Treikort was played quite a lot in Iceland up to the last century. A Treikort is described in old Danish games manuals, but it is unlike the Treikort which was played in Iceland. Some people call this game "3-man Alkort". Here is Ólaf Davíðsson's work describing the game, from his writings on Icelandic amusements (Íslenzkar gátur, skemmtanir, vikavikar og þulur", Ólafur Davíðsson, 1887-1903, Copenhagen).
As alluded to in the name, Treikort is a 3-player game. Just 27 cards out of an ordinary 52 card pack are used.
23 of the 27 cards are as follows: QC (highest unless a 7 is led), 2S, KD, 2H, 4C, 8S, 9H, 9D, Aces, Jacks, Sixes, Eights (except 8S). In addition to these there are the four sevens (bísefarnir): these cannot be beaten if they are led out, but are useless if you have to follow with them to a trick as they cannot beat any card. You are not allowed to lead a seven until you have won a trick. Among equally high cards played to the same trick (e.g. more than one Jack), the card which was played first beats the others.
Each player gets 9 cards, dealt three at a time.
Forehand leads to the first trick and each other player in turn plays a card. Whoever plays the highest card takes the trick and leads to the next trick.
The object of the game is to take as many tricks as possible. A player who wins 13 tricks in 3 games takes the title of Pope, and has the right at the start of the next game to take the highest card from one of his fellow-players and a seven from the other, and to give them in exchange any cards he wants to get rid of. The Pope chooses which player he wants the seven from, and if the chosen player has no seven the Pope gets no card from that player.
The Pope loses his title and the rights described above as soon as he fails to take 13 tricks in any 3 consecutive games.