The example of Blaise Pascal, the famous French mathematician of 17th century, proves that wagering might be not really much a purpose as means. It can be an excellent slot27 exercise for mind, like case with Pascal and another French mathematician – Fermat, who invented data, now known to us as theory of prospects.

“Theory of prospects appeared when Pascal and Fermat started playing wagering games”, stated one of their contemporaries.

These two scientists did sums on theory of prospects by correspondence and the relevant material was obtained during their visits to the wagering house at leisure. Later this correspondence resulted in Pascal’s treatise, “completely new structure on unintended products which govern the wagering games”.

In his work Pascal almost completely casts out phantoms of luck and chance from wagering games, a replacement of them with cold statistic data based on the arithmetic mind. It’s difficult for us to imagine what riot the technology made among the gamblers. We treat theory of prospects as something unimportant, though only specialists are sound on its details, but everyone understands its main principle. But in the times of the French mathematician, the minds of all gamblers were absorbed with such notions as “divine intent”, “lap of Fortune” and other things that only improve the passion by the game adding extra mystical tones to the games. Pascal without any hesitation 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 owing 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 dice that tool a great deal of time. In Pascal’s opinion, the unique feature of the art of mathematic consideration compared to the common statistics is that it obtains its results not from the experiments but is based on “mind foreseeing”, i. e. on intellectual explanations. 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 technology – “method of mathematical expectation”.

Staked money, wrote Pascal, no more belonged to gamester. However, losing nth sum 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 intellectual ability. We are talking about the acquired “right you may anticipate regular gain a possibility can give according to the initial terms – stakes”.

Somebody will say that it is not so encouraging. However seeming dryness of this formulation ends when you just pay your awareness of word combination “regular gain”. Requirement of gain turns out 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 calculates particular values of “right for gain” depending on different initial terms. Thus a completely new definition of right appears in mathematics which differs from the similar explanations of law or ethics.

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

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

For common people “Pascal’s triangle” looked more like magic tables of kabbalists or like a mystic Buddhist mandala. Failure to understand the technology by the illiterate public in 17th century touched the rumour that “Pascal’s triangle” helped to prediction world catastrophes and natural disasters of the remote future. Indeed presentations of theory of prospects in the form of graphic tables or figures and moreover proved by the real game caused almost non secular sensations in uneducated gamblers.

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

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

All this once again proves that mathematical 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 linked with the game that caused controversies in wagering houses and aristocratic mansions in Italy of the time. Among them there was a problem proposed to young Blaise by one of his aristocratic friends.

The problem concerned dice. 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 your bones there are only 36 products 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 possibility to thirty-five to win.