I'm curious what the theoretical maximum yield was, based on the total amount of fissile material in the bomb, and how much of that they expected to undergo fission. Did they have 90% confidence estimate of the power?
I'm asking in connection to a line by admiral Hackett in Mass Effect 3, where he said that there was possibility of setting the Earth's atmosphere on fire with an atomic explosion, but that atomic test went ahead anyway. This was to justify using a crucible device, which they had no idea what would do. However, all I found about this were some wild speculations, easily debunked, by someone who wasn't involved with the development of the bomb.
They knew exactly what the bomb would do if it detonated correctly. A nuclear fission chain reaction wasn't this mysterious thing. It was well understood on a fundamental level. The open question was whether the gadget would work mechanically in order to achieve the expected detonation. Most of the physicists involved were at least a little pessimistic about that; they thought the implosion device would fail to work perfectly and they'd get a partial detonation. In fact, the device worked exactly as designed and the yield was exactly as predicted.
The whole "they thought the atmosphere would ignite" thing was actually a joke on Enrico Fermi's part. The physicists were making bets on the yield of the device, based on what I said before about the success of the gadget. Fermi offered to take bets on whether the bomb would ignite the atmosphere and destroy the world. Somebody high-ranked — I forget who — was livid with Fermi for scaring the military men with his little joke.
I don't know that the official figures have ever been published. The equations they were using are still secret today for obvious reasons. The scientist's unofficial betting pool as had bets from 0 to 50kt with most of the bets in the 10kt range. As /u/MarturinTheTurtle pointed out Fermi jokingly wanted to bet that the bomb would cause the atmosphere to ignite, but this wasn't a serious worry.
One of the people involved in developing the equations they used to calculate the yield gave a very entertaining talk on what it was like working at Los Alamos. He talks a bit about calculating the yield of the bomb about 3/4ths of the way through, but the whole thing is well worth listening to.
As a little post-script, it wasn't really unknown for these guys to make mistakes. One of the early US hydrogen bombs ended up producing a yield of 15 megatons rather than the projected 6 and actually ended up damaging the testing facilities & causing the death of at least one person.