# Poker probability

Gambling and probability are an idea as long before the invention of poker. The evolution of probability theory from the late 1400s was attributed to betting; if playing a game with high stakes, players wanted to know what the prospect of winning is. In 1494, Fra Luca Paccioli released his work Summa de arithmetica, geometria, proportioni e proportionalita which was the first written text on probability. 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 chance and how they had been directly related to gambling. His work didn’t get any instant recognition as it was not published until after his passing. Blaise Pascal (1623-1662) also contributed to probability theory. His buddy, Chevalier de M??r??, was an avid gambler using the goal to become wealthy from it. De M??r?? tried a new mathematical approach to a gambling game but didn’t get the desired results. Determined to understand why his approach was ineffective, he consulted with Pascal. Pascal’s work on this problem began a significant correspondence between him and fellow mathematician Pierre de Fermat (1601-1665). Communication through letters, both continued to exchange their own ideas and ideas. These interactions resulted in fundamental probability theory’s conception. To this day, many gamblers nevertheless trust the fundamental notions of probability theory in order to make informed decisions while gambling.

The next 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. Wild cards aren’t considered. In this chart:

Different hands is the number of distinct techniques to draw on the hand, not counting different suits.

Frequency is the number of methods to draw on the hand, such as the card values in various suits.

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