I know there is a Tosafos in Beitza 12a that discusses playing ball on Yom Tov, but I remember learning another Tosafos which said something like "for children under nine it would be permitted on Yom Tov". I'd appreciate it if someone could help me find where that is.
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The Yam Shel Sh'lomo is the one who, disagreeing with Tosafos, distinguishes between adults and children playing ball on Yom Tov http://hebrewbooks.org/pdfpager.aspx?req=14086&st=&pgnum=22&hilite=:
אלא שחוק של ילדים שלא הגיעו לכלל חיוב הנח
The YS"S can arguably be interpreted to refer to children below the age of chinuch. There is a Tosafos that discusses what the age of chinuch is in general, and one of the possibilities mentioned is nine years old (Tos., Arachin 2b, sv. שהגיע לחינוך):
וי"א כבר תשע כבר עשר
However, Tosafos conclude that these ages are only relevant for fasting...
אבל בשאר מצוות כל אחד ואחד לפי דרכו
Be advised that this information should not be used for halacha l'ma'aseh.