The mathematical theory of gambling games

Despite all the obvious popularity of games of dice among the majority of social strata of various nations during several millennia and up to the XVth century, it is interesting to note the absence of any evidence of the idea of statistical correlations and probability theory. The French humanist of the XIIIth century Richard de Furnival was said to be the author of a poem in Latin, one of fragments of which contained the first of known calculations of the number of possible variants at the chuck-and luck (there are 216). Earlier in 960 Willbord the Pious invented a game, which represented 56 virtues. The player of this religious game was to improve in these virtues, according to the ways in which three dice can turn out in this game irrespective of the order (the number of such combinations of three dice is actually 56).

However, neither Willbord, nor Furnival ever tried to define relative probabilities of separate combinations. It is considered that the Italian mathematician, physicist and astrologist Jerolamo Cardano was the first to conduct in 1526 the mathematical analysis of dice. He applied theoretical argumentation and his own extensive game practice for the creation of his own theory of probability. He counseled pupils how to make bets on the basis of this theory.

Galileus renewed the research of dice at the end of the XVIth century. Pascal did the same in 1654. Both did it at the urgent request of hazardous players who were vexed by disappointment and big expenses at dice. Galileus' calculations were exactly the same as those, which modern mathematics would apply.

Thus, science about probabilities at last paved its way. The theory has received the huge development in the middle of the XVIIth century in manuscript of Christiaan Huygens' «De Ratiociniis in Ludo Aleae» («Reflections Concerning Dice»). Thus the science about probabilities derives its historical origins from base problems of gambling games. Before the Reformation epoch the majority of people believed that any event of any sort is predetermined by the God's will or, if not by the God, by any other supernatural force or a definite being. Many people, maybe even the majority, still keep to this opinion up to our days. In those times such viewpoints were predominant everywhere.

And the mathematical theory entirely based on the opposite statement that some events can be casual (that is controlled by the pure case, uncontrollable, occurring without any specific purpose) had few chances to be published and approved. The mathematician M.G.Candell remarked that «the mankind needed, apparently, some centuries to get used to the idea about the world in which some events occur without the reason or are defined by the reason so remote that they could with sufficient accuracy be predicted with the help of causeless model». The idea of purely casual activity is the foundation of the concept of interrelation between accident and probability.

Equally probable events or consequences have equal odds to take place in every case. Every case is completely independent in games based on the net randomness, i.e.

every game has the same probability of obtaining the certain result as all others. Probabilistic statements in practice applied to a long succession of events, but not to a separate event. «The law of the big numbers» is an expression of the fact that the accuracy of correlations being expressed in probability theory increases with growing of numbers of events, but the greater is the number of iterations, the less frequently the absolute number of results of the certain type deviates from expected one.

One can precisely predict only correlations, but not separate events or exact amounts.

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