Zugzwang

Zugzwang (pronounced tsook-tsvahng)

(1) In chess, a situation in which a player is limited to moves that cost pieces or have a damaging positional effect.

(2) A situation in which, whatever is done, makes things worse.

(3) A situation in which one is forced to act when one would prefer to remain passive.

(4) In game theory, a move which changes the outcome from win to loss.

Circa 1858 (1905 in English): A modern German compound zug+zwang.   Zug (move) is from the Middle High German zuc & zug from the Old High German zug from Proto-Germanic tugiz, an abstract noun belonging to the Proto-Germanic teuhaną, derived from the primitive Indo-European dewk (to pull, lead).  Cognate with the Dutch teug and the Old English tyge.  Zwang (compulsion; force; constraint; obligation) is from the Middle High German twanc from the Old High German geduang.  It belongs to the verb zwingen and cognates include the Dutch dwang and the Swedish tvång.  The word is best understood as "compulsion to move" or, in the jargon of chess players: "Your turn to move and whatever you do it'll make things worse for you", thus the application to game theory, military strategy and politics where there's often a need to determine the "least worse option". 

Chess and Game Theory

The first known use of zugzwang in the German chess literature appears in 1858; the first appearance in English in 1905.  However, the concept of zugzwang had been known and written about for centuries, the classic work being Italian chess player Alessandro Salvio's (circa 1575–circa 1640) study of endgames published in 1604 and he referenced Shatranj writings from the early ninth century, some thousand years before the first known use of the term.  Positions with zugzwang are not rare in chess endgames, best known in the king-rook & king-pawn conjunctions.  Positions of reciprocal zugzwang are important in the analysis of endgames but although the concept is easily demonstrated and understood, that's true only of the "simple zugzwang" and the so-called "sequential zugzwang" will typically be a multi-move thing which demands an understanding of even dozens of permutations of possibilities.

Endgame: Daily Chess Musings quick illustration of the elegance of zugwang.

The concept finds its formal definition in combinatorial game theory. It describes a situation where one player is put at a disadvantage because he has to make a move although the player would prefer to pass and make no move. The fact that the player must make a move means that his position will be significantly weaker than the hypothetical one in which it is his opponent's turn to move. In game theory, it specifically means that it directly changes the outcome of the game from a win to a loss.