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THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems

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THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems ( the-mathematics-lottery-odds-combinations-systems )

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The Rules of Lottery Generally, a lotto game consists of the random draw from an urn of objects holding predefined symbols, followed by establishing the prizes for the players who made correct predictions regarding this draw, according to some predefined rules. The objects to be extracted from the urn can be balls, tickets, lots, plates, etc., and the symbols inscribed on these objects can be numbers, icons, images, letters, words, etc. The technical progress of the game assumes the existence of a shuffling and drawing procedure for the objects in the urn (can be manual or performed by a mechanical or electronic device), the display of the sequence of the drawn objects (called the draw from now on), the registration of the predictions before the drawing, and their comparison with the outcomes. This general definition places the lottery game in the category of games of chance, because the prediction of the player with respect to the draw is, in practicality, equivalent to placing a bet whose stake is the price paid for participation in the game (the player’s cost for the lottery tickets). Particularizing this definition, we find primary forms of lottery such as the drawing of a certain marked object from a bag (the equivalent of drawing lots) or organizing a tombola with objects as prizes. In these particular cases, the players are those who perform the draw, and their bet is on drawing tickets holding the various winning objects with their own hands. (In fact, the prediction is no longer made before the drawing, but simultaneously with it). The most popular form of lottery – the one we deal with in this book – is that which uses numbers as the symbols inscribed on the drawn objects (henceforth called number lottery) and in which the rules for giving the prizes are established based upon the quantity of correct numbers predicted by the player that occur in the random draw (the winning numbers on the playing ticket). The chronological process of the number lottery game is as follows: 1. Players buy tickets before the draw, on which they note their predicted numbers. 11

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