An actual mathematician, Max Tegmark, estimates the odds of global nuclear war at one-in-six.
"The shorthand labels I've given these outcomes (grey boxes) should't be taken too literally: 'Kosovo' & 'Vietnam' refer to scenarios where one side wins outright (breakaway succeeds & Goliath is expunged, respectively). 'Libya', 'Korea' & 'Finland' refer to intermediate outcomes involving simmering war, frozen war and full peace, respectively. I'm not showing the 'Cuba' outcome (invasion averted by negotiated agreement) that was on the table in December 2021, since it's now off the table, as are resumed EU-Russia gas exports via the Nordstream pipelines."
"We are currently in a vicious circle in the form of a self-perpetuating escalation spiral: since 'Kosovo' is deemed unacceptable by Ukraine and the West while 'Vietnam' is deemed unacceptable by Russia, both sides double down and escalate further whenever they fear losing. Such escalation has been both quantitative (more weapons, more mobilization) and qualitative (e.g., novel sanctions, heavier weapons, longer-range weapons, attacks inside Russia, scaled-up attacks on civilian infrastructure, shelling of a nuclear power plant, assassinations, sabotage of gas pipelines and Europe's longest bridge, annexations, and escalatory rhetoric about nuclear use). My assessment is that Russia, whose GDP is similar to Italy's, can no longer compete with the West in terms of quantitative escalation, and that Putin understands that his only chance to avoid the 'Vietnam' outcome is to escalate qualitatively, with nuclear weapons use being his last resort. Last spring, I predicted that once loss of occupied territory loomed, he would annex what he controlled and start talking about nuclear defense of Russia's new borders -- and here we are."
He assigns probabilities to various transitions in his diagram. His diagram is basically a Markov process diagram, although he never uses the term. This is interesting because, I thought, mathematically the way people typically analyzed these kinds of situations is with game theory, not Markov processes. Because you're dealing with events that have never happened (or you have exceedingly low sample counts) so it's hard to estimate probabilities, and you are dealing with conscious actors and have to take their intentions into account.
I got one friend who was freaking out because he thinks there's going to be nuclear war. His wife was like, relax, no there isn't. They have this discussion about whether there is or isn't going to be a nuclear war. I thought whether there will or won't be a nuclear war is the wrong way to think about it. The right way to think about it is there is, say, a 5% chance of nuclear war. Actually I hope the odds are a lot lower than 5%. It's like the old saying, would you get on an airplane if there's a 1% chance of it crashing? You only have to think for 2 seconds to realize 1% odds are way too high -- because the negative outcome is so catastrophic. There's something like 30,000 flights every day in the US, so if 1% crashed, that' would be 300 crashes a day. Obviously, the odds of any plane you step on to are way, way lower than 1%. So if the odds of a nuclear war are 5%, we're in trouble. Subjectively, though, it feels to me like the odds are 5% or thereabouts. My subjective feelings have a history of being unreliable at predicting the future.
I've been trying to be explicitly clear, though, that my "estimate" is entirely subjective and I'm using words like "seems" and "feels" deliberately. I haven't tried to work out a Markov process diagram or do any game theoretical calculations.
The post has extensive comment sections where Tegmark's logic is challenged.
"The real issue with backing down from nuclear threats is what happens when you back down."
"Let's say we force Ukraine to allow Putin to keep the annexed territory because of nuclear weapons. This gives him, every Russian and every dictator around the world a clear message: nuclear weapons are the winning strategy."
"It would make Putin and all warmongers like Prigozhin or Kadyrov look like geniuses. They stood against the whole world and won! Everyone inside Russia who was opposing the use of nuclear weapons would have to admit that it worked. So they need to use this trick more!"
"From my perspective if nuclear threat wins Putin anything significant then Poland will need to try to obtain strategic nuclear weapons as soon as possible and at any cost. We lost every fifth person after 1939 because we trusted foreign powers when we should not have. Russian soldiers did not leave Poland until 1993 and we do not want them back."
"The way out of nuclear escalation is convincing Russia that they have nothing to gain and everything to lose after using nuclear weapons."
Why I think there's a one-in-six chance of an imminent global nuclear war
