Half-elves were rare in Tolkien’s world. Unlike D&D half-elves, in Tolkien’s world they had to choose between being an elf or a human. If they chose to be elves, they had the same immortality as any other elf. Elrond and his brother were the first with this choice. Elrond chose to be an elf. His brother, Elros, chose to be human, although with triple or more the normal human lifespan. Elros led to the Kings of Numenor and later of Gondor and Arnor. Most people know the later tale of Aragorn and Arwen, if not from the books from the Hollywood take on it in the Lord of the Rings movies.

In D&D, half-elves are not described this way. I don’t know if it was D&D or something else that gave rise to the idea that elves have pointy ears. They are obviously much more common in D&D than in Tolkien’s world, and also have about three times the lifespan as humans. They have some of the advantages of elves and are often the best choice for getting the most options out of a character in AD&D. My favorite and longest played character, Griswald, is a half-elf with slightly above average ability scores, but not exceptional. His highest ability is a 14. He is a Fighter/Cleric/Magic-User which lets him wear armor, heal himself and others, and do great damage to enemies. Such a character also takes more time to prepare spells at his level, and there is a lot of information to keep straight, so such a character is hard to play without having built up to that over time. I know that as a DM I could run an NPC with similar abilities without too much trouble, but a DM who has never played such a character will miss out on a lot of the possibilities.