Gambling and probability have been an idea since long before the invention of poker. The development of probability theory from the late 1400s was attributed to gambling; if playing a game with high stakes, players wanted to know what the prospect of winning would be. In 1494, Fra Luca Paccioli introduced his work Summa de arithmetica, geometria, proportioni e proportionalita which was the first written text on probability. Developed by Paccioli’s work, Girolamo Cardano (1501-1576) made further improvements in probability theory. His job from 1550, titled Liber de Ludo Aleae, discussed the concepts of probability and how they were directly associated with gaming. Since it wasn’t released until after his passing his work did not get any recognition. Blaise Pascal (1623-1662) also contributed to probability theory. His buddy, Chevalier de M??r??, was an avid gambler using the wish to become wealthy from it. De M??r?? attempted a new mathematical approach into a gaming game but did not get the desired results. Determined to know why his strategy was unsuccessful, he consulted with Pascal. Pascal’s work with this problem began an important correspondence between him and fellow mathematician Pierre de Fermat (1601-1665). Communication through letters, the two continued to exchange their ideas and thoughts. These interactions resulted in fundamental probability theory’s conception. To this day, many gamblers still trust the basic concepts of probability theory so as to make informed decisions while gambling.
The following graph enumerates that the (absolute) frequency of every hand, given all mixtures of 5 cards randomly drawn out of a full deck of 52 without replacement. Wild cards are not considered. In this graph:
Different hands is the lot of different techniques to draw the hand, not counting different suits.
Frequency is the number of methods to draw the hand, including the identical card values in different suits.
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