3 ball bag is ALWAYS a bad idea, solely because I've seen too many airlines turn it down. Strongly suggest 2 two-ball bags. much easier to handle, more balls as an option at the tournament, less damage to the ball bags, etc, etc.
Many airlines will not allow any bowling balls as a carry-on since they can't be put under most seats and they're far too dangerous to be put into the overhead compartments. YOu risk them not allowing it on the outgoing or the incoming flight.
caution recommended!
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"...for advice is a dangerous gift, even from the wise to the wise...."
J. R. R. Tolkien