Комбінаторний аналіз лотерей

Abstract

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. 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. But the most important element contributing to the public's fascination with lottery games is the amount of the prizes, especially for the highest winning category. The possibility (physically real, mathematically too improbable) of getting «the big hit» – winning the big prize – provides a motivation with complex psychological roots that often overlooks the practical aspects, such as the investments in lottery tickets and the mathematical aspects of the game, especially the winning probabilities. It has been proven mathematically that in ideal conditions of randomness, no long-term regular winning is possible for players of games of chance; therefore, gambling is not a good way to make a living. Most gamblers accept this premise, but still work on strategies in hopes of multiple wins over the long run.