The example of Blaise Pascal, the famous French mathematician of 17th century, proves that gambling might be not so much a purpose as means. It can be an excellent exercise for mind, as in case with Pascal and another French mathematician – Fermat, who invented calculations, now known to us as theory of probabilities.
“Theory of probabilities was created when Pascal and Fermat started playing gambling games”, stated one of their contemporaries.
These two scientists did sums on theory of probabilities by correspondence and the relevant material was obtained during their visits to the gambling house at leisure. Later this correspondence resulted in Pascal’s treatise, “completely new composition on accidental combinations which govern the gambling games“.
In his work Pascal almost completely casts out phantoms of luck and chance from gambling games, substituting them with cold statistic calculations based on the arithmetic mind. It’s difficult for us to imagine what riot the invention made among the gamblers. We treat theory of probabilities as something trivial, 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 enhance the obsession 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 actually is 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 mathematics 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 definitions. 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 invention – “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 to expect regular gain a chance can give according to the initial terms – stakes”.
Somebody will say that it is not so encouraging. However seeming dryness of this formulation ceases when you just pay your attention to word combination “regular gain”. Expectation 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 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 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 definitions of law or ethics.
“Pascal’s triangle” or where theory of probabilities fails.
Pascal summed up the results of 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 invention by the illiterate public in 17th century touched the rumour that “Pascal’s triangle” helped to forecast world catastrophes and natural disasters of the remote future. Indeed presentations of theory of probabilities in the form of graphic tables or figures and moreover proved by the real game caused almost religious sensations in uneducated gamblers.
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 destiny governs such things – and Pascal never debated 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 stake (card, lead, etc.)
Pascal’s invention is even more amazing if to take into account that its famous triangle was known to Muslim mathematician of certain religious 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. Awareness of this fact enraptured by Pythagorean’s, philosophers who deeply and emotionally perceived it at that time.
One to thirty-five.
Pascal more and more often faced similar complications connected with the game that caused controversies in gambling houses and aristocratic mansions in France of that 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 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 bones 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 chance to thirty-five to win.
The result of these simple calculations can cast down many fans of dice, but on the other hand, the rapture of those lucky ones throwing double six is staggering. Because they know the exact devil number of opposite outcomes that opposed their luck!