Reposting the comment that I gave when I restacked a particular portion of the article, because it is my pet peeve when fine-tuning arguments throw out this particular number in a way that completely misuses it:

The general thrust of this article is just about how to reason with epistemic probabilities, and I agree with most of what it says there. But people need to stop citing this 10^120 number when talking about the constants of the universe being finely tuned for life because this value has absolutely nothing to do with fine-tuning for life, making everything that comes after it about throwing darts at atoms completely irrelevant to the fine-tuning argument. Where this value actually comes from is a theoretical attempt to calculate how much vacuum energy there should be based on quantum field theory, which ends up getting an absolutely gigantic amount. On the standard interpretation, the cosmological constant is proportional to the energy density of the vacuum, so this leads to an absolutely gigantic value for the cosmological constant. On the other hand, we can roughly calculate the value from astronomical observations, and we get a very small, but nonzero value, which is about 120 orders of magnitude smaller than the value predicted by quantum field theory. Or, at least, it’s 120 orders of magnitude smaller than early attempts to calculate the vacuum energy - the predicted values actually vary wildly depending on the calculation technique, and the 10^120 discrepancy comes from one that ignores Lorentz invariance. Taking it into account gives you a much smaller, though still enormous, discrepancy of about 10^54.

But none of this has anything to do with whether the cosmological constant is finely tuned to allow for life. The usual version of the FTA claims that some constants have to fall into extremely narrow and apparently arbitrary ranges - if the constant varied by just a tiny fraction of its actual value, life would be impossible. This isn’t true for the cosmological constant, and absolutely no physicist thinks it is. It would be quite bizarre if we somehow knew that the cosmological constant needs to be some exact value, to 120 digits, or life would be impossible, considering that we only know one digit of the cosmological constant (Yes, seriously, just one. You’ll sometimes see quoted values that show more than one digit, but that’s because they’re assuming that a particular measurement of the Hubble constant is right. We have conflicting measurements of the Hubble constant, which would result in different measured values of the cosmological constant, depending on which one, if any, is right). In reality, the cosmological constant could actually vary by a factor of infinity and still allow for life. That’s because life would still be possible if the cosmological constant was exactly zero. In fact, for a long time (from 1929 to 1998), we thought it was zero. Of course, it couldn’t vary by infinity in the other direction, but it could vary by multiple orders of magnitude. So the cosmological constant is definitely not finely tuned for life. This much is uncontroversial.

What is controversial, of course, is the explanation of why the cosmological constant is so small. It’s currently one of the biggest unsolved problems in physics, though there are plenty of proposals. One of the proposals (which most physicists don’t find very promising) is that the contributions from the Standard Model could be canceled out almost exactly by some unknown contribution from new physics that has no relation to the SM contribution but coincidentally has a near-perfect cancellation with it. This unknown contribution would have to be finely-tuned to match the Standard Model contribution to at least 54 orders of magnitude (depending on what calculation you go with) in order to reproduce the observed value, and that’s where the idea of fine-tuning in relation to the cosmological constant comes from. But notice that this has nothing to do with fine-tuning for life. It’s about fine-tuning to match observations. It also isn’t even the cosmological constant itself which is finely tuned, but a specific contribution from it, and all of this is dependent on a completely speculative solution to the cosmological constant problem, which most physicists think is the wrong solution!