Odds and Combinations of Poker Hands

There are a total of 2,598,960 possible poker hand combinations in a 52-card pack poker game. Nearly half (1,302,540 - to be exact) of these combinations are high cards while the rest are higher ranked hands (pairs and above). That is, you have only a 50% chance of getting a hand ranked higher than or equal to a pair.

The following table lists all the possible number of combinations, odds, and probabilities of a 52-card pack poker hands.

As can been in the table, there are only 40 Straight Flush combinations (including the 4 Royal Flushes). Thus, the odds of getting any Straight Flush are 1 in 64,974. The odds of a Royal Flush are 1 in 649,740. In other words, the probability of a hand being a Straight Flush is 0.000015 or 0.0015% - a very unlikely scenario.

It is also important to note that, apart from a High-Card, you have the highest chance of getting a Pair than any other hand by a large margin. As can be seen on figure, while Two-pairs and Three-of-a-kind have quite a significant likelihood, the rest of the high end hands have a very low probability of showing up. Moreover, since there are 13 possible pairs, the number of combinations of each pair is 1,098,240/13 = 84,480. It follows that the odds of a specific pair such as a pair of Aces is 1:31; and thus the probability is 3.25%.

As regards to High Cards, the Ace has the highest probability, followed by King, and down the line. The lowest High Card is the Seven High. (Please explain to yourself why it is impossible to have a Six high, a Five High, etc.?)