[dontbeevil1992]

Another issue with this logic is that the probabilities are not independent.

Saying that you have probability x of nuclear war every year and so probability (1-x)^n of no nuclear war in n years assumes independence. In fact, if you don't have nuclear war on year 1, I would assume that the reasons for that lead to inferences and correlations that would affect the probability of nuclear war on year 2, possibly making it lower.

[LeonB]

No, that’s not quite right. Measuring “did we have a nuclear war?” is not the input you’d ever want to use there, it’s only one binary digit of information.

Instead take info like “did we have events/incidents with a high potential of nuclear war?”

If three “Cuban missile crisis” level events happened in year X, then the probability of nuclear war in year x+1 is higher than it was in other years — even though nuclear war didn’t occur in either year. If national leaders make no statements threatening war in year A, then it’s probably safer than year B where there were 100 such threats.

[dontbeevil1992]

I might not have said this clearly enough - I'm not saying that conditioning on "did we have a nuclear war" will change the probability to be less. I'm saying that the event "did we have a nuclear war in year n" is not independent from "did we have a nuclear war in year n+1" "n+2", ... because there are shared factors influencing them. Therefore the model of independent probabilities multiplying year over year and seeming to imply that nuclear war is inevitable because (1-p)^n goes to 0 as n grows doesn't make sense mathematically speaking.