How do proponents of the Fine Tuning argument for God, refute the puddle comparison?

The argument ignores the narrow range of constraints to permit intelligent life. As water fits in any size of object, the critic assumes that there could be a totally different form of life, other than our carbon based life form. Robin Collins' website is the best source for understanding the fine tuning argument, covering detailed objections.

Objection 2: Other Forms of Life Objection

Another objection people commonly raise to the fine-tuning argument is that as far as we know, other forms of life could exist even if the parameters of physics were different. So, it is claimed, the fine-tuning argument ends up presupposing that all forms of intelligent life must be like us. The answer to this objection is that most cases of fine-tuning do not make this presupposition. Consider, for instance, the case of the fine-tuning of the strong nuclear force. If it were slightly larger or smaller, no atoms could exist other than hydrogen. Contrary to what one might see on Star Trek, an intelligent life form cannot be composed merely of hydrogen gas: there is simply not enough stable complexity. So, in general the fine-tuning argument merely presupposes that intelligent life requires some degree of stable, reproducible organized complexity. This is certainly a very reasonable assumption.

The answer seems simple: consider what happens when you change the parameters. If you make a small change to the shape of a hole in the ground, you still have an almost identical puddle. If you make a small change to the universal gravitational constant, then as you say, the universe falls apart. It's all about the probability of the conditions being right. For a puddle, the probability is close to one; for the universe, it's close to zero. Except, of course, that in an infinite space of possibilities, improbable things are likely to happen quite often.

Whether that gives any validity to the "fine tuning" argument is another question. To me it seems an abrogation of scientific and philosophical enquiry to suggest that the universe "just happened" without any cause, but how closely that cause resembles the "creator" of our imagination is a very open question.

I hope this counts as an answer. The puddle idea is just a metaphor or perhaps better stated, a parable. It does not contain or purport to contain the whole of the argument - it merely illustrates it in an easily understandable way.

The actual philosophical debate that the puddle merely illustrates is the Anthropic Principle. I quote:

The anthropic principle, also known as the "observation selection effect", is the hypothesis, first proposed in 1957 by Robert Dicke, that there is a restrictive lower bound on how statistically probable our observations of the universe are, because observations could only happen in a universe capable of developing intelligent life. Proponents of the anthropic principle argue that it explains why this universe has the age and the fundamental physical constants necessary to accommodate conscious life, since if either had been different, we would not have been around to make observations. Anthropic reasoning is often used to deal with the notion that the universe seems to be finely tuned for the existence of life. https://en.wikipedia.org/wiki/Anthropic_principle

Personal note As a radical agnostic (i.e. I profess to know nothing for certain except for my own existence) and a pragmatist, I don't really care about cosmic accidents or creators when it comes to living my daily life. However I often wonder why believers feel the need to justify their faith - especially by science - isn't it enough for them to simply believe? If they have to prove the existence of a god, then that indicates they are doubting Thomases and not true believers.

In other words, claiming that rather than the universe being fine tuned, it just fit the existing conditions out of necessity.

No, the puddle argument is a response to the claim that the environment is particularly suited to humans, and it asserts that, rather than the environment being suited to humans, humans are suited to the environment.

The most common response from eg atheists is comparing the situation to water in a puddle remarking on how the hole in the ground is exactly the right shape to hold it.

Really? When I Googled "puddle analogy", I got these results:

1. Wikipedia article— Explaining the anthropic principle.

2. Stand to Reason article "Why the Puddle Analogy Fails against Fine-Tuning"—A Christian apologist explaining why the analogy doesn't defeat fine-tuning.

3. Reasons to Believe article "Does the Puddle Analogy Explain Cosmic Fine-Tuning?"—ditto

4. Quora question "What does Douglas Adams’ Puddle Analogy mean?"—Question about the analogy

5. The Truth Will Make You Mad article "The Puzzle of Existence and a Puddle of Doubt"—Christian apologist attacking Douglas Adams, claiming that he misrepresents the fine-tuning argument.

Now, here are the results for "fine-tuning rebuttal":

1. Why Evolution Is True article "Sean Carroll debunks the “fine-tuning” argument for God"—No mention of "puddle" in the article, although someone brings it up in the comments.

2. Stanford Encyclopedia of Philosophy article "Fine-Tuning"—No mention of "puddle".

3. Reasons to Believe article "Fine-Tuning: Responding to a Common Objection"—One of the Christian apologists from above.

4. The Atheist Voice video "A Rebuttal to the Fine-Tuning Argument"—Does mention puddle, but only once, in passing.

5. Rash*m*n Effect video interview "Intelligently Design, Rebuttal To Fine Tuning Argument | Richard Carrier PhD"—No mention of "puddle".

My search for "puddle analogy" was dominated by Christians claiming that it was an argument made by atheists, without any results (at least not in the top 5) of atheists actually making the argument, and my search for rebuttals of the fine-tuning argument was dominated by non-puddle arguments, with a few off-hand mentions of the puddle argument.

Now, let's look at Douglas Adams' original puddle analogy:

Where does the idea of God come from? [...] Now imagine an early man surveying his surroundings at the end of a happy day's tool making. He looks around and he sees a world which pleases him mightily: behind him are mountains with caves in - mountains are great because you can go and hide in the caves and you are out of the rain and the bears can't get you; in front of him there's the forest - it's got nuts and berries and delicious food; there's a stream going by, which is full of water - water's delicious to drink, you can float your boats in it and do all sorts of stuff with it; here's cousin Ug and he's caught a mammoth - mammoth's are great, you can eat them, you can wear their coats, you can use their bones to create weapons to catch other mammoths. I mean this is a great world, it's fantastic. But our early man has a moment to reflect and he thinks to himself, 'well, this is an interesting world that I find myself in' [...] early man is thinking, 'This world fits me very well. Here are all these things that support me and feed me and look after me; yes, this world fits me nicely' and he reaches the inescapable conclusion that whoever made it, made it for him.

This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'

There is absolutely no mention of the fine-tuning argument here. Adams is not responding to the argument that the conditions are the only ones that make life possible, he is responding to what he imagines the belief of early humans to be, namely that the conditions of humans were particularly suited to humans. One can argue that the label "fine-tuning" sort of fits this line of thinking, but it is a particular sort of fine-tuning, and is not the argument that people usually use "fine-tuning" to refer to.

So, all of that is a frame challenge. What about your actual question? Well, the Christian apologist response to the puddle argument is quite simple: they present an argument that it was never presented as a rebuttal to, point out that it's not a rebuttal to that argument, and then smugly pat themselves on the back about how smart they are. In Adams' analogy, the puddle corresponds to humans, the shape of the puddle corresponds to humans' evolutionary adaptations to their environment, and the hole corresponds to that environment. Humans of course couldn't evolve to fit a universe that didn't allow life in the first place, so of course the puddle analogy doesn't address the claim that the universe is uniquely capable of supporting life. There are plenty of other explanations for how the fine-tuning argument is incoherent, fallacious nonsense, such as in Rational wiki's article "Argument from fine tuning" (again, no mentions of puddles).

The fine-tuning argument implicitly (or, more rarely, explicitly) relies on the intuition that is formalized in Bayesian analysis. But for us to do Bayesian analysis on this question, we would have to take the total number of universes with fine-tuning and a God and divide that by the number of universes with fine-tuning with or without a God. Besides the question of what possible meaning this could have, and how we could figure out what number of universes have fine-tuning and a God (and how asserting that this number is large isn't begging the question), the argument pivots crucially on asserting that the number of universes with fine-tuning and no God is minuscule, at least compared to the number with fine-tuning and a God. This is a positive claim, and the burden of proof is squarely on the apologist. And yet when atheists dispute this claim, for instance by pointing out that there are hypotheses under which such a large multitude of universes are created with different constants that it is inevitable that some of them will have "fine-tuning", this is dismissed by apologists as a "cop-out" with "no evidence" and purely "philosophical" "grasping at straws", as if it's the atheists that somehow have the burden of proof.

What is the "obvious" refutation of the puddle analogy that everyone seems to know?

TL;DR: Puddles can exist in holes of any arbitrary shape, but life can exist only in a Universe that has extremely specific fundamental constants.

The puddle analogy relies on the ridiculousness of the belief that the hole either changes, or was specifically created, to match the shape of the puddle.

In reality, it is the shape of the water that changes to match the shape of the hole.

• Empirically, we see that this happens for billions of puddles, but no one has recorded an instance of a puddle that didn't quite fit into the hole.
• Scientifically, we know that this effect is caused by the force of gravity acting on a substance that will naturally change shape to minimize its centre of gravity.

Applying that analogy to the Universe, if the fundamental constants changed, they must have very rapidly changed from their initial values in order to become what they are today (telescopic images show what the universe looked like billions of years ago, and the constants appear to be the same then as now). So those constants must have been established at or near the beginning of time.

• Empirically, we know that the constants are correct, otherwise we wouldn't be here now considering this question.
• Scientifically, we must conclude that the Universe had the correct values right from its beginning, so it must have been designed to support life.

The puddle comparison claims that this conclusion is just as ridiculous as the idea that the hole's shape was determined by the puddle.

It would be if life (not necessarily in our form) could exist in a universe with arbitrarily different fundamental constants. But we know that almost all other theoretically possible universes would exist for only a brief moment or would be unsuitable for life.

"The Fine-Tuning Design Argument", linked in the Question provides some examples:

• if gravity had been stronger or weaker by 1 part in 10⁴⁰ power, then life-sustaining stars like the sun could not exist.
• If the initial explosion of the big bang had differed in strength by as little as 1 part in 10⁶⁰, the universe would have either quickly collapsed back on itself, or expanded too rapidly for stars to form. In either case, life would be impossible.

Those two factors alone account for 100 decimal places of precision, and that is only enough to guarantee the existence of suns. Include all the factors that affect what is required to support life and it could be in the thousands of decimal places. That's about as close to impossible as one could imagine.
(E.g. compare 10¹⁰⁰ with taking 4 grains of sand from the Sahara and then burying them in random locations throughout northern Africa. Now ask someone else to randomly choose 4 grains of Saharan sand. Would you believe it if they picked the exact same grains?)

By analogy, we could observe that many holes leak and won't hold a puddle. But we can't observe (or even theoretically imagine) any instances of non-leaking holes that won't naturally fit the water that is in them.

Since puddles can exist in holes of any arbitrary shape while life can exist only in a universe that has extremely specific fundamental constants, one must ask: what caused our universe to have those specific values?

It's very difficult to answer that question without either:

• assuming that an arbitrarily large number of possible universes exist and that this one simply happens to have the right fundamental constants.
• assuming something from outside-of-universe that already knew the required values.

Each is a concept for which there is no scientifically acceptable proof.
Each is rejected as ad hoc fantasy by believers in the other.