The earliest forms of lottery date back to ancient China, under the Han Dynasty, around 205–187 BC. The game, ancestor of modern keno, was called "baige piao" (白鸽票, white pigeon ticket) and served to finance colossal state projects — including, according to tradition, the construction of the Great Wall. Players selected characters from among the 120 in the Thousand Character Classic, and results were carried to remote villages by carrier pigeons, hence the game's name. In ancient Rome, Emperor Augustus organized lotteries during Saturnalia festivities: every ticket won a prize, ranging from precious vases to slaves.
The modern European lottery was born in Italy in the 15th century. In 1449, Milan organized the first documented public lottery to fund its war against the Republic of Venice. But it was in Genoa that the concept took its definitive form: from 1576, the "Lotto di Genova" allowed citizens to bet on the names of five councillors drawn by lot from 90 candidates. This system — choosing 5 numbers from 90 — is the direct model for the Lotto as we know it. In France, King Francis I created the "Loterie royale de France" in 1539 by the Edict of Châteaurenard, inspired by the lotteries he had discovered during the Italian Wars.
In the 17th and 18th centuries, lotteries became a major financial instrument across Europe. In England, the "English State Lottery" founded in 1694 by Queen Anne helped finance London's aqueduct and the founding of the British Museum (1753). In France, Louis XV established the École Militaire in 1757 with revenue from the Royal Lottery. Voltaire and mathematician Charles Marie de La Condamine exploited a flaw in the Paris municipal lottery in 1729: they systematically purchased tickets whose stakes were lower than the potential winnings, pocketing approximately 500,000 livres — equivalent to several million euros today.
The mathematics of lotteries rests on combinatorial analysis. For the French Loto (5 numbers from 49 + 1 lucky number from 10), the probability of matching all 5 main numbers is 1 in C(49,5) × 10 = 1 in 19,068,840. For EuroMillions (5 from 50 + 2 stars from 12), the jackpot probability is 1 in C(50,5) × C(12,2) = 1 in 139,838,160. Mathematician Leonhard Euler was one of the first to formalize these combinatorial calculations in the 18th century, even advising Frederick the Great of Prussia on organizing the Berlin state lottery in 1763.
The psychology of lotteries reveals fascinating cognitive biases. The "availability bias" identified by Tversky and Kahneman (1973) explains why people overestimate their chances of winning: the media widely showcase winners but never the millions of losers. The "illusion of control" described by Ellen Langer (Harvard, 1975) shows that players who choose their own numbers believe they have better odds than those who use a random draw — even though the probability is strictly identical. In France, according to FDJ data, 70% of Loto players use "lucky" numbers (birthdays, anniversaries), concentrating choices between 1 and 31, which paradoxically increases the risk of having to share the jackpot.
Today, lotteries represent a global industry worth over 300 billion dollars annually according to the World Lottery Association (2023). The Française des Jeux (FDJ), privatized in 2019 for 1.89 billion euros, returns approximately 27% of its revenues to the French state. The largest jackpot in history was the American Powerball of 2.04 billion dollars won in November 2022 in California. EuroMillions holds the European record at 240 million euros won in December 2024. Online random number generators use CSPRNG algorithms (Cryptographically Secure Pseudo-Random Number Generators), guaranteeing perfect equiprobability that the human brain, with its biases, is incapable of replicating.