Half-Elves

[Acacia]

Rereading the Silmarillion rather confused me on what is and is not considered a Half-Elf.

Let's start with Luthien. If you want to get technical, she was only half elf; her mother was a Maia. Her son Dior was half human, one-quarter elf, and one-quarter Maia. There is no record of his being offered the choice of what to be, which means either he was *not* considered a half-elf, or it doesn't mean anything; he was killed before the Valar decided to give half-elves this choice.

Then he married an elf; their daughter Elwing would have been one-eighth Maia, one-quarter human, and five-eighths elf. She *was* given her choice.

Earendil- fairly straightforward- half elf, half human. He got his choice.

Their children, Elrond and Elros, would have been- ~grabs a calculator~ -one-sixteenth Maia, three-eighths human, and nine-sixteenths elf.

Here's where I start getting confused.

IIRC Elrond's children (25/32 elf, 3/16 human, 1/32 Maia) were considered half-elves and had their choices, though as can be seen they were far more elf than human.

But Elros'? He married a human, so they'd have been 11/16 human, 9/32 elf, and 1/32 Maia. And they weren't considered half-elves, none of them got their choice.

Also, the child(ren) of Arwen and Aragorn, who for the sake of sanity and me not having to do insane amounts of math we will assume to be purely human, was.. 25/64 elf, 19/32 human, and 1/64 Maia. And didn't get their choice.

So: Is a Half-Elf someone who is at least half elf, and also possesses mortal blood?

Does the mortal have to be human, or would dwarves or hobbits work as well?

Could elves breed with dwarves or hobbits?

For that matter, could they breed with orcs who, after all, were elves initially? And would *that* be considered a half-elf? And that's a rather disturbing mental picture so I'll break off that train of thought *right* there..