This text is talking about pearls.
更胜一筹， 略胜一筹：slightly better, a cut above.
Maybe, this comes from an ancient drinking game:
You got more arrows in the pot than your opponent, he had to drink more 白酒 as punishment.
The Chinese like drinking games! (Me too!)
baidu: 笴: 箭杆 gě, gǎn
Maybe 筹 was the classifier for 笴?? What is 筹 in 更胜一筹？