I disagree with you in the fact that there is a potential large upside if Putin can make the West/NATO withdraw their almost unconditional support to Ukraine and even larger if he can put a wedge in the alliance somehow. It's a high risk path for him to walk down that line, but he could walk it if he is forced: this is why most experts are talking about "leaving him a way out"/"don't force him in the corner". It's also the strategy the West is pursuing, as we haven't given Ukraine weapons that would enable them to strike deep into Russian territory.
I am also very concerned that the nuclear game theory would break down during an actual conflict as it is not just between the US and Russia but between many parties, each with their own government. Moreover, Article 5 binds a response for any action against a NATO state but doesn't bind a nuclear response vs a nuclear attack. I could see a situation where Russia threatens with nukes a NATO territory of a non-nuclear NATO state if the West doesn't back down and the US/France/UK don't commit to a nuclear strike to answer it, but just a conventional one, in fear of a nuclear strike on their own territory. In fact, it is under Putin himself that Russia's nuclear strategy apparently shifted to "escalate-to-deescalate", which it's exactly the situation we might end up in.
Fundamentally, the West leaders would have to play game of chicken with a non-moral restrained adversary that that they do not know the complete sanity of.
From what I have read, and how much nuclear experts are concerned, I am thinking that the chances of Putin using a nuclear warhead in Ukraine over the course of the war is around 25%. Conditional on that happening, total nuclear war breaking out is probably less than 10%, as I see much more likely the West folding/deescalating.
Reading this makes me think that it might be inconsistent to think that both Putin won't use nukes for fear of escalating to nuclear war, and that the west will avoid escalating to nuclear war in the case that Putin does deploy a nuke. Of course both sides want to project strength and ensure that there is significant uncertainty around the actions they will take, but we probably can't be highly confident in both.
The reason, of course, is that if Putin were highly confident that the west would not escalate all the way to nuke war, then he would not feel deterred in using nuclear weapons.
I still think that there's not really a tactical use for the weapons, which is an independent reason to not use them.
I do agree that game theory is much less clear in multiparty games, and that there's a lot of complexity on the ground. On the other hand, the US has ~all the nukes that Putin cares about, so in that sense it's much less complex.
anthropics cannot be used here.
The global stockpile of Nuclear weapons are not and never was sufficient to wipe out the human race. Nuclear war would be catastrophic but not close to the end of the world. In fact, even an all-out nuclear war would leave 50% of US population untouched.
You need to be aware of the climate effects of nuclear war. Follow the link Max included in his article: https://www.nature.com/articles/s43016-022-00573-0
This estimates potential global deaths from starvation (and does not include deaths from breakdown of society) of around 5 billion. You can legitimately claim these are overestimates, but to say half the US population would be untouched is dangerous and absurd.
By sheer coincidence, I wrote an analysis of that exact paper earlier today.
https://www.lesswrong.com/posts/sJK6HN5vTPPnuuNgQ/that-one-apocalyptic-nuclear-famine-paper-is-bunk
https://www.lesswrong.com/posts/jnDibtfvWNHLucf4D/actually-all-nuclear-famine-papers-are-bunk
The United States has anywhere between 1.5-5+ years of food supplies in grain storage alone, depending on the time of year. And that's not counting anything in the fields. In addition, the paper you cited makes some very bad assumptions (no change in crops to account for different weather, no increase in land cultivated, not taking into account existing food stores after year 1) that make the conclusions effectively useless.
These estimates are questionable. You should be aware that historically the nuclear winter hypothesis has been the darling of Soviet propaganda.
https://apps.dtic.mil/sti/citations/ADA165794
I think your 5% figure of KABOOM given retaliation fails to condition on kaboom.
I would estimate an 8% chance of kaboom (broadly following prediction markets, going by a 10% chance of the order to nuke Ukraine and an 80% chance of it actually happening) and an 80% chance of retaliation. For KABOOM, either the West or Russia would drop the first strategic nuke. For the West, the probability is somewhere around 0.1% given kaboom. For Russia, while the probability of KABOOM given escalation is probably less than 5% (more like 1%, I'd guess), kaboom has happened, and so the probability of Russia dropping a strategic nuke is closer to 12.5%. And so, the final probability of KABOOM is closer to 0.9% than 0.25%.
This is a response to Max's post Why I think there's a one-in-six chance of an imminent global nuclear war.
Max's thesis is that Putin is likely to use nuclear weapons if the war in Ukraine goes badly for Russia, that the west will retaliate, and both sides will continue to escalate until we have a full nuclear exchange. In particular, he estimates a 30% chance that Ukraine is nuked, an 80% chance of a significant conventional retaliation, and a 70% chance that things further escalate from there all the way to KABOOM.
I think the first and last terms in that equation are much too high. I think the center term is perhaps slightly too low (it's hard to believe that nuclear weapon use will be tolerated because it sets up terrible incentives for future nuclear weapon use), but I won't explore that here in depth.
Initial nuclear strike
An initial use of tactical nuclear weapons is unlikely because:
The war against Ukraine can't really be won by bigger explosions. The Ukrainian military is broadly dispersed across a huge front, operating on both sides of the line. Similarly their equipment is not stored in a small number of supply depots.
Infrastructure and logistical networks can be disrupted with conventional explosives, and both Ukraine and Russia are attacking enemy logistics (Ukraine with rather more success than Russia). But the Russian ineffectiveness is due to missiles getting shot down and poor targeting, neither of which is helped by nukes.
And of course there are significant downsides to using nukes, which is that it risks a serious escalation with the west, one that could endanger Russia's future as a country and Putin's leadership and life, as well as losing support domestically, allowing Putin's political rivals to argue (perhaps correctly!) that he is a madman taking irrational and highly risky actions, and needs to be stopped.
There is exactly the case that he is a madman to worry about. I think this is unlikely; perhaps he has been corrupted by power, or is succumbing to dementia, but absent those Putin has showed himself to be a careful strategic actor in the past.
Overall I put the likelihood of an initial tactical nuclear strike by Putin to be south of 5%. Most of the probability mass is the possibility that Putin is mentally unstable, or that there's a series of mistakes / bad judgments that lead to a very ill-considered decision.
Strategic considerations
I think my fundamental disagreement with Max on an apocalyptic cycle of escalation is this: Putin and his advisors don't want a nuclear war (that's terrible for Russian and Putin personally), and are very familiar with game theory, since that's the framework that's governed strategic nuclear weapon use for many decades. Similarly, nobody in the west wants a nuclear war either. The logic of nuclear standoffs is such that there are strong incentives to go to the brink, but not to go over, so I think in general tense situations feel scarier than they actually are. And we should expect lots of threats and posturing, because signaling that you are willing to go over the edge gives you negotiating leverage.
Therefore the most likely analysis is that Putin is essentially bluffing -- his nuclear threats are not credible.
(To be clear, I think this dynamic is awful, because it puts us in a position where mistakes are much more likely to have terrible consequences; therefore escalatory situations do make nuclear war more likely. However 80% is a huge overestimate.)
We've seen brinksmanship in the past, and it hasn't resulted in nuclear war, though in the Cuban missile crisis it came close. But note the dynamic: a nuclear weapon was almost used due to a mistake, not due to a decision by leadership. The Cuban crisis was much scarier because the US felt that this was an existential threat and were willing to go all the way; nothing in Ukraine is like that, at least for now.
Of course history is not necessarily a clear guide, due to the anthropics problem that if nuclear war had happened we wouldn't be here to talk about it. Nonetheless, while there were many close calls, it is still the case that at no point did leadership decide to start a nuclear war, and really only in the Cuban missile crisis was it remotely plausible.
I think that almost all of the probability mass of a nuclear war is some kind of accident. After all, the entire logic of mutually assured destruction is to ensure that nobody has an incentive to start a nuclear war.
How much more likely is some kind of accident in a time of high tensions and active conflict, such as a NATO retaliation for some kind of Russian atrocity? Many times more likely but over a very low baseline. Call it 5% -- maybe 1% chance that such an accident will happen over the rest of the conflict, and the rest is just uncertainty about how rational all the actors are.
Estimate
Using Max's framework, my estimate is 5% x 90% x 5% = about a quarter of a percent.
This is far enough below e.g. prediction market estimates that I think it's probably a bit higher, but overall I believe that the game theoretical considerations (nobody wants nuke war) and the tactical considerations (nothing really is served by using tactical nukes) both point towards risk being much lower than outlined elsewhere.