If we run each universe-program with probability 2 to the power of minus L, where L is the length of the program in bits, and additionally assume that a valid program can’t be a prefix of another valid program, then the total probability sums to 1 or less (by Kraft’s inequality). In this setup shorter programs carry most of the probability weight despite being vastly outnumbered by longer ones. I think the same holds for most other probability distributions over programs that you can imagine.
If we run each universe-program with probability 2 to the power of minus L, where L is the length of the program in bits, and additionally assume that a valid program can’t be a prefix of another valid program, then the total probability sums to 1 or less (by Kraft’s inequality). In this setup shorter programs carry most of the probability weight despite being vastly outnumbered by longer ones. I think the same holds for most other probability distributions over programs that you can imagine.