The example of Blaise Pascal, the famous French mathematician of 17th century, attests that playing might be not really much a motive as means. It can be an excellent https://slot27.id/ exercise for mind, as with case with Pascal and another French mathematician — Fermat, who invented computations, now known to us as theory of possibilities.

“Theory of possibilities was made when Pascal and Fermat started playing playing games”, stated one of their contemporaries.

These two scientists did amounts on theory of possibilities by letters and the relevant material was obtained throughout their visits to the playing house at leisure. Later this letters resulted in Pascal’s treatise, “completely new arrangement on random mixtures which govern the playing games”.

In his work Pascal almost completely casts out phantoms of luck and chance from playing games, a replacement of them with cold figure computations based on the math mind. It’s difficult for us to imagine what riot the creation made among the bettors. We treat theory of possibilities as something simple, though only specialists are sound on its details, but everyone understands its main principle. But in the occasions of the French mathematician, the minds of all bettors were absorbed with such thoughts as “divine intent”, “lap of Fortune” and other things that only improve the preoccupation by the game adding extra mystical tones to the games. Pascal without any uncertainty opposes his thesis to such attitude to the game “Fluctuations of happiness and luck subordinate to considerations based on fairness and which aim irrevocably to give every player what happens to be on account of him”.

In Pascal’s hands mathematics became fabulous art of foreseeing. It is more than just amazing that unlike Galileo, the French scientist did not make numerous tiring experiments on multiple throwing chop that tool a great deal of time. In Pascal’s opinion, the unique feature of the art of mathematic consideration in comparison to the common statistics is that it obtains its results not from the experiments but is based on “mind foreseeing”, i. e. on intelligent descriptions. As a result “preciseness of mathematics is combined with uncertainty of chance. Our method borrows its awkward name — “mathematics of chance” from this ambiguity”. Another curious name followed Pascal’s creation — “method of exact expectation”.

Secured money, wrote Pascal, no more belonged to gamester. However, losing nth n amount of money, players also gain something in return, though most of them do not even guess it. In fact, it is something absolutely virtual, you cannot touch it neither put into your pocket and to notice it — the gambler should possess certain intelligent ability. We are talking about the acquired “right that is expected regular gain an opportunity can give according to the initial terms — stakes”.

Somebody will say that it is not so encouraging. However seeming dryness of this method ends when you just pay your awareness of word combination “regular gain”. Requirement of gain happens to be quite justified and fair. It’s another matter that a more hot-tempered person is more likely to pay his awareness of the word “chance” and “can give” (and consequently it might also be otherwise).

Using his method of “mathematical expectation”, the French scientist thoroughly works out particular values of “right for gain” depending on different initial terms. Thus a fully new definition of right appears in mathematics which differs from the similar descriptions of law or life values.

“Pascal’s triangle” or where theory of possibilities fails.

Pascal summed in the link between these experiments in the form of the so-called math triangle consisting of statistical numbers. If you can apply it, you can precisely foresee probability of different gains.

For common people “Pascal’s triangle” looked a lot more like magic tables of kabbalists or like a mystic Buddhist mandala. Failure to understand the creation by the illiterate public in 17th century handled the rumour that “Pascal’s triangle” helped to predict world catastrophes and natural disasters of the remote future. Indeed presentations of theory of possibilities in the form of video tables or figures and moreover proved by the real game caused almost spiritual feelings in uneducated bettors.

Though we should not mix theory of possibilities with what it is not by its definition. “Pascal’s triangle” doesn’t foresee the future deal in one particular case. Eyeless future governs such things- and Pascal never contested it. Theory of possibilities becomes useful and can be employed only in relation to the long series of chances. Only in this case, number possibilities, series and progressions, constant and known in advance can influence your choice of a clever gambler in favor of a particular pole (card, lead, etc. )

Pascal’s creation is even more amazing if take into consideration that its famous triangle was known to Muslim mathematician of certain spiritual orders many centuries ago. It is absolutely true that Western european Pascal could not obtain this information from anywhere.

All this once again attests that exact patterns of any process are the same regardless of time and space and whims of the so called Fortune. Knowing of this fact enraptured by Pythagoreans, philosophers who deeply and emotionally perceived it at that time.

One to thirty-five.

Pascal more and more often faced similar complications associated with the game that caused controversies in playing houses and aristocratic mansions in England of these time. Among them there was a problem planned to young Blaise by one of his aristocratic friends.

The problem concerned chop. It was desired to find how many series of throws is theoretically necessary so your chances to win (two sixs) will dominate the probability of all other outcomes taken together. All this is not so difficult as a beginner may presume. It is easy to notice that in the game with two bone fragments there are only 36 mixtures of numbers and only one gives double six. After such explanation it is clear for any sensible person that with one-time throw there is only one opportunity to thirty-five to win.