The example of Blaise Pascal, the famous French mathematician of 17th century, shows that betting might be not really much an intention as means. It can be an excellent slot27 exercise for mind, like for example case with Pascal and another French mathematician : Fermat, who invented information, now known to us as theory of possibilities.
“Theory of possibilities is fashioned when Pascal and Fermat started playing betting games”, stated one of their contemporaries.
These two scientists did chunks on theory of possibilities by messages and the relevant material was obtained in their visits to the betting house at leisure. Later this messages resulted in Pascal’s treatise, “completely new make up on unintentional mixtures which govern the betting games”.
In his work Pascal almost completely casts out phantoms of luck and chance from betting games, a replacement of them with cold fact information based on the maths mind. It’s difficult for us to imagine what riot the advent made among the players. We treat theory of possibilities as something insignificant, though only specialists are sound on its details, but everyone understands its main principle. But in the changing times of the French mathematician, the minds of all players were absorbed with such ideas as “divine intent”, “lap of Fortune” and other things that only improve the infatuation by the game adding extra mystical tones to the games. Pascal without any concern 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 due to 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 cube that tool a great deal of time. In Pascal’s opinion, the unique feature of the art of mathematic consideration when compared to the common statistics is that it obtains its results not from the experiments but is based on “mind foreseeing”, i. e. on mental meanings. 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 advent : “method of statistical expectation”.
Attached money, wrote Pascal, no more belonged to gamester. However, losing nth sum of cash, 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 mental ability. We are talking about the acquired “right to anticipate regular gain the chance can give according to the initial terms : stakes”.
Somebody will say that it is not so encouraging. However seeming dryness of this ingredients ends when you just pay your awareness of word combination “regular gain”. Requirement of gain actually is 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 figures particular values of “right for gain” depending on different initial terms. Thus an entirely new definition of right appears in mathematics which differs from the similar meanings of law or honesty.
“Pascal’s triangle” or where theory of possibilities fails.
Pascal summed the link between these experiments in the form of the so-called maths triangle consisting of mathematical numbers. If you can apply it, you can precisely foresee probability of different gains.
For common people “Pascal’s triangle” looked similar to magic tables of kabbalists or like a mystic Buddhist mandala. Failure to understand the advent by the illiterate public in 17th century carressed the rumour that “Pascal’s triangle” helped to predicted world catastrophes and natural disasters of the remote future. Indeed presentations of theory of possibilities in the form of visual tables or figures and moreover proved by the real game caused almost orlando sounds in uneducated players.
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 inevitably your destiny governs such things- and Pascal never disputed 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 position (card, lead, etc. )
Pascal’s advent is even more amazing if take into consideration that its famous triangle was known to Muslim mathematician of certain orlando orders many centuries ago. It is absolutely true that Eu Pascal could not obtain this information from anywhere.
All this once again shows that statistical 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 in touch with the game that caused controversies in betting houses and aristocratic mansions in Portugal of this time. Among them there was a problem offered to young Blaise by one of his aristocratic friends.
The problem concerned cube. 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 halloween bones 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 an opportunity to thirty-five to win.