In nuclear strategy, assured destruction refers to the ability to survive a nuclear first strike with enough weapons to ensure the destruction of the opponent in the retaliatory strike.
In a system of mutual assured destruction both sides are have the ability to response to a first strike. The goal of assured destruction is to deter one's opponent from launching a nuclear attack in the first place, and if an attack takes place, the strategy can be considered to have failed.
In order to have assured destruction capability, a nuclear power must have enough nuclear weapons to be able to respond to a first strike. This may cause an open-ended arms race in which neither side is more secure after building weapons. To prevent this outcome, both sides can negotiate a nuclear disarmament treaty.
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