What mathematical principles lie behind online casinos?
The popularity of many people in the game of dice is obvious. The more surprising is the absence of any mention of any attempts for thousands of years in any way to determine mathematically, or by the statistics of games, the probability of a favorable outcome. For the first time more or less serious attempts to describe the game mathematically only in the XVI century. Although, in the poem, the authorship of which is attributed to the French poet-humanist XIII century. Richard de Funnival, there is a fragment, which probably contains the very first attempt to calculate the number of possible options for three bones (there are 216 in all). In the tenth century, a game was invented, the purpose of which was not monetary gain.
The player was instructed to improve in one of the 56 virtues. It is interesting that the number of options in this version of the game is really 56, so that each corresponds to one virtue. Thus, the church tried to distract the players from the addictive habit of gambling. The invention of this game is attributed to a pious Uibold. However, to determine the probability of occurrence of a given combination did not try in any of these cases, satisfied with the calculation of the total number of options. For the first time, the mathematical analysis of the popular dice game was conducted by the Italian mathematician Gerolamo Cardano in 1526. His probability theory was based on his own playing practice and rather serious theoretical grounds. Based on these developments, he even tried to develop a system of tips on how to make bets. At the end of the sixteenth century continued the exploration of the game of dice from the point of view of mathematics Galileo.
Where does modern casino come from?
Pascal tackled this issue as early as 1654. Galileo and Pascal studied the game at the insistence of unfortunate players who lost significant amounts of bone. In principle, Galileo’s calculations did not differ from those that modern mathematicians would also use. It can be argued that it is at this moment that a section of mathematics appears devoted to probabilities. A real breakthrough in the study of probabilities was the «De Ratiociniis in Ludo Aleae» of Christian Huygens, published in the middle of the seventeenth century. So, it was the destructive passion for the game that became the true engine of the development of probability theory.
Beliefs of people
Prior to the Reformation, almost all people firmly believed that all events are predetermined and directed by some supernatural powers. Mathematical theory, which argued that very many events are purely accidental, that is, they are absolutely not governed by anyone and nothing and occur without any predetermination or «higher goal,» practically had no chance of publication, let alone approval. Mathematics of MG Kendall belongs to the thesis that humanity needed several centuries to get used to living in a world, events in which can occur completely without a reason or depend on a reason so remote that they could be predicted accurately enough by using causeless model. Representations about the relationship between random events and their probabilities are based on the idea of absolute randomness.
Law of Large numbers
Events or the onset of any consequences, the probability of which is equal, have equal chances in each trial. That is, in each game the probability of occurrence of any result is the same as in the rest. The well-known «Law of Large Numbers» reflects the fact that the accuracy of the proposed probability of the relationship increases with the number of events. In the absolute, the expected result is the less the actual one, the more events described. Precisely to predict it is possible only a result of a series from a huge number of identical events, but not the result of each event separately.