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 betting; if playing a game with high stakes, players wanted 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 probability. Motivated by Paccioli’s work, Girolamo Cardano (1501-1576) made further improvements in probability theory. His job from 1550, titled Liber de Ludo Aleae, discussed the concepts of chance and the way they were directly related to gambling. Since it was not published until after his passing his work didn’t 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 know why his approach 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). Communicating through letters, both continued to exchange their ideas and thoughts. These interactions led to the conception of fundamental probability theory. For this day, many gamblers nevertheless rely on the fundamental concepts of probability theory in order to make informed decisions while gambling.

The next chart enumerates that the (absolute) frequency of each hand, given all mixtures of 5 cards randomly drawn from a complete deck of 52 without replacement. Wild cards are not considered. In this chart:

Different hands is that the lot of different techniques to draw on the hands, not counting different suits.

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

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