('chiefly US') The chess champion will 'match wits' [='compete'] with a computer. = ('chiefly Brit') He will 'pit his wits' against a computer.
He needed a moment to 'gather/collect his wits' [=to become calm and able to think clearly] after the collision.
I was 'scared out of my wits'! [=I was very scared; I was so scared that I couldn't think clearly]
(..) - I mean the matter you read, my lord - Slanders, sir For the satirical rogue says here that old men have grey beards, that their faces are wrinkled... ...and that they have a plentiful lack of wit, together with most weak hams All of which, sir, though I most powerfully and potently believe it... (..)2015 Hamlet
(..) This must be known what majesty should be, what duty is... Why day is day, night night and time is time, were nothing but to waste night, day and time Therefore, since brevity is the soul of wit... ...and tediousness the limbs and outward flourishes, I will be brief Your noble son is mad (..)2015 Hamlet