Ghost (also known as ghosts or endbee) is a written or spoken word game in which players take turns adding letters to a growing word fragment, trying not to be the one to complete a valid word. Each fragment must be the beginning of an actual word, and usually some minimum is set on the length of a word that counts, such as three or four letters. The player who completes a word loses the round and earns a "letter" (as in the basketball game horse), with players being eliminated when they have been given all five letters of the word "ghost". Ghost can be played by two or more players and requires no equipment, although it can be played with pencil and paper instead of being spoken aloud. The player whose turn it is may — instead of adding a letter — challenge the previous player to prove that the current fragment is actually the beginning of a word. If the challenged player can name such a word, the challenger loses the round; otherwise the challenged player loses the round. If a player bluffs, or completes a word without other players noticing, then play continues. When a round ends, play generally passes to the left. Winning strategy Since the game tree of Ghost can be derived from the list of combinations of letters that are considered to be words, the game (as played by two players) can be easily "solved" to find a winning strategy for one player. Alan Frank, a member of the National Puzzlers' League, constructed a sample winning strategy in 1987, based on the Official Scrabble Players Dictionary.<ref>"Ghostbusters", Word Ways, 1987, page 206</ref> Randall Munroe posted a sample winning strategy in 2007 on the news page of his webcomic, xkcd. He based his solution on the Ubuntu dictionary. Variants Superghost (also known as Fore-and-Aft in Hoyle's Rules of Games, Lexicant, or Llano), is played by choosing either the beginning or end of the growing word fragment and adding a letter there. For example, given the fragment ERA, a player might offer BERA or ERAD. This version was played by James Thurber and his circle of friends. Superduperghost is played by deciding whether to reverse the letters of the word fragment before adding a letter to the fragment's beginning or end. For example, given the fragment ERA, a player might offer BERA, ERAD, NARE, or AREN. This