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Certain they do play exhibition/pre-season games against public schools. My uncle who played for Coolidge HS in NW DC played against DeMatha a few times outside of the regular season. When I was there we played against 2 public schools b4 the season started. I cant remember which schools they were I havent kept up with the program since i left sos they could've changed but while i was there and when my cousin was there 6 years b4 me they played public schools in scrimmages/exhibition