The two very different men engage in a battle of wits.
After that the whole adventure became a battle of wits between him and me.
You are not challenging her to a battle of wits.
This is no longer a battle of software or even human wits.
In that case, I challenge you to a battle of wits.
It was going to be a battle of wits from this point forward.
But in a battle of wits, he was far from unarmed.
To take too long would lose him face in this battle of wits.
He would spend time after the play in a battle of wits with the audience.
Up to now it was a simple battle of wits.
Idiomy