Tetris is Hard, Even to Approximate

Figure 1: The tetrominoes Sq (“square”), LG (“left gun”), RG (“right gun”), LS (“left snake”), RS (“right snake”), I, and T, with each piece’s center marked. of the top row of the gameboard, and falls downward at a constant speed. As it falls, the player can rotate the piece and slide it horizontally. If, when the piece comes to rest, all gridsquares in an entire row h of the gameboard are filled, row h is cleared : all rows above h fall one row lower, and the top row of the gameboard is replaced by an entirely unfilled row. As soon as a piece is fixed in place, the next piece appears at the top of the gameboard. Typically a one-piece lookahead is provided: when the ith piece begins falling, the identity of the (i + 1)st piece is revealed. A player loses when a new piece is blocked by filled gridsquares from entirely entering the gameboard. The player’s objective is to maximize his or her score (which increases as pieces are placed and as rows are cleared).