The first phase is unusual for a trick-taking game, in that there is asynchronous sloughing of cards that match played cards, while play goes around the table. In a variation common in the United States, the second phase is unusual because sequences of cards are played, connected, and picked up during the rummy phase.
As far as available information suggests, the main version of the game popular in the United States is due to Etan Savir, who learned the game from a Swedish man whilst visiting Greece in the late 1970s. It is not surprising that this version differs significantly from the original version, as both the instructor and pupil were drunk at the time. For example, it wasn't until Mr. Savir's friend Matthew Merzbacher asked a Swedish acquaintance about the meaning of the word did anyone realize that the game is not called "Wheatcuba." Variations on Mr. Savir's version have erupted as the game has spread.
Some Skitgubbe traditions that may or may not be due to Mr. Savir's interpretation of the game are:
A detailed explanation of the rules nearly as Mr. Savir originally explained them can be found at the second link below. These are due to Matthew Merzbacher, to whom Mr. Savir taught the game himself. This version is best played with 4 players, but can work with 3 or 5+. The version on the first page possibly predates Mr. Savir's version, and it is best played with 3, but can work with 2 or 4.