Hellman says:

I have been unable to find any comparable estimates of the time horizon for an even more dire event, a failure of nuclear deterrence resulting in a nuclear war. The risk analysis component of our effort therefore asks the international scientific community "to undertake in-depth risk analyses of nuclear deterrence and, if the results so indicate, to raise an alarm alerting society to the unacceptable risk it faces as well as initiating a second phase effort to identify potential solutions."

It seems to be challenging to figure out what the the chances of even this much milder event are.

Of course, ignorance should not lead to complacency.