Yes, but you're calculating the probability of a particular endpoint. Like with what you say about evolution, where you're calculating the probability of ending up with homo sapiens. If you start from scratch and figure out the probability of a specific endpoint (like humans), yeah, the number looks astronomical. But evolution doesn't care about ending up with humans. If you calculate the probability of ending up with something viable--which is all evolution cares about--the number gets a lot smaller.
To use exDemMom's analogy: if you calculate the odds of me winning the lottery, the numbers are huge. But if you calculate the odds of someone winning the lottery, they're not nearly so scary. I'm not sure if there's a similar analogy for dice, since they have a limited, predefined set of outcomes. Maybe something like, rather than calculating the odds of rolling a 7, calculating the chances that someone in a roomful of people would have whatever number you threw, regardless of what the number was.
I started to write a very long response and on reflection, stopped. This is a problem of computing the probability of getting from point A to point B using the pathway and rules of the road evolutionists claim should apply. Evolution claims it produced a man from a universe without life, so how was it done? Given that mutations are random and that they are either harmful, neutral or beneficial, what is the probability that what had to happen did happen on that path?
Not once has anyone claimed evolution cares about specific outcomes, so why is it raised as a defense of a perfectly legitimate inquiry into evolution? Just because people don’t like the numbers isn’t good enough. Man is but one of many endpoints, but so what? If an evolutionist wants to check out a clam, let them go to it. Checking one pathway does not preclude any other possible pathway and result.
The only reasoned argument I have seen against probability concerns how natural selection should be treated. It is not an argument against the use of probability for a specific endpoint. Nonetheless, unless a case can be made that natural selection greatly or totally negates randomness, it don’t see it faring to well.
By the way, Huxley used a horse for his endpoint. Curious that evolutionists, even today don’t jump up and down and throw tantrums over that, but he was one of theirs. Huxley didn’t like the result though and went about trying to undermine it.