost always negative — that is even the economic definition of a commercial gambling product. FDJ publishes an indicator, the player return rate (TRJ), which directly gives the share of stakes redistributed as prizes. For the Loto, that rate dropped in January 2026 from 55.35% to 54.85%. Concretely: out of €100 staked across all players, €54.85 are paid back as prizes, and €45.15 stay split between the State (taxes), FDJ (operating costs and profit) and the retail distributors.
For you, an individual player, that means a €2.20 grid has an average expected payout of around €1.21. You lose, on average, €0.99 per grid in the long run. That figure is not an opinion or a prediction about your next ticket — it is the honest price tag on the entertainment that the Loto is. You pay roughly €1 per grid for the right to dream for three days, and the mechanism is designed for that to be the case on average.
This is the pivot point. As long as you reason in terms of ‘I’ve got a chance’, any bet looks reasonable because the chance does exist. As soon as you reason in terms of ‘how much does this chance cost me, on average’, the question shifts to: am I willing to pay this price for this entertainment? The answer can be yes — that is a perfectly legitimate leisure choice. But it is a choice, not a winning calculation.
Why we keep playing in spite of these numbers
If the expected value is negative and the probability tiny, why do 25 million French people play a draw game every year? Several cognitive biases, well documented in psychology, stack up.
The availability bias, formalised by Tversky and Kahneman as early as 1973, makes us overestimate how often an event happens when it comes easily to mind. You see the winner’s smile on television; you never see the 19,068,839 losers from the same draw. Mental images make the win feel close at hand.
The illusion of control, demonstrated by American psychologist Ellen Langer in her landmark 1975 article, pushes us to believe we have influence over purely random events. Choosing your ‘lucky’ numbers — the children’s birthdays, the house number — gives a sense of acting on the outcome. Langer’s experiments showed that participants valued a ticket they had picked themselves up to four times more than an identical ticket assigned at random. But probability-wise, your ‘lucky’ figures and the combination 1, 2, 3, 4, 5 have rigorously the same chance of coming up: pull the Number Generator twenty times between 1 and 49 and you will get, every time, a sequence that looks less likely than another, even though none of them is.
The gambler’s fallacy, to which we devote a whole article, makes us believe a combination ‘has to come up eventually’ or that a number ‘is due’. False: every draw is independent, the FDJ machine remembers no past draw.
Finally, the utility asymmetry theorised by Kahneman and Tversky in their 1979 paper Prospect Theory explains why an honest calculation isn’t enough to stop the gesture. A €2.20 loss every week is felt as a trivial, almost invisible expense — a coffee, a newspaper. A hypothetical €5 million win is felt as a complete change of life. Our brain doesn’t weight these two quantities in proportion to their probability; it feels them in proportion to their imagined impact. That is the exact psychological mechanism that makes the weekly grid so hard to give up, even when you know the figures perfectly.
The awkward question: a regressive tax?
The debate exists in the social sciences and deserves to be named. Several studies — including one published in 2020 in the journal Sociologie des jeux d’argent by a French team using the Baromètre santé surveys from INPES and OFDT — describe gambling as a mechanism with regressive taxation. The share of income devoted to stakes is greater among less well-off households, while a guaranteed slice of every stake goes to the State as taxes. The term ‘regressive tax’ is used technically by some researchers; it is not a campaign slogan, it is a statistical observation.
This data assigns no moral responsibility to players — it describes an economic structure. To name it is simply to acknowledge that the Loto is not a neutral leisure product: it is a leisure product whose financial mechanics are socially oriented.
Chance plays for no one
Once these figures are laid out, the dream is still possible — that is in fact its official role. The Loto sells dreams, and a dream that costs €2.20 for three days of hope is not, in itself, a bad product. The trap isn’t the ticket; it is believing that ticket is a rational calculation. It isn’t. It is leisure at its sticker price, no more, no less.
To go further, you can read our article on cognitive biases in the face of randomness, or step back with What is randomness? — a 3,000-year tour through a notion that, despite all our efforts, plays for no one. If the distinction between probability, proportion and variance interests you on a simpler scale — a coin rather than 19 million combinations — our article on the real probabilities of Heads or Tails covers these notions in detail across 10,000 tosses, with the standard deviation and the log₂(N) formula for long streaks.
