The Number of Variations of Poker Hands

Knowing about the numbers behind a game enables any player to understand more its rules, and better yet, it also aids the player in making winning strategies. Gamblers playing poker are no exception.

The typical poker game uses the standard deck, which is made up of four suits with 13 cards each, for a total of 52 cards. A poker hand consists of five cards. Using the standard deck, 10 kinds of poker hands can be created.

However, there are games wherein the dealer may opt to add one or more wildcards or jokers to the 52 cards. If this is the case, the number of poker hands that can be created is 11. Why is this so? The most superior poker hand, the five of a kind, is only possible when there is a wildcard, which is a card that can be of any value that the player wishes it to be. The five of a kind is made up of 4 cards that are equal in value (one from each of the 4 suits such as a jack of spades, jack of diamonds, jack of clubs and jack of hearts) plus a wildcard to complete the hand.

There are 13 possible variations of this hand. The most superior variation, of course, is a hand with four aces and a wildcard.

In poker games where there is no wildcard, the total number of variations of the 10 possible hands is 2,598,960. Let's break this number down so you can see how the variations all add up.

With the exemption of the five of a kind hand, poker hands are more superior when it has fewer variations. This is only logical because it is harder to come up with those hands. The hand with the fewest variations, and therefore the most superior hand in games where there is no wildcard, is the royal flush. The royal flush has only 4 variations because each royal flush has to be made up of an ace, king, queen, jack and ten which all must come from the same suit. Since there are only 4 suits, only 4 variations can be created.

The straight flush has 36 variations while the four of a kind hand has 624. The full house has 3,744 variations while the flush has 5,108. There are 10,200 kinds of straight hands, 54,912 three of a kind variations and 123,552 versions of the two pairs hand.

The one pair and no pair hands have the most number of variations, with 1,098,240 and 1,302,540 respectively.

Never assume that knowing statistics such as the number of variations of a poker hand is trivial. Being well-versed with the mathematics of poker games increases your chances of winning and quality of decision-making during play.