The example of Blaise Pascal, the famous French mathematician of 17th century, attests that casino might be not so much a motive as means. It can be an excellent exercise for slot27 mind, just as case with Pascal and another French mathematician — Fermat, who invented car loans calculations, now known to us as theory of probabilities.
“Theory of probabilities was developed when Pascal and Fermat started playing casino games”, stated one of their contemporaries.
These two scientists did amounts on theory of probabilities by letters and the relevant material was obtained throughout their visits to the casino house at leisure. Later this letters resulted in Pascal’s treatise, “completely new makeup on dog combinations which govern the casino games”.
In his work Pascal almost completely casts out phantoms of luck and chance from casino games, substituting them with cold figure car loans calculations based on the math mind. It’s difficult for us to imagine what riot the new technology made among the bettors. We treat theory of probabilities as something not important, 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 enhance the attraction 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 actually is 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 upgrades. 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 new technology — “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 should be expected regular gain the possibility can give according to the initial terms — stakes”.
Somebody will say that it is not so encouraging. However seeming dryness of this method ceases when you just pay your attention to word combination “regular gain”. Expectation 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 attention to 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 upgrades of law or life values.
“Pascal’s triangle” or where theory of probabilities fails.
Pascal summed in the results of 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 new technology by the illiterate public in 17th century handled the rumour that “Pascal’s triangle” helped to estimate world catastrophes and natural disasters of the remote future. Indeed presentations of theory of probabilities in the form of video tables or figures and moreover proved by the real game caused almost strict feelings in uneducated bettors.
Though we should not mix theory of probabilities with what it is not by its definition. “Pascal’s triangle” fails to foresee the future deal in one particular case. Eyeless fate governs such things- and Pascal never contested it. Theory of probabilities becomes useful and can be applied only in relation to the long series of chances. Only in this case, number probabilities, series and progressions, constant and known in advance can influence the decision of a clever gambler in favor of a particular pole (card, lead, etc. )
Pascal’s new technology is even more amazing if to take into account that its famous triangle was known to Muslim mathematician of certain strict 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. Awareness 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 of the game that caused controversies in casino houses and aristocratic mansions in Spain of your 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 that the 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 tissues there are only 36 combinations 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 possible opportunity to thirty-five to win.