Since it is possible to approximate Chaitin's constant ($\Omega$) for some systems, is it known whether these numbers are somehow related to another when considering similarly operating Turing Machines?
Say, is the halting probability value for the (24,2)-Universal Turing Machine (UTM) somehow connected to the one for the (2,18)-UTM, and less connected to a specific different turing machine that has a very different style of computation?