# How mathematical calculations are used in games of chance

Today there is a wide variety of gambling entertainment and all games have one important characteristic in common. This is chance, that is, the winnings do not depend on the skills of the player, but only on chance. However, despite this, players can determine the probability in a particular combination, and also know about their chances of winning. And this can only be done with the help of mathematical calculations. In this article, we will describe in detail how mathematics is applied in the world of online betting.

Gambling has a long history. In ancient Greece and India there was already an entertainment such as dice. Only instead of modern dice they used animal dice (astragalus). Since the Middle Ages, people began to wonder, how many possible outcomes can there be in a game of dice? And in how many ways can these combinations be obtained?

These questions were answered by Vibold, a French bishop, who in AD 960 wrote a work devoted to the mathematical calculations of the dice. Bishop Wiboldus calculated that by rolling three dice, there are only 56 possible outcomes of the game. But as it turned out later, that number 56 did not reflect the actual number of possibilities. This was because each of the 56 probable outcomes of the game could be obtained by adding up different number combinations.

For example, Bishop Wiebold stated that the number 4 could be obtained if the combinations of 2 + 1 + 1 fell on the dice. However, there are actually 3 combinations that add up to the number 4:

• 2 + 1 + 1
• 1 + 2 + 1
• 1 + 1 + 2

In 1494, the Italian mathematician Fray Luca Bartolomeo de Pacioli published a book in which he describes how to divide the total of the bet between two participants, if the game ended prematurely. He suggested dividing the bet in proportion to the points both competitors scored. But as it turned out later, this Italian mathematician solved the problem incorrectly.

Another Italian mathematician, engineer, philosopher, physician, and astrologer, Gerolamo Cardano, also wrote a book on dice in the 15th century. This book was an attempt to explore the mathematical theory of games of chance.

Gerolamo Cardano, in his reasoning, was the first to approach the general concept of probability theory. The Italian mathematician pointed out that there is a general rule for the calculation. One must always consider the total number of possible outcomes and the number of ways these outcomes can appear. Then you have to find the relationship between the last number and the number of possible combinations remaining.

In addition, brilliant scientists such as Blaise Pascal and Pierre de Fermat made important contributions to the science of probability theory. In their scientific work they were able, for the first time, to correctly solve the problem of dividing a bet between two participants, which the Italian mathematician Fray Luca Bartolomeo de Pacioli had previously been unable to do.

The solutions proposed by Blaise Pascal and Pierre de Fermat contain elements of the use of mathematical expectation, as well as other theorems on the addition and multiplication of probabilities. Over time, a series of scientific works carried out by these scientists formed the basis of modern probability theory.

Subsequently, many famous mathematicians such as Christiaan Huygens, Abraham de Moivre, and Jakob Bernoulli also used mathematics as a science to calculate the results of games of chance.