Etymology
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game (n.)

c. 1200, from Old English gamen "joy, fun; game, amusement," common Germanic (cognates: Old Frisian game "joy, glee," Old Norse gaman "game, sport; pleasure, amusement," Old Saxon gaman, Old High German gaman "sport, merriment," Danish gamen, Swedish gamman "merriment"), said to be identical with Gothic gaman "participation, communion," from Proto-Germanic *ga- collective prefix + *mann "person," giving a sense of "people together."

The -en was lost perhaps through being mistaken for a suffix. Meaning "contest for success or superiority played according to rules" is first attested c. 1200 (of athletic contests, chess, backgammon). Especially "the sport of hunting, fishing, hawking, or fowling" (c. 1300), thus "wild animals caught for sport" (c. 1300), which is the game in fair game (see under fair (adj.)), also gamey. Meaning "number of points required to win a game" is from 1830. Game plan is 1941, from U.S. football; game show first attested 1961.

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game (adj.1)
"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.)).
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game (adj.2)
"ready for action, unafraid, and up to the task;" probably literally "spirited as a game-cock," 1725, from game-cock "bird bred for fighting" (1670s), from game (n.) in the "sport, amusement" sense. Middle English adjectives gamesome, gamelich meant "joyful, playful, sportive."
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game (v.)
Middle English gamen "to sport, joke, jest," from Old English gamenian "to play, jest, joke;" see game (n.). The Middle English word is little recorded from c. 1400 and modern use for "to play at games" (1520s) probably is a new formation from the noun; and it might have been re-re-coined late 20c. in reference to computer games. Related: Gamed; gaming.
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game-cock 
cock bred for fighting or from fighting stock, 1670s, from game (n.) in the sporting and amusement sense + cock (n.1). Figurative use by 1727.
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board-game (n.)
also boardgame, 1867, from board (n.1) + game (n.). Compare German Brettspiel.
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ballgame (n.)
also ball-game, 1848, from ball (n.1) + game (n.).
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gamey (adj.)
also gamy, 1844, "spirited, plucky," from game (n.) + -y (2). Meaning "tasting or smelling strongly" is from 1863.
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gamekeeper (n.)
one who has responsibility for animals kept for sport, 1660s, from game (n.) in the "wild animal caught for sport" sense + keeper.
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gamely (adv.)
"courageously," 1861, from game (adj.2) + -ly (2). In Old English and Middle English the adverb meant "artfully; joyfully."
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