Gaming and probability have been an idea as long before the creation of poker. The development of probability theory in the late 1400s was imputed to betting; when playing a game with high stakes, players wished to know what the prospect of winning is. In 1494, Fra Luca Paccioli released his work Summa de arithmetica, geometria, proportioni e proportionalita that was the first written text on chance. Motivated 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 chance and how they were directly related to gaming. As it wasn’t published until after his passing, however, his work did not get any recognition. Blaise Pascal (1623-1662) also contributed to probability theory. His friend, Chevalier de M??r??, was an avid gambler using the wish to become wealthy from it. De M??r?? tried a new mathematical approach into a gaming game but did not get the desired results. Determined to know why his approach was ineffective, 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 probability theory’s conception. For this day, many gamblers still trust the fundamental concepts of probability theory in order to make informed decisions while betting.
The next chart enumerates that the (absolute) frequency of each hand, provided all combinations of 5 cards randomly drawn out of a full deck of 52 without replacement. Cards are not considered. In this graph:
Distinct hands is the lot of different ways to draw on the hands, not counting different matches.
Frequency is the number of methods to draw the hand, including the same card worth in suits.
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