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Introduction Lottery is by far the oldest and the most widely known game of chance, having been practiced since antiquity. In its various forms, the lottery preserves a basic structure and technical procedure that makes it the easiest and most popular game of chance: the random draw from an urn of some objects (balls, tickets, lots, plates, slips, etc.) containing predefined symbols (numbers, images, words, etc.), followed by the distribution of prizes for players who made correct predictions regarding this draw, according to some pre-established rules. Particularizing this definition, we find forms of lottery even in the simple procedures of drawing lots or organizing tombolas. Nowadays, the most prevalent form of lottery is that with randomly selected numbers; winning categories are based on the number of numbers correctly predicted on the playing ticket. The most popular forms of these games are the national and state lotteries. The early history of the lottery can be traced back to the second millennium B.C. In the Chinese The Book of Songs there is a reference to a game of chance known as “the drawing of wood”, which in context appears to describe the drawing of lots. The first signs of a lottery trace back the Han Dynasty between 205 and 187 B.C., where ancient Keno slips (a form of lottery also practiced nowadays) were discovered. The first known European lottery occurred during the Roman Empire. The earliest record of a public lottery offering tickets for sale is the lottery organized by the Roman Emperor Augustus Caesar. Proceeds went for repairs to the city of Rome, and the winners were given prizes in the form of valuable articles. The first recorded lotteries to offer tickets for sale with prizes in the form of money were held in the Low Countries during the period 1443–1449, and their funds were used for town fortifications. In the 17th century, it was quite common in the Netherlands to organize lotteries to collect money for the poor; the prizes were paintings. The Dutch were the first to shift the lottery to solely monetary prizes and to base prizes on odds (roughly about 1 in 4 tickets winning a 5PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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