How do poker hand rankings relate to the rarity of each hand?

In poker, the ranking of a hand is directly tied to its mathematical rarity. The value of a hand is in inverse proportion to its frequency; essentially, the more unusual or statistically improbable a combination of cards is, the higher that hand ranks.12

Because poker is based on these probabilities, the science of the game relies on understanding the relative expectancies of different holdings. For example, a royal flush is the rarest hand, occurring with odds of approximately 1 in 649,740, and therefore holds the highest rank. Conversely, hands that are statistically common, such as "no pair," have the lowest rank.34

This mathematical foundation allows players to evaluate the strength of their hand relative to others. By knowing the frequency of specific combinations, a player can determine the likelihood that their hand is superior to those held by opponents, which is a fundamental principle of skillful play.4