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I wouldn’t really say the Black Jacks are a ‘bmx’ tyre. I think they are too skinny to be used by anyone serious about bmx riding. I thought they’d be more...I dunno, junior mtb?
In terms of proper bmx tyres I’d consider there’s two options, a primarily slick street tyre that’d take high pressure (100psi+) and be reasonably puncture resistant or a knobbly dirt tyre that’d be much lighter weight and hence, less puncture resistant and takes lower pressure so would look good but not be so much use for urban use.
I’m perhaps over simplifying things and basing this on outdated buying experiences though as I’m sure there’s tyres available nowadays that work both on and off road and are available in 20” size.
Also there's these - they are actuall called "Schwalbe Knobbly", though they don't look very knobbly to me -
Don't know, figure they might look cute on a small bike like that, but really not sure that tyre pattern is practical for anything.