The relative value of five-card poker hands is established based on the probability of each combination of cards. The criterion is simple—the lower the probability the higher the ranking. However, finding the actual likelihood of a particular set of cards occurring involves some complicated mathematical computations. A recent discussion of these calculations explained the basic fundamental math concepts necessary for determining these values.

A quick review

Probability is defined to be the ratio of possible successes divided by the total possible successes and failures. To determine the number of possibilities it must be established whether these hands are permutations or combinations. Both of these measures require that there be no repeating terms in the set of values being considered. This requirement is not an issue since all 52 cards in a standard deck are unique. Permutations require a specific order; combinations do not. Consequently poker hands which are not dependent upon the precise sequence in which the cards are dealt are defined to be combinations.

A two-step process is required to compute the number of possible combinations. First, the total number of potential options must be found. For example, if three cards are to be drawn from a standard deck the first option would be 52, the second would decrease to 51 and the third to 50. The product of those three numbers (132,600) would then be divided by the “factorial” of the number of terms. The factorial is defined to be the multiplication of numbers by decreasing values of one. An exclamation mark (!) is used to represent the factorial. Since three cards are being selected the divisor in this problem would be 3! (3 x 2 x 1). The possible combinations of any three cards would be 52 x 51 x 50 (132,600) divided by 3! (6) and the result would be 22100.

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