Gaming and probability have been an idea since 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 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 initial written text on chance. Motivated by Paccioli’s work, Girolamo Cardano (1501-1576) made further improvements in probability theory. His work 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 immediate recognition. Blaise Pascal (1623-1662) also contributed to probability theory. His friend, Chevalier de M??r??, was an avid gambler with the wish to become wealthy from it. De M??r?? attempted a new mathematical approach to a gaming game but didn’t get the desired results. Determined to know why his strategy was ineffective, he consulted with Pascal. Pascal’s work on 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 own ideas and thoughts. These interactions led to probability theory’s conception. To this day, many gamblers still trust the fundamental notions of probability theory in order to make informed decisions while betting.
The following chart enumerates that the (absolute) frequency of each hand, provided all combinations of 5 cards randomly drawn out of a complete deck of 52 without replacement. Wild cards aren’t considered. In this chart:
Different hands is that the number of distinct ways to draw on the hands, not counting different matches.
Frequency is the number of methods to draw on the hand, such as the identical card worth in various suits.
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