The Mathematical Theory Of Gambling Games

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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