If we could have some information about your drivetrain we could also help. As well, I don't believe adding tape is the way to go to increase traction.
To answer your question about the competition carpet, as per Section 2, The Arena,
Quote:
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The Court is covered with carpet (Shaw Floors, Philadelphia Commercial, Neyland II, 20, 30753, “park bench”).
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This is the carpet to be used at competition.