Ok, so here's what I understand, based on the Wiki and on @Streetwind's guide, etc.
You don't really need to understand the number exactly, just understand that if it's higher, your odds are better.
Density search tells you about the column above/below the first block you broke in your search.
The results don't guarantee ore will be there, they just give you an estimate of how likely it is to spawn.
The numerical result is in parts per 1000 blocks, not parts per 100 (i.e. percent)
Okay, cool. So you don't need to correct me on any of that, please.
But... here's my question: out of every1000 blocks... what... exactly?
I guess the number could mean "out of 1000 blocks, X blocks have the chance to generate ore Y." i.e., a cassiterite reading of 0.15%o, for example, would mean that out of 1000 blocks, 0.15 bocks could possibly generate cassiterite.
First, let's convert 0.15%o into a more intuitive number.
If we're only going to find 0.15 of something out of every 1000 searches, how many searches do we have to do before we're almost guaranteed to find one? 0.15 multiplied by what is 1? About 6.6. So we multiply 1000 by 6.6 as well and end up being able to say "that's about one block out of every 6.6k blocks."
So, if we go back to our "only this many blocks have a chance to spawn ore," we can pretty easily tell that this isn't what it means. Only one (on average, in aggregate) blocks in 6.6k blocks could even POSSIBLY spawn as cassiterite, you'd end up searching dozens of thousands of blocks, and you might find one or two. That doesn't match experience.
However...
You could interpret a 0.15%o cassiterite reading to mean, "out of every 1000 blocks, you will, on average, find 0.15 cassiterite blocks." Or, "you'll probably find about 1 cassiterite block in every 6.6k blocks you search in this area."
Just some quick math, here. Node search mode, by default, goes 6 blocks in every direction, even diagonal. (I just tested this in creative.) In other words, every time you node search, you get results 6 blocks up, 6 down, 6 north, 6 south, 6 east, and 6 west. That ends up being a 13x13x13 block cube. Soooo... if you are digging straight down, all the way to the mantle, and then prospecting every 6 blocks as you go back up, you're going to be searching a 13x13x120ish (with normal worldgen) column.
For the sake of simplicity, let's say it's a 13x13x100 column. That's just under 17,000 blocks. And most of us know what'll happen if you search 13x13x100 blocks underneath a "high" cassiterite reading. If you *don't* get positive hit on node search, you're unlucky af. And with each positive hit, you're probably going to find at least a handful of ore blocks once you marco-polo your way to them.
So that "one in 6.6k, on average" interpretation of "High Cassiterite 0.015%" seems to too low. It really seems like there is *more* than one in 6.6k (on average, not guaranteed, I *know*).
So what gives? Anybody know?
Am I doing math wrong somewhere? Is that number telling us something else about the probability of finding ore in an area? Do I need to stop overthinking it and just play the darn game?
What does everyone think?