The example of Blaise Pascal, the famous 17th-century French mathematician, proves that the game may not have as much an objective as a means. It can be an excellent exercise for the mind, as in the case of Pascal and another French mathematician – Fermat, who invented calculations, now known to us as the theory of probabilities.
“The theory of probabilities was created when Pascal and Fermat started playing games of chance,” said one of his contemporaries.
These two scientists made sums on the theory of probabilities by correspondence and the relevant material was obtained during their visits to the leisure bookmaker. This correspondence later resulted in Pascal’s treatise, “a completely new composition on accidental combinations that govern games of chance”.
In his work, Pascal casts almost ghosts of luck and chance in games of chance, replacing them with cold statistical calculations based on the arithmetic mind. It is difficult for us to imagine what an uproar the invention made among the players. We treat probability theory as trivial, although only experts are solid in its details, but everyone understands its main principle bandarq. But in the days of the French mathematician, the minds of all players were absorbed with notions like “divine intention”, “return of fortune” and other things that only add to the obsession with the game, adding extra mystical tones to the games. Pascal, without any hesitation, opposes his thesis to such an attitude towards the game “Fluctuations of happiness and luck subordinated to considerations based on justice and which aim irrevocably to give each player what is really due to him”.
In Pascal’s hands, mathematics has become a fabulous art of predicting. It is more than astonishing that, unlike Galileo, the French scientist did not carry out numerous tiring experiments on various time-consuming launch data. In Pascal’s opinion, the unique feature of the art of mathematical consideration compared to ordinary statistics is that it derives its results not from experience, but is based on “mind prediction,” that is, on intellectual definitions. As a result, “the precision of mathematics is combined with the uncertainty of chance. Our method lends its strange name -” mathematics of chance “from that ambiguity”. Another curious name followed Pascal’s invention – “mathematical expectation method”.
Staked money, wrote Pascal, no longer belonged to the player. However, losing the umpteenth sum of money, players also earn something in return, although most of them don’t even think about it. In fact, it is absolutely virtual, you cannot touch it or put it in your pocket and realize: the player must have a certain intellectual capacity. We are talking about the “right to expect a regular win that a chance can give under the initial terms – bets”.
Someone will say that it is not so encouraging. However, the apparent dryness of this formulation ceases when you pay attention to the word combination “regular gain”. The expectation of gain ends up being quite justified and fair. Another issue is that a more temperate person is more likely to pay attention to the word “chance” and “can give” (and, consequently, it can also be the other way around).
Using his method of “mathematical expectation”, the French scientist carefully calculates the particular values of “entitlement to gain”, depending on different initial terms. Thus, a completely new definition of law appears in mathematics that differs from similar definitions of law or ethics.
“Pascal’s Triangle” or where the probability theory fails.
Pascal summarized the results of these experiments in the form of the so-called arithmetic triangle that consists of numerical numbers. If you can apply it, you can accurately predict the likelihood of different gains.