Probability and gambling have been an idea as before the invention of poker. The development of probability theory from the late 1400s was attributed to gambling; when playing a game with high stakes, players wished to understand what the chance of winning would be. In 1494, Fra Luca Paccioli introduced his work Summa de arithmetica, geometria, proportioni e proportionalita which was the initial written text on chance. Developed by Paccioli’s job, Girolamo Cardano (1501-1576) made further developments in probability theory. His job from 1550, titled Liber de Ludo Aleae, discussed the concepts of probability and how they were directly related to gambling. Since it was not published until after his passing, his work did not receive any 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 gambling game but didn’t get the desired benefits. Determined to know why his strategy was unsuccessful, he consulted with Pascal. Pascal’s work with this problem began a significant correspondence between him and fellow mathematician Pierre de Fermat (1601-1665). Communication 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 rely on the fundamental concepts of probability theory in order to make informed decisions while betting.
The following chart enumerates the (absolute) frequency of each hand, provided all mixtures of 5 cards randomly drawn out of a complete deck of 52 without replacement. Wild cards are not considered. In this chart:
Different hands is that the lot of different ways to draw the hand, not counting different matches.
Frequency is the number of methods to draw the hand, including the identical card values in different suits.