WI: World War 3

I'm sure this has been done to death, but, what are so probable times that that WW3 could have begun, and between whom?

Obviously the US and USSR, but over what?

I came up with:
- Bay of Pigs invasion successful, USSR declares war to support Castro
- Operation Unthinkable goes ahead
- USSR joins Korean War
- Checkpoint Charlie flashpoint ignites
- NATO intervention in Hungary 1956/Czechoslovakia 1968
- Ukraine and Russia go to war, after a supposed Ukrainian offensive against Crimea
- US and Arab forces intervene against ISIL on the ground in Syria, Putin declares such an action as aggressive against Assad
- North-South Korean diplomatic collapse leads to all out war
 
I thought I read once some Soviet missile silo commander made a big mistake and almost started WW3.
 
- Bay of Pigs invasion successful, USSR declares war to support Castro

The USSR isn't going to declare war over the Bay of Pigs. They haven't yet committed their international prestige to supporting Castro, and their military isn't any shape to handle a war with the US.

- Operation Unthinkable goes ahead

Hard to see a PoD that could make this happen.

- USSR joins Korean War

I like this one, though I think an initial escalation by the United States' part is much, much more likely. Say, Truman decides the Pusan Perimeter is not going to hold and orders nuclear strikes.

- Checkpoint Charlie flashpoint ignites

You mean the 1961 Berlin Crisis? Yeah, that could happen.

- NATO intervention in Hungary 1956/Czechoslovakia 1968

This one probably couldn't. NATO's not going to intervene unless they're looking for an excuse to start World War III.

- Ukraine and Russia go to war, after a supposed Ukrainian offensive against Crimea

If that happens, NATO will not involve itself directly.

- US and Arab forces intervene against ISIL on the ground in Syria, Putin declares such an action as aggressive against Assad

Putin is not going to go to war with NATO to protect Assad.

- North-South Korean diplomatic collapse leads to all out war

North Korea isn't really a Russian vassal state anymore, these days they hang out with China.

A few suggestions of my own:

The Cuban Missile Crisis. Surprised you missed that one.
The Suez Crisis escalates.
Grigoriy Romanov, a hardliner, was elected instead of Gorbachev. I've seen a quote from a former Politburo member saying he expected WW3 would have erupted within a few years if that had happened.
ABLE ARCHER 83. Probably not as close a scare as people make it out to be, but still too close for comfort.

To answer the "What If" part: it really depends on when and the circumstances. From about 1950 to about 1965, the United States could meaningfully win a nuclear war with the Soviet Union, though Europe would be wrecked, and the price the US would pay would increase over time. After about 1970, Destruction is Mutually Assured, as they used to say. There were various theories about Limited Nuclear War and Intrawar Deterrence and so on, and I guess it's not impossible that they'd work, but I have a hard time believing it.
 
I would lean towards the Korean War one to start WW3. One question, is WW3 going to be nuclear?

It depends on the time when it starts, whether WW3 will definitely be nuclear or only almost certainly nuclear. In the 1950's, the United States' opening move would have been nuclear bombardment of Russia's cities.
 
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