I haven't read the third book, but I have read the Wikipedia synopsis. My understanding is that in the third book there's a new swordholder who the Trisolarans

I haven't read the third book, but I have read the Wikipedia synopsis. My understanding is that in the third book there's a new swordholder who the Trisolarans think won't go through with MAD, so they call Earth's bluff and turn out to be correct. However, the swordholder doesn't need to be certain of the consequences in order for the scheme to work. All that's required is that the Trisolarans are certain of the consequences, and they believe that the swordholder will push the proverbial button. If Luo Ji said, "Look, I'm like 60% sure that if I broadcast our location we'll all be killed, but I will do it if you continue." What could the Trisolarans do? Call his bluff? Then he'd say, "Okay then. I'm actually more likely to do this while I'm unsure, since there's a 40% chance nothing will happen. My being unsure has only made it more likely I'll press the button. Here we go..." The Trisolarans would need to respect the threat regardless, which would confirm Luo Ji's theory without the need to wait a century to get results.