The SMB3 mini-game was based on the original Mario Bros; The author describes Punch Ball as a distinct game:
> This is almost identical to the original Mario Bros, except you can't knock enemies upside down by hitting the platform they're standing on. The only way to defeat them is by hitting the POW block or throwing the Punch Ball which Mario and Luigi carry around.
Was it based on the original Mario Bros? I'm talking about the mini game you can play when Luigi and Mario occupy the same space.
You can knock enemies out by hitting the platform they're on OR by hitting the POW block and there's no ball, but other than that, the enemies and level layout seem to be identical.
Since the level layout is identical (and I don't remember a POW block in the original SMB), it seems more like the mini-game is based on Punch Ball rather than the original Mario Bros.
> This is almost identical to the original Mario Bros, except you can't knock enemies upside down by hitting the platform they're standing on. The only way to defeat them is by hitting the POW block or throwing the Punch Ball which Mario and Luigi carry around.