If I am very intelligent but believe I am not very intelligent, that makes me dellusional.
If I am very intelligent and believe I am very intelligent, that makes me arrogant.
Under these rules, a very intelligent person cannot win.
Not at all. Mostly it'll depend on whether the intelligence is associated with self-worth. It's just whether there are people who do not believe subconsciously that they are better than other individuals due to this trait of theirs.
I'm special vs everybody is a special unique snowflake.