QUESTION: how many different bowling balls am I allowed to use in one game?
There are no limitations short of the number of shots in a game.
Some events require equipment be "registered." Potentially, there might be a limitation if a tournament, league or event imposes one.
Thanks for the question, roll on.
---------- FOLLOW-UP ----------
QUESTION: Warren, thank you for answering my question.
However I now must ask the question in a different way: is there a specific rule that a professional bowler can only use one bowling ball per game in a sanctioned tournament.
The reason why I am asking this question is that I have a friend (non bowler) who insists a pro bowler can use only one ball per game.
Thank you in advance for your reply.
In the case of the Pros, they, to a greater degree, use all their option. Often using a "strike" ball and spare ball, most of the time. Often multiple balls are used in any given game.
The issue with the pro's is that often time a ball that suits their game is in "their bags" in multiple variations (various layouts/drillings). It may look like they throw the same ball, but they throw the same ball drilled in different ways to facilitate different reactions.
I would tell you in no uncertain terms, (as I have participated in professional tournaments) your friend is wrong.
Thanks for the question. Good luck and good bowling.