throw up the sponge/throw in the sponge/throw in the towel

THE ADVENTURES OF HUCKLEBERRY FINNの一節です。
He whitened a little; he couldn't help it; and it was mighty still in there, and everybody bending a little forwards and gazing at him. Says I to myself, NOW he'll throw up the sponge -- there ain't no more use.
"throw up the sponge" はどう見ても慣用表現の様なので辞書を見ます。
・Webster's Revised Unabridged Dictionary (1913): To give up a contest; to acknowledge defeat; -- from a custom of the prize ring, the person employed to sponge a pugilist between rounds throwing his sponge in the air in token of defeat. [Cant or Slang] ``He was too brave a man to throw up the sponge to fate.''
ボクシングから来た表現ですね。　そう言えば "throw in the towel" なら聞いたことはあります。
"throw up the sponge" は載っていなくても、"throw in the towel" ならたいていの辞書に説明がありました。
・McGraw-Hill Dictionary of American Idioms and Phrasal Verbs: throw in the towel and throw in the sponge; toss in the sponge; Fig. (From boxing, where this is done by a boxer's trainer to stop the fight.) to signal that one is going to quit; to quit. When John could stand no more of Mary's bad temper, he threw in the towel and left. Don't give up now! It's too soon to throw in the sponge.
・Cambridge Dictionary of American Idioms: throw in the towel; to admit defeat or failure The union was forced to throw in the towel and settle their bitter dispute with the company.
Etymology: based on the literal meaning of throwing a towel into the ring in boxing (signaling that a fighter can no longer continue by throwing a towel into the area where the fight takes place)
世界卓球を見ていると0-2から逆転して3-2になる試合も結構あります。最後まであきらめない "not throw in the towel" がスポーツでは重要だと思います。