The addition of a joker to the ordinary 52-card deck makes for some slight adjustment in the total number of hands, their frequencies and the odds. The following table shows the changes (compare with table on page 114). There are now 2,869,685 possible hands:

The interesting fact revealed by this table, aside from the increased frequency of almost all hands (except hands less than one pair, which remain the same) and the addition of a new hand, five of a kind, is that three of a kind, formerly scarcer than two pairs, is now more frequent. This makes two pairs an even less likely winning hand than in Five-Card Stud or Draw Poker without the joker.

Although giving the 4 deuces special powers does not change the total number of hands possible, it does drastically alter the order and frequency of the hands. Compare the following table with those on pages 114 and 123:

This table also reveals some interesting realignments: Five of a kind is much more difficult to get than a straight flush and accordingly ranks above it. Four of a kind is more common than either a flush or a straight and more common than the frequency of both together. Three of a kind will occur almost four times as frequently as two pairs, making it understandably the
playable hand.