Poker probability

The development of probability theory in the late 1400s was attributed to gambling; when playing a game with high stakes, players wanted to know what the chance of winning would be.

In 1494, Fra Luca Pacioli released his work Summa de arithmetica, geometria, proportioni e proportionalita which was the first written text on probability.

Motivated by Pacioli's work, Girolamo Cardano (1501-1576) made further developments in probability theory.

His work from 1550, titled Liber de Ludo Aleae, discussed the concepts of probability and how they were directly related to gambling.

His friend, Chevalier de Méré, was an avid gambler with the goal to become wealthy from it.

De Méré tried a new mathematical approach to a gambling game but did not get the desired results.

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 ideas and thoughts.

To this day, many gamblers still rely on the basic concepts of probability theory in order to make informed decisions while gambling.

The following chart enumerates the (absolute) frequency of each hand, given all combinations of five cards randomly drawn from a full deck of 52 without replacement.

It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.

As can be seen from the table, just over half the time a player gets a hand that has no pairs, threes- or fours-of-a-kind.

Some players do not ignore straights and flushes when computing the low hand in lowball.

In some variants of poker a player uses the best five-card low hand selected from seven cards.

The table does not extend to include five-card hands with at least one pair.

Its "Total" represents the 95.4% of the time that a player can select a 5-card low hand without any pair.

Some players do not ignore straights and flushes when computing the low hand in lowball.