You Should Be Scared of German Ghost

Abstract

Ghost is a popular word game played by two or more players. Players take turns adding a letter to the end of a growing word fragment, trying not to be the first to complete a valid word. We show that the game, when played on a regular language, is PSPACE-hard, and extend the result to four variants of the game. In addition, we take advantage of a quirk of the German language — that German words can be concatenated together to form longer words — to give a fun extension of our proof of PSPACE-hardness to subsets of the German language.