Here is a remarkable variation on that puzzle. A tiny change makes it work out completely differently.

Same setup as before, two private dice rolls. This time the question is, what is the probability that the sum is either 7 or 8? Again they will simultaneously exchange probability estimates until their shared estimate is common knowledge.

I will leave it as a puzzle for now in case someone wants to work it out, but it appears to me that in this case, they will eventually agree on an accurate probability of 0 or 1. And they may go through several rounds of agreement where they nevertheless change their estimates - perhaps related to the phenomenon of "violent agreement" we often see.

Strange how this small change to the conditions gives such different results. But it's a good example of how agreement is inevitable.