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In 1x06 "Rick Potion #9" (Cronenberg incident), Rick mentioned that
It's not like we can do this every week anyways. We only get 3 or 4 more of these tops
In 3x08 "Morty's Mind Blowers" (the squirrel incident), Rick mentioned that
I said that we can only do that a couple of times!
What gives?
Answer updated after reviewing the episode transcript.
Rick specifically mentions in this episode that R&M occurs in an infinite multiverse:
There's an infinite number of realities, Morty, and in a few dozen of those, I got lucky and turned everything back to normal. I just had to find one of those realities in which we also happen to both die around this time. Now we can just slip into the place of our dead selves in this reality and everything will be fine. We're not skipping a beat, Morty. Now, help me with these bodies.
In itself, this is a paradox: If there were infinite realities, there would be a limitless number of realities wherein Rick's exact criteria are met. If Rick is speaking figuratively here (assigning the value of "infinity" to an enormous [but limited] number of universes as a simplification for Morty), my original answer (below) may still apply, but I'm inclined to take Rick's words as literal and demonstrative of the show's philosophy.
Before this scene, Rick says:
I do have one emergency solution that I can use that'll kind of put everything back to normal, relatively speaking. Here, Morty, put this on while I do a little bit of scouting.
Rick has to search for these universes where he's solved their problems and he and Morty die (so "original" Rick and Morty can easily assume their identities). Regardless of your theoretical approach, this creates all kinds of problems in the context of infinite universes (essentially, infinite realities beget infinite solutions). Moreover, as you mention, Rick's words relay concern for the future in "Morty's Mind Blowers" ("I said that we can only do that a couple of times!"), which doesn't make sense unless the number of universes where Rick and Morty exist is limited, again bringing us to my original 'limited multiverse' answer.
It's possible (maybe, I'm not an expert on any of this scientific theory) that Rick and Morty occurs in an infinite multiverse containing a limited number of universes that feature Rick and Morty. (This is what Rick's own words suggest, by my logic.) This doesn't really make sense with respect to the meaning of "infinite," but Rick and Morty thrives on these paradoxes. As Rick expresses early in the episode, our understanding is limited and everything is up for interpretation:
Okay, well, sometimes, science is more art than science, Morty. A lot of people don't get that.
It’s partly for comedic effect, but it also uses the subtext of Rick’s frustration to curb the ‘infinite’ part of ‘infinite realities.’ (Truly infinite realities would be limitless, and Rick’s concern that he and Morty might “run out” of suitable replacement worlds would be misguided.)
A limited multiverse is more sensible in-context: In this scenario, Rick is aware of the available replacement worlds and recognizes that a vast majority of other universes are not habitable long-term for him and Morty (e.g. the Cronenberg world).
These suitable replacements feature minimal variance from Morty’s home universe and are limited in quantity as a function of basic statistics: Imagine “universe characteristics” follow a Poisson distribution – any given set of desired characteristics in the overall group (when that characteristic group has as many parameters as a universe) is going to be statistically unlikely and occupy a comparatively small solution space. (Here, that small solution space is the “three or four” universes out of billions+ options.)
My perception of the situation.
The number of universes is infinite. Unfortunately our abilities to acknowledge their existence is finite. No matter how smart Rick is, he still can only store information about a finite number of them. He is at some point limited by matter and energy.
So as I assume Rick spends lots of time observing and cataloging universes. We know he has lots of plans to survive anything. 99.999 to the infinity are useless. They are earths that exploded or can't support carbon life. So every time Rick finds a useful one he adds it to his catalog. His catalog could have billions of universes in it, but he can only search them so fast, and thus the catalog is limited. If they just keep using up universes, eventually he is going to be out of any that are in his catalog. And then bam, nowhere to go.
We should also consider that the number of Ricks at least known to the Ricks is finite. We see this in "Close Rick-counters of the Rick Kind" when Rick is showing Evil Rick. This is most likely for the same reason. The Ricks can only be aware of that many Ricks. No matter what they are still not god, and can't know infinity.
Alright, we know that there is a seemingly infinite amount of universes. But remember when Rick said that they can only ditch their own universe (and replace another Rick and Morty) for maybe 5 or 6 times in Rick Potion #9? And why did the voucher for one free Morty mean anything if there are so many universes? Especially since that think was given as an apology for nearly sending a Rick to a faith worst than death.
So, I had that theory on my mind for about 6 years but never wrote it down. Well I did it here about 1 day ago. Anyway, let's look at the problem.
First proposal, the multiverse is not truly infinite but just really, really, really big. Why? Basically every time a decision can be made the universe splits and takes both decisions. Every particle that may move in two directions will split the universe into two copies. This means that the universe constantly splits into new realities. A mindbogglingly big number. But not infinite. Just nearly not infinite.
So, like the universe has a (gigantic) size, the multiverse has also a (gigantic) count of universes.
Still, this should still mean that we have a quasi-infinite amount of Ricks and Morties, right?
Well, we can omit all universes that are barren. This not only means no live, this also means every universe that never created a Rick or Morty. No Rick and Morty means no live to replace and no Morty for a Rick that is missing one.
But this is still an incredible big number! Well, only if not something equally infinite balance out the math. A very big number divided by a equally big number results in 1 after all.
So what could be something that is (a) universal to all universes that can harbor a Rick (b) so incredibly deadly that it rivals the size of the multiverse?
The answer: Mortys incompetence! The incompetence of session 1 Morty, to be exact. The Morty that hasn't yet learned to handle Rick. The only force in the universe that can counter the incredible size and weight of said universe.
Remember that Neutrino Bomb from the Pilot? The very first scene we saw? Tell me, how likely is it that a Morty, without any training or experience, may disarm that thing? Remember, Morty is just a child at this point. A child with sub-par mental faculties, a lack of assertiveness and a lack of sleep. Oh, and he also has just a few seconds to disarm it (given by the noise the thing makes at the very end of the scene).
I tell you how unlikely it is, about as unlikely as the size of the multiverse!
That's right, I propose that one of the universal constants (those that are true for all universes) is Ricks self destructive behavior. That every Rick in every universe tried to destroy that universe. That is what makes a Rick a Rick. That is why Ricks and Mortys are scarce. Because every Rick that exists does so due to the fact that his Morty was infinitely lucky and managed to disarm that bomb (or other contraption). And deep down the Rick knows that. He knows that he needs the Morty. Not just for his brainwaves. But for his ever increasing talent to save him from himself.
