The Great American Trading Company combs European shores for all manner of abstract games. Most of their line involves wooden pieces, but Zatre— a cross between dominoes and Scrabble, represents a change of pace for them.
The object of the game is to place tiles on the board to form connected lines totalling 10, 11, or 12. The plastic tiles have dot patterns like the faces of a die, with values from one to six. Only tiles connected in a horizontal or vertical line score points, and only for values of 10-12. A 1 or 2 can be added to a line of 10 or 11 to score that line again, but no line may ever total more than 12. A fiendish limitation, that.
The unusual scoring system is reminiscent of Facts in Five. Each player has a scoresheet with columns for doubles, 10s, 11s, and 12s. When you score, you put a number (1 for a 10, 2 for 11, 4 for each 12) in the topmost vacant space of the corresponding column. If you form multiple lines of the same total (2 12s, for example) on the same turn, you add the scores together and put them in a single space. Doubles are checked off when a player places tiles on special spaces on the board, and these too are marked from the top of the sheet downward.
Each row of the sheet has a bonus value associated with it, increasing as you move down the scoresheet. If you fill all columns of the row, the bonus is added to that row's score. A row's score is doubled if its double box is checked.
The scoring system rewards balanced play of 10s, 11s, and 12s, so even though 12s are worth more you strive for as even a distribution as possible. It can also be worth more overall to score fewer points on a turn, if in doing so you get multiples of the same total which may ultimately get doubled.
The above notwithstanding, Zatre has less scope for strategic play than it seems. Players hold only two tiles at a time and play them both each turn, so you're forced to do the best you can with what you've got. You may wish to allow players to hold onto one tile if they wish, to allow players to set up scoring possibilities for their next turn.
Each turn feels like a puzzle, with the player trying to find the best possible play for that moment. It's senseless to worry about the future too much, since openings are rarely still available by the next turn. It's reasonable to expect opponents to have a good play option and there's no rack management as in Scrabble, so the prevailing philosophy in Zatre is carpe diem. I'm not sure if the scoring system is refreshingly novel or maddeningly obscure. A pleasant way to pass time, but not overly satisfying as a strategic or mental exercise.