On the power of lookahead in single-player PuyoPuyo

Abstract

PuyoPuyo is one of the Tetris-type games, which is dealt with as a single-player game in this paper. The player has a winning strategy if the player can keep playing the game infinitely on a gameboard of a constant height. In this paper, we consider how lookahead of input pieces affects the existence of winning strategies in PuyoPuyo, and show conditions that the player cannot win even with lookahead. First, we show the number of colors sufficient to make the player lose on the gameboard of width w when the number of lookahead pieces is m. Next, we show that ten and twenty-six colors are sufficient to make the player lose on the gameboards of width two and three, respectively, no matter how large the number of lookahead pieces is.