Triominoes

The game comes with 56 such pieces, each of which has one number on each of its three corners, which represents one of each possible combination of three numbers (but only one of the two possible arrangements of each trio of three different numbers). That's 20 pieces with three different numbers, 30 pieces with two of one number and one of another, and 6 triples, pieces with three identical numbers.

Each round of a game begins by shuffling all the pieces face down. Then each player draws a certain number of pieces (which varies depending on the number of players). The player with the highest triple begins the round by playing it (with tiebreakers for the piece with the highest sum of numbers, if nobody has a triple), and scores as normal for playing it plus a 10 point bonus. In turn, each player adds a piece to the ones already played, such that it shares at least one edge with a previously played piece, and any corners that touch corners of other pieces must match on all such corners (at least two for each play), and scores a number of points equal to the sum of the numbers on that piece. A player who cannot play draws a piece and suffers a 5 point penalty. If there are no pieces remaining to draw, a player who cannot play loses 10 points and the turn passes to the next player.

When a player goes out by playing his last piece, he scores a bonus of 25 points plus the sum of the values of the pieces in other players' hands. If there are no remaining pieces to draw and all players pass in succession, the hand ends and each player loses the sum of the values of the pieces in his hand. After these calculations at the end of a round, if any player has a score of 500 or more points, the player with the highest score wins the game.

If a player plays a piece such that all three corners touch (and therefore, match) corners of pieces already in play, that player receives a bonus. If that piece closes a hexagon of 6 pieces around a common center, the bonus is 50 (and I always played that the occasional play that closes 2 of 3 hexagons simultaneously scores for all of them). Otherwise, the play is a bridge, and scores a bonus of 40 points.

Note that each bonus play requires a piece with three numbers in a specified order; aside from the likelihood of the piece already being played elsewhere, if the three numbers are all different, there is a high probability of it needing the opposite order of those numbers from the piece that exists in the game.