[BSOhealth]

Is there some probabilistic named theory for thinking there is greater chance for life to exist the closer to the center of a solar system? almost like sluice box or coin sorter, where as outer planets develop life, get blasted by asteroids, and the remains drift further inwards?

At least up to some distance where carbon vaporizes by whatever heat source exists.

In other words, what’s the mathematical principle for Goldilocks zones

[clarionbell]

Water, not carbon. Carbon itself isn't enough, in order for the fine machinery of life to work you need solvent. On Earth it's water. Limits of Earth bound life are determined in great part by properties of water, when it boils and when it freezes.

The Goldilocks zone itself is a bit of an outdated concept now. Largely because we now know that liquid water exists way beyond the orbit of Mars, in oceans of Europa and Enceladus at very least. Something similar is the case with Venus. Surface is too hot for liquid water, but high atmosphere is pretty much fine.