  The game of Hangman is a classical asymmetric two player game in which one
player, the setter, chooses a secret word from a language, that the other
player, the guesser, tries to discover through single letter matching queries,
answered by all occurrences of this letter if any. In the Evil Hangman variant,
the setter can change the secret word during the game, as long as the new
choice is consistent with the information already given to the guesser. We show
that a greedy strategy for Evil Hangman can perform arbitrarily far from
optimal, and most importantly, that playing optimally as an Evil Hangman setter
is computationally difficult. The latter result holds even assuming perfect
knowledge of the language, for several classes of languages, ranging from
Finite to Turing Computable. The proofs are based on reductions to Dominating
Set on 3-regular graphs and to the Membership problem, combinatorial problems
already known to be computationally hard.
