Theists: What is the most compelling argument you have heard for Atheism?

[SteveII]

And the question is, why, against all odds is the universe the way it is?

In what way is it "against all odds" that the universe turned out the way it did?  Ignoring the fact that you can't rule out necessity as a possible reason the universe is the way it is, the universe had to turn out "some way" and the way it did turn out is not special in any regard with respect to the universe itself.  It's special to you because you're a life form and you have an emotional investment in existing, but as far as universes go, there's nothing unique about this one.  You assume a teleological stance with respect to life, but this ignores the fact that life in this universe is opportunistic; it didn't have to be, it conformed itself to what was available.  All that the fine tuning argument says is that if things had been different, then things would have been different.  Where you get the existence of a god out of that, I don't know.

If it is astronomically improbably that the universe turned out the way it did, I think it is reasonable to infer a designer. If you want to go with chance, you certainly are welcome to. 

Multiply those very small number by the other probabilities of life permitting ranges given the overall possible ranges of any given constant and you have a number so small that there are so many zeroes in it that there are not enough molecules in the universe to cover the odds.

Using a frequentist view of probability, the odds are given how many times life would occur given a number of trials.  Unfortunately for your argument, life conforms to the conditions existing, not the other way around, so you have no way of specifying what a "life permitting range" is.  You're simply assuming that it's close to the conditions which currently exist, which is circular.  Victor Stenger has done simulations in which the parameters of the universe are adjusted and seeing what kind of universe results, and in over half of the simulations, stable universes resulted.  So you're simply tailoring your region to your argument.  That's a faulty argument. (I also note that you claim there to be "possible ranges" of the given constants.  How you know what a possible range for these constants is constitutes a remarkable fact, as science doesn't even know what suitable ranges for these constants are.  Care to share where you got this astounding information from?)

I'm not a physicist but it does seem that Stenger cherry-picked his scenario. If you care to see a detailed look, click here where Luke Barnes, a post-doctoral researcher on cosmology says in conclusion: 

Allow me to state my conclusions with the kind of candour only allowed in the blogosphere: MonkeyGod is bollocks. It is worse than irrelevant – it is misleading. It is a distraction, encouraging us to simply look the other way, to condescending dismiss the evidence for the fine-tuning of the universe for life. It is utter garbage, thinly concealed behind a veil of mathematics.

It is interesting that I cannot find any critique of the Monkey God simulator for some years now. If you have something that would support its findings, please paste link.