Is it farther or further?
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."
(1.) Of children (Zech. 8:5; Matt. 11:16). The Jewish youth were also apparently instructed in the use of the bow and the sling (Judg. 20:16; 1 Chr. 12:2). (2.) Public games, such as were common among the Greeks and Romans, were foreign to the Jewish institutions and customs. Reference, however, is made to such games in two passages (Ps. 19:5; Eccl. 9:11). (3.) Among the Greeks and Romans games entered largely into their social life. (a) Reference in the New Testament is made to gladiatorial shows and fights with wild beasts (1 Cor. 15:32). These were common among the Romans, and sometimes on a large scale. (b) Allusion is frequently made to the Grecian gymnastic contests (Gal. 2:2; 5:7; Phil. 2:16; 3:14; 1 Tim. 6:12; 2 Tim. 2:5; Heb. 12:1, 4, 12). These were very numerous. The Olympic, Pythian, Nemean, and Isthmian games were esteemed as of great national importance, and the victors at any of these games of wrestling, racing, etc., were esteemed as the noblest and the happiest of mortals.