遊戯

/jiu ki/ → /jiuɡi/ → /juːɡi/

From Middle Chinese compound 遊戲 (MC yuw xje).

• (Tokyo) ゆうぎ [yúꜜùgì] (Atamadaka – [1])^[1][2]
• IPA^(key): [jɯ̟ːɡʲi]

遊(ゆう)戯(ぎ) • (yūgi) ^{←いうぎ (iugi)?}

1. a game

   Synonym: 遊び (asobi)

2. a play (activity for amusement, especially for the young)

   Synonym: お遊戯 (o-yūgi)

遊(ゆう)戯(ぎ)する • (yūgi suru) ^{←いうぎ (iugi)?}suru (stem 遊(ゆう)戯(ぎ)し (yūgi shi), past 遊(ゆう)戯(ぎ)した (yūgi shita))

1. to play (a game)

   Synonym: 遊ぶ (asobu)

/jiu ke/ → /jiuɡe/ → /juːɡe/

Possibly from Middle Chinese compound 遊戲 (MC yuw xje), or a shift from yūgi above, utilizing the goon-reading of ke instead of ki/gi. (Can this⁽⁺⁾ etymology be sourced?)

• (Tokyo) ゆうげ [yùúgé] (Heiban – [0])^[1]
• IPA^(key): [jɯ̟ːɡe̞]

遊(ゆう)戯(げ) • (yūge) ^{←いうげ (iuge)?}

1. (uncommon) Same as ゆうぎ (yūgi) above

遊(ゆう)戯(げ)する • (yūge suru) ^{←いうげ (iuge)?}suru (stem 遊(ゆう)戯(げ)し (yūge shi), past 遊(ゆう)戯(げ)した (yūge shita))

1. (uncommon) Same as ゆうぎ (yūgi) above

/jiu ke/ → /juke/ ↔ /juɡe/

Likely the oldest borrowing from Middle Chinese 遊戲 (MC yuw xje), attested in Heian period literature.

遊(ゆ)戯(げ) or 遊戯(ゆけ) • (yuge or yuke) 

1. a game
2. an amusement
3. (Buddhism) freedom, said of the Buddha, bodhisattvas, or other enlightened beings

   Synonym: 遊化 (yuke)

• 遊戯(ゆげ)三昧(ざんまい) (yuge-zanmai)

遊(ゆ)戯(げ) • (Yuge) 

1. a surname