"one who shaves," early 15c., agent noun from shave (v.); sense of "fellow, chap" is slang from 1590s. Meaning "shaving tool" is from 1550s. Mad shaver (1610s) was 17c. slang for "a swashbuckler, roisterer."
To get a gambling or money advantage by failing to score as much as one could; fraudulently lose a game: Did they think I liked shaving the points? (1971+ Sports & gambling)