It's pretty much accepted on all sides of the theism/naturalism debate that a life-permitting universe existing by chance is astronomically improbable and that the chance organization of a self-replicating cell is likewise astronomically improbable.
Theists therefore conclude that chance explanations are literally incredible and that the best inference from these improbabilities is that the universe and living things are not the result of chance processes but are instead intelligently orchestrated.
Naturalists sometimes reply with a shrug and a dismissive claim that improbable things happen all the time so we shouldn't get excited over the fact that a finely-tuned universe or an exceedingly complex biological cell are improbable. After all, they say, your own existence is highly improbable, given all the contingencies that needed to occur for you to be conceived. Yet here you are.
There is, however, something wrong with this response.
To see the error consider poker. The odds of being dealt a royal flush (Ace, King, Queen, Jack, and ten of the same suit) are the same as being dealt any other combination of five cards, but if you were dealt a royal flush in a high stakes poker game you wouldn't be lackadaisical about it. You'd be stunned at your good fortune. But why should you be if a royal flush is no less likely than any other hand?
There are at least two reasons, the second being related to the first:
First, a royal flush has an apriori significance. It's the highest, most valuable, hand in poker. It's that specified prior significance which makes the royal flush so much more extraordinary than any other hand of equal probability.
Second, even though a royal flush is no more improbable than any other particular five card hand, what would astonish a poker player who was dealt a royal flush is that being dealt some other, non-royal flush combination of cards is unimaginably more likely than being dealt a royal flush. In other words, being dealt the specific combination of cards that has the highest specified value in the game is far less likely than being dealt any other combination that lacks these two properties.
This is similar to the lottery. What makes winning the lottery so improbable is not that the particular combination of numbers on your ticket is less likely than any other possible combination but that it's far more likely that any ticket you purchase will not be a winning combination of numbers. It's astronomically less likely that a lottery player will buy the ticket which specifies the particular combination of numbers that specifies a big payout than that he or she would buy a ticket displaying some other combination of numbers.
Or consider throwing a bucket of paint against a wall. Let's assume that the chances of any particular pattern being formed by the splattered paint are the same as any other particular pattern. Yet the chances of producing some random pattern are perhaps infinitely greater than the chances of producing a picture of the Mona Lisa.
The odds that a universe would exhibit all the precise values for the parameters, constants, and forces that specify a life-sustaining universe, out of the endless possible values it could've had, are like the odds of getting the Mona Lisa by splashing a bucket of paint against the wall. And that's why the "improbable events occur all the time" argument fails to impress.
That's also why so many thinkers who wish to avoid the conclusion of theism embrace the multiverse hypothesis. If only we're dealt enough hands, the thinking goes, if only we buy enough tickets, if only we splash enough paint, we're bound to get a royal flush, a winning ticket, or the Mona Lisa eventually.
So, if there's an infinity of different universes out there then all possible universes must exist, and, since ours is a possible universe, there just has to be one as improbable as ours. There has to be a Mona Lisa in that infinity somewhere, the multiverse proponents tell us, and we just happen to be it.
