Guest Puss, we had one of the white, deaf cats years ago. He really was totally deaf, but it was difficult to tell, as his ears swivelled just as much as any other cat's ears, and he kept an eye on our other cats for cues.
Snow was a very big cat, not fat, just big and powerful, very confident, easygoing, and we kept a supply of paper balls to throw at him when he was up to mischief. It was no use shouting.
I expected him to get run over or killed by a dog, but he died of natural causes at a good age.

The only cat we've ever had who didn't leave the room when I played the concertina. Are cats accordion/melodeon critics?