The Mathematical Theory Of Gambling Games

The lack of any proof of the concept of statistical correlations and probability theory is intriguing, given the clear popularity of games of dice across the majority of social strata of many cultures over the course of several millennia and up to the XVth century. 

According to legend, French humanist Richard de Furnival wrote a Latin poem in the thirteenth century, and one of its surviving parts contains the first recorded computation of the number of permutations at the chuck-and-luck dice game (there are 216). Willbord the Pious created a game in 960 that stood for 56 moral qualities. 

The goal of this religious dice game was to help the player develop these characteristics by providing a variety of outcomes for three dice (the number of such combinations of three dice is actually 56). 

But neither Willbord nor Furnival ever attempted to specify the relative odds of individual permutations. It is widely believed that Jerolamo Cardano, an Italian mathematician, physicist, and astrologer, was the first to perform a mathematical study of dice around 1526. He developed his own theory of probability using theoretical logic and his own substantial game experience. 

He taught his students how to place wagers in accordance with this approach. At the close of the XVIth century, Galileus revived the study of dice. And in 1654, Pascal accomplished the same thing. Both did so at the behest of risky gamblers who were frustrated by repeated losses and high costs. The results of Galileo’s computations matched those obtained using contemporary mathematical methods. 

So, probabilistic science paved the way. Towards the middle of the XVIIth century, the theory saw significant growth thanks to a document by Christiaan Huygens titled “De Ratiociniis in Ludo Aleae” (Reflections Regarding Dice). The study of probabilities, then, has its roots in the rudimentary challenges posed by gambling.

Prior to the time of the Reformation, the vast majority of people thought that everything that happens is predestined, either by God or by some other supernatural power or distinct being. Up to this day, this view is shared by a sizable population; indeed, it may be the norm. During that time period, that kind of thinking was universal.

In contrast, the mathematical theory predicated on the counterargument that some events can be casual (that is, regulated by the pure case, uncontrollable, occuring without any special goal) had little hope of being published or authorized. 

It took humanity “several millennia to become used to the idea about an universe in which some events occur without a reason or are specified by a reason so remote that they may be anticipated with adequate accuracy using a causeless model,” as noted by mathematician M.G.Candell. The relationship between accident and probability is based on the idea of haphazard action.

When the probability of two events or outcomes are identical, we say that they are equally probable. In games based on the net randomness, every case is totally independent, meaning that every game has an equal chance of achieving the same result. In actuality, probabilistic claims were applicable to a chain of events but not to a single occurrence. 

The “law of the big numbers” describes how the precision of probability-theoretic correlations improves with an increasing number of events, while the frequency with which the absolute number of results of a specific type deviates from the expected one decreases with increasing iterations. Only correlations, not individual events or specific amounts, can be predicted with any degree of accuracy.

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