Francesco Piscina, in 1565, explained Matto and Bagatto.
I do not want to leave out unmentioned another explanation, even if it will seem to be a joke. In order to make it clear, you must know that it can be read, in a very pleasant and acute comedy written by the very learned Intronati, of the famous Academy in Siena, not devoid of seriousness, of the amusing controversy between two very tight-fisted innkeepers: all people of any kind, when they had to travel, used to go to the Inn of the Mirror, but for a long time they had preferred to go to that of the Fool, more appropriate to their will and their actions. This is why, with great mystery, we see the Fool in the game of Tarot being represented in such a way that he looks behind towards a mirror, making fun of the fame of the Mirror, that is lost among all people, who once used to go to that inn. This is why his face is so joyful; he rejoices and glories in the credit he receives, so that all men run behind him. He is followed by the one that is called the Bagat, dressed as an innkeeper, not without subtlety, because as the signs of the Inns are seen by travellers in search of lodging before they see the innkeepers, as the signs used to give good reputation to the inns, as we see in those of the Lilies, Eagles, Falcons, Crowns and Kings, that in all good and famous cities show good lodging, in the same way the Fool, being the figure of the inn, has been put before the Bagat, who is the Innkeeper, meaning that famous inn to which most people used to go.
... where Angels fear to tread. (Alexander Pope)