maneuver
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military exercise
A large-scale exercise by military units such as soldiers, ships, or aircraft to train for a real emergency.
Die Bundeswehr hält im Herbst ein großes Manöver ab.
The German armed forces are holding a large military exercise in the fall.
You can recognize the meaning of 'Manöver' (maneuver) from the context. If it is about the military or soldiers, it means an exercise. In connection with vehicles or sports, it refers to a skillful movement. In political or social contexts, it often means a ploy.
Das NATO-Manöver findet in der Nordsee statt.
The NATO exercise is taking place in the North Sea.
The noun 'Manöver' (maneuver) is related to the verb 'manövrieren' (to maneuver). 'Manövrieren' (to maneuver) means to steer something (e.g., a ship, a car, or oneself) skillfully through a narrow or difficult situation.
Der Kapitän manövrierte das große Schiff sicher in den Hafen.
The captain maneuvered the large ship safely into the harbor.
In a military context, a 'Manöver' (military exercise) is often 'abgehalten' (held), 'durchgeführt' (carried out), or 'beobachtet' (observed). Typical adjectives are 'militärisch' (military) or 'groß angelegt' (large-scale).
Die Armee hält jedes Jahr ein großes Manöver ab.
The army holds a large military exercise every year.
In the meaning of 'geschickte Bewegung' (skillful movement), 'Manöver' (maneuver) is often part of compound nouns. Well-known examples are 'Überholmanöver' (passing maneuver) when driving, or 'Ausweichmanöver' (evasive maneuver).
Das Überholmanöver auf der Landstraße war sehr riskant.
The passing maneuver on the country road was very risky.
When a ploy is meant, 'Manöver' (maneuver / ploy) often appears with adjectives such as 'taktisch' (tactical), 'politisch' (political), or 'raffiniert' (clever). A common compound is 'Ablenkungsmanöver' (diversionary maneuver).
Die Ankündigung des Politikers war ein rein taktisches Manöver.
The politician's announcement was a purely tactical maneuver.
game / play
'das Spiel' and 'das Manöver' can both describe a planned or strategic action between people or groups. 'das Spiel' refers more to the whole complicated situation in which several sides act tactically or influence others. 'das Manöver' is more like a single skillful action within this situation. It can also be a trick used to deceive others. The words can be confused because both are used not only literally, but also figuratively. 'Spiel' fits when you mean the entire tactical situation; 'Manöver' fits when you mean a specific action or trick.
Mit diesem Manöver wollte der Fahrer einem Unfall entgehen.
With this maneuver, the driver wanted to avoid an accident.
In der Politik durchschaute sie das Spiel der anderen Partei schnell.
In politics, she quickly saw through the other party's game.