You are correct that in the sniper analogy, the extreme improbability of all the snipers missing by chance does make some other explanation considerably more likely. Practically certain, given the very low probability of them all missing by chance.

Before I go on, let me mention that the chance of a deity existing with the properties described in any specific religious tradition is also an extreme case of fine tuning. Much more extreme than any scientific theory, due to the inherent complexity of a thinking, acting being. That said:

The Anthropic Principle doesn't really justify any particular hypothesis about the universe's creation. The Anthropic Principle is only post-hoc. If a prior hypothesis is complex (has a long minimum description length), then that hypothesis is a priori unlikely, and the Anthropic Principle does not make it more likely.

The prior probability of a hypothesis is exponentially lower as the minimum description length grows.

If a physical theory requires certain constants to be fine-tuned to particular values to obtain the universe as we see it, then every bit in those values does add to the minimum description length of the theory. And it's not enough simply to get the bits in the right range to permit intelligent life; if a theory demands a constant be a specific measurable value, then every single bit in that value to the finest precision we can measure, must be counted in the description length of the theory.

Solomonoff's theory of inductive inference is the ultimate word on how we should reason about hypotheses about the universe's creation. Roughly speaking (simplifying a bit), if M is the minimum description length of a hypothesis, the prior probability of that hypothesis is (approximately) k^(-M) for some base k. Then, you simply check, for each of the (infinite) possible hypotheses, whether that hypothesis exactly matches observations. If it doesn't match, you cross it out. Then, you sum up the probability mass of all the hypotheses not crossed out, to get a normalizing constant Z. The posterior probability of a hypothesis is then k^(-M) / Z. And roughly speaking, in practice, the hypothesis with minimum M wins and gets a probability near 1, and all other hypotheses lose and get probabilities near 0.

So, it all comes down to whether M_T, the minimum description length for a scientific theory T, is shorter or longer than M_G, the minimum description length for a thinking deity. If M_T requires fine-tuned constants, then that hurts it in comparison to M_G. But M_G is likely very, very long; how long would be a computer program that would let you simulate a human being? And it's not enough to specify just any intelligent being; M_G has to be a specification of an intelligent being that would produce the exact universe we observe. So if M_T is still under a few kilobytes, then M_T probably still wins, by a landslide.

You are correct that in the sniper analogy, the extreme improbability of all the snipers missing by chance does make some other explanation considerably more likely. Practically certain, given the very low probability of them all missing by chance.

Before I go on, let me mention that the chance of a deity existing with the properties described in any specific religious tradition is also an extreme case of fine tuning. Much more extreme than any scientific theory, due to the inherent complexity of a thinking, acting being. That said:

The Anthropic Principle doesn't really justify any particular hypothesis about the universe's creation. The Anthropic Principle is only post-hoc. If a prior hypothesis is complex (has a long minimum description length), then that hypothesis is a priori unlikely, and the Anthropic Principle does not make it more likely.

The prior probability of a hypothesis is exponentially lower as the minimum description length grows.

If a physical theory requires certain constants to be fine-tuned to particular values to obtain the universe as we see it, then every bit in those values does add to the minimum description length of the theory. And it's not enough simply to get the bits in the right range to permit intelligent life; if a theory demands a constant be a specific measurable value, then every single bit in that value to the finest precision we can measure, must be counted in the description length of the theory.

Solomonoff's theory of inductive inference is the ultimate word on how we should reason about hypotheses about the universe's creation. Roughly speaking (simplifying a bit), if M is the minimum description length of a hypothesis, the prior probability of that hypothesis is (approximately) Ak^(-M) for some base k and constant A. Then, you simply check, for each of the (infinite) possible hypotheses, whether that hypothesis exactly matches observations. If it doesn't match, you cross it out. Then, you sum up the probability mass of all the hypotheses not crossed out, to get a normalizing constant Z. The posterior probability of a hypothesis is then Ak^(-M) / Z. And roughly speaking, in practice, the hypothesis with minimum M wins and gets a probability near 1, and all other hypotheses lose and get probabilities near 0.

So, it all comes down to whether M_T, the minimum description length for a scientific theory T, is shorter or longer than M_G, the minimum description length for a thinking deity. If M_T requires fine-tuned constants, then that hurts it in comparison to M_G. But M_G is likely very, very long; how long would be a computer program that would let you simulate a human being? And it's not enough to specify just any intelligent being; M_G has to be a specification of an intelligent being that would produce the exact universe we observe. So if M_T is still under a few kilobytes, then M_T probably still wins, by a landslide.