Neo-Tac's Renew-It and Black Magic are the two easiest polishes that I know about that can get a decent shine on a ball by hand. BUT it still does not compare to what can be done with a spinner AND how easy it is to do it. A spinner can cost less than the price of ONE new ball. If you're serious about bowling it is the one best investment (after the proper coach, of course).
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"We get old too fast, and too late, smart."