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1620s, "an athlete," agent noun from game (v.). Meaning "one devoted to playing video or computer games" is attested from 1999. Gamester is attested from 1590s but meant "prostitute" (cf. old slang the first game ever played "copulation"), later "a man fit and ready for anything, a player" (mid-17c.).
Old English gamen "game, joy, fun, amusement," common Germanic (cf. Old Frisian game "joy, glee," Old Norse gaman, Old Saxon, Old High German gaman "sport, merriment," Danish gamen, Swedish gamman "merriment"), regarded as identical with Gothic gaman "participation, communion," from Proto-Germanic *ga- collective prefix + *mann "person," giving a sense of "people together."
Meaning "contest played according to rules" is first attested c.1300. Sense of "wild animals caught for sport" is late 13c.; hence fair game (1825), also gamey. Game plan is 1941, from U.S. football; game show first attested 1961.
"lame," 1787, from north Midlands dialect, of unknown origin, perhaps a variant of gammy (tramps' slang) "bad," or from Old North French gambe "leg" (see gambol (n.)).
"brave, spirited," 1725, especially in game-cock "bird for fighting," from game (n.). Middle English had gamesome (adj.) "joyful, playful, sportive."
A brave and enterprising player, esp one who works with pain or against the odds: what is known in the business as a gamer, a guy who pitches with pain, who wants the ball/ When Jean Fuggett played for the Dallas Cowboys, his teammates called him a gamer
[1980s+ Baseball & football; probably fr game, ''brave, determined''; in the 1620s the word meant ''an athlete,'' and the current sense is conceivably though improbably a survival]