Earlier quoted context omitted.
While my humble opinion is that MAD was effective, let's be careful not to infer causation from a sequence of events (the rooster crows and then the sun rises). And the events of 'MAD' and 'peace' are not in sequence: WWII ended in 1945. MAD wasn't an idea until the 1960s and not implemented in a treaty until the 1972 Anti-Ballistic Missile (ABM) Treaty, AFAICT.[0] It makes more sense if you remember that nuclear wea…
Your timeline is wrong. Bernard Brodie came up with Nuclear deterrence in 1946. The Soviets would have read his work or understood the implicatikns. There was a reason they raced to get the bomb.
Mutually Assured Destruction is not the same as Brodie's Nuclear Deterrence AFAIK (which admittedly isn't much). In 1946, neither side could come close to assuring destruction of the other; the Soviets didn't have any atomic bombs until 1949, the U.S. didn't have the H-bomb until 1954, and of course neither had ICBMs, The best production rocket was probably the V-2.