In 1962 CE the Soviet army was twice as strong as the American one; the USA was superior in the air and on sea.
The USA had approximately 4:1 superiority in ICBMs, while the USSR had more medium-range missiles that could hit Europe.
Despite this, the USA claimed a 'missile gap' with the USSR and was rapidly building new nuclear missiles.
This gave the former a large 'first strike' capability.
The USSR sought to even the odds by placing medium range missiles in Cuba, from where they could hit targets deep inside the USA.
The Soviet leader Nikita Khrushchev calculated that if the USA would resist, he could trade their removal for control over West Berlin in Germany.
In 1959 CE a revolution led by Fidel Castro had made Cuba communist.
The USA, unhappy with a communist neighbor, three years later had backed up the Bay of Pigs Invasion, an attack of Cuban exiles who wanted to overthrow the government.
The ill-prepared attempt failed miserably and helped the USSR to convince Castro to allow the Soviet missiles to be stationed in Cuba.
He did not relish the idea of looking like a Soviet puppet, but the promise of additional short-range tactical nuclear weapons persuaded him.
The weapons were accompanied by air defense and army units; all were shipped in using "maskirovka", i.e. secrecy, denial and misinformation.
Nonetheless the USA noticed the movements and risked sending in a U-2 spyplane to photograph them, which confirmed the suspicions.
It considered several responses, ranging from doing nothing to an all-out invasion of Cuba.
The US military were all for the latter option, but president Kennedy and his ministers were more cautious.
They realized that the missiles in Cuba did not seriously alter the nuclear-strategic situation and chose a naval blockade of the island.
The USA further showed its muscles by raising its alert state to DEFCON 2, the 2nd highest level.
For about a week tensions were high, though behind the scene diplomatic negotiations were already taking place.
A few Soviet ships tried to slip through the blockade; a U-2 spyplane was shot down.
A Soviet submarine that, unknown to the Americans, was armed with a nuclear torpedo, was attacked, cornered and nearly fired it.
Finally an agreement was reached.
The USSR withdrew the nuclear missiles from Cuba.
In return the USA removed its own medium-range missiles from Turkey and Italy and promised not to invade Cuba.
A hotline was established between Washington and Moscow that remains operational to this day.
War Matrix - Cuban Missile Crisis
Cold War 1945 CE - 1991 CE, Wars and campaigns