Meaning of 本気 in Japanese

ケンさん、君は本気かい。
Are you on the level, Ken?

「まあ、それでも君よりは、はるかに僕の方が点数高いけどね。」「なんですって！私が本気を出せば、あなたなんて、目じゃないわ！」
"Well, even so my score is far above yours isn't it?" "What did you say!? If I was to go all out you'd be as nothing to me!"