The probabilities/frequencies are always incompatible. No matter whatever hierarchy of hands is introduced, However, if one changes the ranking in this way, so that two of a kind ranksĪbove three of a kind, three of a kind immediately become less frequent again and should Obviously, one would choose whichever hand had the highest rank, which in this case wouldīe three of a kind, but by doing this, one actually makes frequency of a two pair hand lessįrequent than a Three of a Kind hand, which ought to rank two of a kind above three of a kind If one were to be dealt 2D 2C 6S 8H WC, one would have aĬhoice as to whether to call the WC an 8 (making 2 pair) or a 2 (making 3 of a kind). Let us assume that we introduce one joker as a wild card (WC) and retain the standard hierarchy of handsĪs tabled above. However, by introducing wild cards a paradox is created: Used to count as any card, thus increasing the probability of making a high-ranking hand. (which are often jokers but can be any of the standard 52 cards) can then be “Wild cards” are sometimes introduced to a deck in order to liven up a game.

Ranking of Poker Hands and Their Frequencies of Occurrence When wild cards are introduced, it becomes impossible to rank the hands according to theirįrequency there will always be at least one hand that is ranked below a hand of higher frequency.įor a normal deck of 52 cards the frequencies/probabilities are easily calculated and result in the following hierarchy of hands: The probability of receiving a hand, the higher the hand is ranked. In poker hands are ranked according to the frequency with which they occur when one is dealt 5 random cards from a standard deck – the lower However it is one of the less well known paradoxes, and it should be of interest to anyone who plays poker or has a mathematically curious mind for the paradoxical. This is not the most exciting paradox you will come across at .uk.

Poker hands rank with jokers