According to Giampaolo Dossena: Giochi di Carte Italiani (Arnaldo Mondadori 1984), the name Coteccio or Cotecchio is applied to various negative point trick games in Italy. He goes on to describe Cottecchio alla Carpigiana, which is played in Modena.
The game of Coteccio described here is played in Trieste. The following account is based on games played during the 1989 Convention of the International Playing Card Society (IPCS).
This is a negative point trick game; normally whoever takes the most points in tricks loses, but if one player takes all the tricks, that player wins.
Up to 7 players using an Italian suited 40 card pack (Triestine regional pattern). From high to low, the cards in each suit rank:
1 (ace), Re (king), Caval (knight), Fante (jack), 7, 6, 5, 4, 3, 2.
Ace = 6, Re = 5, Caval = 4, Fante = 3, other cards = 0, last trick = 6. This caused some excitement at the IPCS Convention because it is exactly the same system as was used in the famous game Trappola. Trappola is now thought to be extinct, and as far as we know Coteccio is the only surviving game using this point system. It seems likely that Coteccio and Trappola were related, perhaps deriving from a common ancestor; the probability of this is slightly increased by the fact that Coteccio, like early forms of Trappola, is played without trumps. On the other hand the structure of the pack used is different, and one of the main features of Trappola, the bonus for winning a trick with a two, is absent from Coteccio.
The game is played anticlockwise. 5 cards are dealt to each player. The player to dealer's right leads to the first trick. Players must follow suit; if unable to do so they may play any card. There are no trumps; the highest card played of the suit led always wins the trick. The winner of a trick leads to the next. Tricks are kept face up in front of the player who won them.
At the beginning, everyone contributes an equal stake to a pool - say 1000 Lire. Each player begins with four lives. Normally at the end of a hand the player whose tricks contain most card points (including the 6 extra for whoever took the last trick) loses one life. If two or more players tie for most points they each lose a life. However if the first four tricks are all won by the same player, that player has two options:
A player with no lives left can call the doctor, provided that there remain at least two other players in the game who have not lost all their lives. The price of calling the doctor must be agreed before the game (say 500 Lire), and a maximum limit is usually placed on the number of times the doctor may be called. The player in ned of the doctor pays the doctor's fee to the pool and receives in return a number of lives equal to those of the player who has fewest lives left (for example if there are 3 other players left in the game when I lose my last life and they have 3, 1 and 4 lives, then I get one life for my 500 Lire; if they have 2, 2 and 4 lives then the doctor gives me 2 lives).
A player with no lives who cannot or does not wish to call the doctor drops out of the game. Those left alive continue until only one player remains. This last player wins and collects the entire contents of the pool.
As players drop out, the turn to lead to the first trick continues to rotate anticlockwise, passing to the next player if the player whose turn it would have been is dead. The dealer is always the player to the left of the leader. So for example if the player who was about to deal dies, the same player who dealt the previous hand will deal again.
If all the remaining players have one life and they all tie for most points, thus dying simultaneously, none of them can win the pool. In such a case the game is restarted; all the players (including any who died earlier) are given 4 lives and they continue playing for the same pool. This situation most commonly occurs when only two players are left in the game with one life each and they tie for most points on what was to have been the last hand.
You can download a freeware Coteccio program from Thanos Card Games.