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Given the vastness of cosmos and the richness of star systems it's just ludicrous to assume earth-like planets are somehow special and rare.

At these scales nothing is rare.

Actually, they are possibly rare. Rareness is a percentage, so as long as only 1% or less of planets are earth like, that's rare, even if there are millions of them.
Isn't that such an interesting thing to think about. They're "rare" as a percentage, but because of their abundance, they're not "rare" at all.
Anyone know of a language that has vocabulary that distinguishes these two meanings of rarity?
Feels similar to the distinction between accurate and precise
I think English could work here with terms like "sparse" vs "low in number".
That seems like a great way to mitigate the availability bias.
Maybe “uncommon” vs “scarce”?
Their rarity might mean that its impossible to travel to one, despite positing millions in existence
No, in my book, these are different things.

Rare: if we take a sample of N random planets, only n << N of them will be Earth-like. E.g. 0.1% is "rare".

Scarce / few: if we take all the planets in the Universe, only a small absolute number of them will be Earth-like. E.g. 100 Earth-like planets is "scarce" or "few".

That is, Earth-like planets can be not scarce at all, but still rare. Much like while all water in Earth oceans contains 20 megatons of dissolved gold, molecules of gold are rare among molecules of water, which makes extraction of them impractical.

There is also the angle, rare as in practically relevant to us. Too low percentage, a human will never come into contact with a not even single photon originating in these worlds.
That’s not true. A large universe does not mean “nothing is rare.” An infinite universe would have an infinity of “rare” phenomena.
If vastness is One Quadrillion and earth-like planets are one in Quadrillion, it is still rare.

E.g: Given All things equal till the point of your parents birth, the probability of you existing is still astronomical -- 1 x 10^25 or something like that and that is just a 30 year event.

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The milky way is pretty small in comparison to the rest of the cosmos.
At this scale, and with the speed of light being so ludicrously low, you can't benefit from that much.

If there are billions of Earth-like worlds, but distances between most of them are all in millions of light years range, we are still effectively alone in the region of the Universe which we can reach in the duration of existence of our species. Any communication even to the closest Earth-like planet, even if it builds a civilization like ours and we have something to talk about, becomes impossible, too; only one-way broadcasting could reach us (or them).

So no, Earth-like planets abundance has a lot of implications for our species (or our close descendant species) to be able to ever settle in another star system.

Related: I have always considered that the chance of finding life (or intelligent life) is unknown, because unless we don't find a second data point (first being us) it is not possible to estimate how common or rare it is.

We can talk all we want about filters and stages to intelligent life, but it doesn't really mean anything until a 2nd case is observed.

Outputs of the Drake Equation are looking better and better, but I'm starting to worry that detecting intelligent life is going to be much harder that we previously thought. Even if a million radio-capable civilizations arose within the Milky Way, what are the chances of two such civilizations within a distance of say 100 light years having that capability at the same time?

Even then, the chances of contact seem slim. The other day, I was doing some back-of-the-envelope calculations to see what's needed for a near-Earth colony (say at about 5 light years) to send data back to Earth. Even with the tightest possible beam, even after pumping a massive amount of power into the transmitter, even after using square-kilometers worth of receivers, very little signal seemed to get through.

I'm starting to feel like there might be a lot of needles out there in a cosmic haystack that we'll never be able to sort out in our civilization's lifetime...

I’m pessimistic on the Drake equation because the single data point we have, ourselves, makes it look like after a civilization reaches radio capability it might quickly turn to over-harvesting of resources and in a few thousand years eliminate its advanced civilizations and return to a primitive state.
Intelligent life seems rare on Earth. We all seem to like it a lot, but we're the only ones in the entire history of Earth, we've not been around for very long, and we seem to be slowly sabotaging our existence. How far could someone with our technology actually pick up the signals we sent out? How many planets are realistically in that range? Then again, our existence on Earth is so brief and recent, for how long have we been looking? Less than a hundred years. That's barely anything when you talk about planets and galaxies.