@Mainac "As I've said if there were just 52 events that needed to happen, then life could still be unique based on the math of shuffling cards."
- that makes certain assumptions about the size of the universe.
We don't know how big the universe is, or if it is infinite. We do know it is at least 1 cosmic horizon in every direction. And the cosmic horizon is pretty damn lager (more than 13.7 billion light years, with assuming uniform mass density, and near flat curvature - as close to flat as we can measure...)
Regardless of your proposed uncertainties, life could be very common and yet not densely spread (in either time or space)
"Unless we know precisely what caused life on earth and how many separate events that took, then the rest is guess work." but we do know something about the seperate events, the steps toward abiogenesis.
And we do know that it happened at least once on earth, and the type of circumstances which lead to it happening here. But you are also right, the error in a count is the square root of the count, so 1 example of life starting on earth, gives us an error of Root(1) = +/- 1.
So we know from out data that the number of event it takes for life to occur (within 4.6 billion year, and on an earth-like planet; which we know there are many in each galaxy based on recent evidence) are such that the number of times it will happen is between 0 and 2 (that is 1 +/- 1)
So you are betting on 0 - which is impossible without an interventionist god - or so close to 0 that human life is unique. But evolution considerably reduces the number of events you need; once you get self-replicating machines, they inevitably evolve - thus we only need that first step. ~(ok you also need an energy source, which drastically limits us to places with stars nearby, but that is a given when discussing planets around stars)
To the point. UNLIKE random shuffling, we have reason to believe that life builds on itself. ONCE you get step 1, it doesn't matter what step is next, so long as step 2 happens eventually in the pattern. It is more like drawing cards from a deck which is randomly shuffled, and then a second card is drawn - eventually you get the Ace of spades. Then you shuffle and draw until you get to 2 of spades... and so on; this number is considerable smaller than your total number of arrangements.
The system is decidedly NOT random.
"Unless we know precisely what caused life on earth and how many separate events that took, then the rest is guess work." - no, educated guesses do not require exact precision. And we have very educated people to tell. We know certain thing, like life needs a source of entropy, we know crystals grow, we know oil drop form cell-like micro-environments, and we know evolution takes off once you get self-replicating molecules which can code for information (crystals can code information, and self-replicate, but replicating the info is not easy) We have no reason to believe that one of these steps is impossible. No educated guesses tell us that at all.
And you're not saying that is it, merely that it must be somewhere between 0 and 2, thus it may be infinitesimally close to 0.