Etymology
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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 (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 (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.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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end (v.)
Old English endian "to end, finish, abolish, destroy; come to an end, die," from the source of end (n.). Related: Ended; ending.
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end (n.)

Old English ende "end, conclusion, boundary, district, species, class," from Proto-Germanic *andiaz (source also of Old Frisian enda, Old Dutch ende, Dutch einde, Old Norse endir "end;" Old High German enti "top, forehead, end," German Ende, Gothic andeis "end"), originally "the opposite side," from PIE *antjo "end, boundary," from root *ant- "front, forehead," with derivatives meaning "in front of, before."

Worldly wealth he cared not for, desiring onely to make both ends meet. [Thomas Fuller, "The History of the Worthies of England," 1662]

Original sense of "outermost part" is obsolete except in phrase ends of the earth. Sense of "destruction, death" was in Old English. Meaning "division or quarter of a town" was in Old English. The end "the last straw, the limit" (in a disparaging sense) is from 1929. The end-man in minstrel troupes was one of the two at the ends of the semicircle of performers, who told funny stories and cracked jokes with the middle-man. U.S. football end zone is from 1909 (end for "side of the field occupied by one team" is from 1851). The noun phrase end-run is attested from 1893 in U.S. football; extended to military tactics by 1940. End time in reference to the end of the world is from 1917. To end it all "commit suicide" is attested by 1911. Be-all and end-all is from Shakespeare ("Macbeth" I.vii.5).

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rear-end (n.)

by 1868, "the back part of anything;" by 1937, "the buttocks;" from rear (adj.) + end (n.). As a verb, "to collide with (another vehicle) from behind," from 1976. Related: Rear-ended; rear-ending.

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butt-end (n.)
"thick end," 1580s," from butt (n.1) + end (n.). Meaning "the mere end," without regard to thickness, is from 1590s.
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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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bag-end (n.)
"bottom of a bag," c. 1400, from bag (n.) + end (n.).
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