# Poker probability

Gaming and probability have been an idea as long before the invention of poker. The evolution of probability theory in the late 1400s was attributed to gambling; when playing a game with high stakes, players wished to know what the chance of winning would be. In 1494, Fra Luca Paccioli introduced his work Summa de arithmetica, geometria, proportioni e proportionalita that was the initial 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 chance and how they had been directly related to gaming. Since it was not released until after his death, his work did not get any instant recognition. Blaise Pascal (1623-1662) also contributed to probability theory. His buddy, Chevalier de M??r??, was an avid gambler with the goal to become wealthy from it. De M??r?? attempted a new mathematical approach into a gambling game but didn’t get the desired benefits. Determined to understand why his approach 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). Communication through letters, both continued to exchange their ideas and thoughts. These interactions resulted in fundamental probability theory’s conception. To this day, many gamblers still trust the basic notions of probability theory so as to make informed decisions while gambling.

The next chart enumerates the (absolute) frequency of every hand, given 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 that the lot of distinct ways to draw the hand, not counting different suits.

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

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