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Two of the races you're allowed to use in D&D are half-elf and half-orc. My first character was a half-elf. Usually the other half is human but is it possible to have a character who is half-elf and half-orc?
Are any of the other main races compatible? I heard someone saying the dwarves were half-human and half-gnome but I don't think that's correct.
It's always the GM's decision how this work in each specific campaign.
To my knowledge, there have never been any orc-elf crossbreeds in official D&D sources and no half-elf/half-orc ones either.
Dwarves being half-gnomes is also not in any D&D books.
Regarding dwarves, there is one notable exception. In the Dark Sun setting there are human/dwarf hybrids called Mul. Mul can not reproduce on their own and are only found as gladiators in arenas run by the immortal sorcerer kings (or used to be gladiators but escaped), so they appear to be all created with magic help and can not be produced naturally.
Monster Manual p245:
The orcs' drive to reproduce runs stronger than any other humanoid race, and they readily crossbreed with other races. When an orc procreates with a non-orc humanoid of similar size and stature (such as a human or a dwarf), the resulting child is either an orc or a half-orc.
Any cross breed produces an orc or a half-orc. Half-orc characters can of course have appearance traits of the other race, but the stats will be as a half-orc.
In the Dragonlance books, if dwarves and gnomes mate, their offspring are called "gully dwarves" and are found to be living in dumps and slums, have extremely low intelligence and are frightened extremely easily. For that reason, the mating between these two races is forbidden.
