Bloxx! is a Tetris-style roll-and-write game in which you try to fill as much of your scoring sheet as possible, while not covering the numbers with which you can score points.
Each player starts with their own sheet of paper that has a grid ten squares tall and seven wide. Four of the rows are colored, and some squares have numbers in them. On a turn, the active player rolls two dice, then each player chooses the polyomino showing on one of the dice and draws this shape in their grid as if they had just dropped it into the grid from the top.
Each polyomino has a circle in one position while the rest of its squares have a large X in them. The active player chooses a polyomino before all other players, and if anyone else chooses the polyomino on this die, those players must place an X on their sheet instead of a circle. This is bad since if you can place a circle in the same location as a number, you score points equal to that number at the end of the game.
If you're the first player to fill in all spaces in a colored horizontal row, then you score 4 points; if you complete this same row after someone else, you score only 2 points.
The game ends once two players can't fit either of the current polyominoes into their grid. Players score positive points for completed rows and numbers circled, then lose 1 point for each space left uncovered, whether due to them creating gaps when "dropping" the polyominoes or just not being able to fit a polyomino in the top of their grid. Whoever has the highest score wins!