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A Bastard is someone whom is born out of wedlock and is therefore illegitimate.
A royal bastard is a child of a reigning monarch born out of wedlock. The king might have a child with a mistress, or the legitimacy of a marriage might be questioned for reasons concerning succession.
The word bastard is from the Old French "bastard," which in turn was from medieval Latin "bastardus." According to some sources, "bastardus" may have come from the word "bastum," which means packsaddle, the connection possibly being the idea that a bastard might be the child of a passing traveller (who would have a packsaddle). In support of this is the Old French phrase "fils de bast" loosely meaning "child of the saddle," which had a similar meaning.
Bastardy was not a status, like villeinage, but the fact of being a bastard had a number of legal effects on an individual.
One exception to the general principle that a bastard could not inherit occurred when the eldest son (who would otherwise be heir) was born a bastard but the second son was born after the parents were married.
Since bastards aren't part of any house Bash says that they are allowed to pick their own symbol to represent them and most of them do. Sebastian chose to be represented by a lion which he has an engraving of on the heel of his sword. Tomas chose to be represented by a dragon in which he had imprinted on the sail of his ships.