Gaming and probability are an idea since before the invention of poker. The evolution of probability theory in the late 1400s was imputed to gambling; when playing a game with high stakes, players wished to understand what the prospect of winning is. 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 additional developments in probability theory. His work from 1550, titled Liber de Ludo Aleae, discussed the concepts of probability and how they had been directly related to gambling. His work did not receive any recognition as it wasn’t released until after his passing. Blaise Pascal (1623-1662) also contributed to probability theory. His buddy, Chevalier de M??r??, was an avid gambler with the wish to become wealthy out of it. De M??r?? tried a new mathematical approach into a gambling game but did not get the desired benefits. Determined to know why his approach 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). Communicating through letters, the two continued to exchange their ideas and thoughts. These interactions resulted in the conception of basic probability theory. For this day, many gamblers nevertheless rely on the fundamental concepts of probability theory in order to make informed decisions while betting.
The following graph enumerates that the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn out of a full deck of 52 without replacement. Cards are not considered. In this chart:
Different hands is that the lot of distinct ways to draw on the hand, not counting different suits.
Frequency is the number of ways to draw on the hand, including the same card worth in various suits.
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