I'm curious about this move duo.
I see this quite a bit, and I'm trying to figure out under which conditions that playing Kb1(b8) is normally preferred.
In some openings, such as the Sicilian Dragon, White will castle long followed up by playing Kb1. In such cases, there are some rather real threats against the castled position there (Bg7 pointing at b2, open c-file with Rc8, active Black Queen).
However, I'm more curious about some of the more quieter positions where there doesn't appear to be any obvious threats. In some cases, I see players, and even computer programs, play Kb1(b8) immediately. I've analyzed some of these lines and never seem to find any reason why Kb1(b8) is played.
I've always been of the mind to just leave the King at c1(c8) unless there is some obvious threat.
Why is Kb1(b8) played in some of these positions? What types of threats can the other player come up with to require Kb1(b8) to be played?