From what I've read, Each cell contains from dozens to a hundred+ mitochondrias. When cell splits then some mitos go to one child and some to another.

Mitochondria are self replicating. When the cell splits some of the mitochondria are present in each new cell.

Yeah, this was how I was thinking as well.

But to continue the analogy, it's more like you split yourself into two smaller "you"s, and in the process each new "you" gets half a coin in the pocket of each new "you".

To clarify, it would be more like you have a group of 10 coins and each of your offspring get 5, but grow back to having 10 during development

Yes, they carry on growing.

That’s because creation of new coins is external to your reproduction. Eukaryotic cells are not scavenging in the wild for new mitochondria; they control the replication of mitochondria within them, including how they are passed to offspring through reproduction

An interesting thing about mitochondria too— we receive all of our mitochondria from our mother. So for every human, there is an unbroken line of direct mitochondrial ancestors leading all the way back to the first biologically unique Homo Sapian women