D&D General Should players be aware of their own high and low rolls?

[Maxperson]

in theory you can run D&D with the PHB and Monster Manual... this is why people joke about not reading the DMG

Yep. As written, the DMG is only advice for ways to run the game, not rules. You don't need advice to actually run the game. It is very helpful, though, especially if you are new.