Shortened stay on arrival

I had a guest book a week ago for a 3 night stay arriving today.
He arrived and said he is now only staying for 2 nights. He didn’t mention or hint at a refund but is he entitled to one?
He hasn’t officially cancelled, he just doesn’t need to stay the 3rd night.
I suppose if he goes through Airbnb they may refund 50% (I read that somewhere) but that wouldn’t seem fair to me as the night is blocked out.

If he hasn’t requested a refund through Airbnb he won’t receive one.

What cancellation policy do you have?

He’s arrived; type of cancellation is not relevant. He has already been charged for three days, regardless of how many he stays. Do not refund him anything. If he wants a refund he, not you, must apply to AirBnb.