A stable rule it is, that World (highest trump), Pagat (second lowest or lowest trump, depends on the definition of the Fool card) and Fool (lowest trump or not-trump, which can't be captured) have the speciality, that they are valued with higher points (5 or 4 points; compare the counting page) and additionally have some special functions. Usually the Pagat is "hunted" cause its high point value (occasionally the capture of the Pagat is followed by a special payment from loosing party to winning party; the rules vary around the Pagat, its main aim is to capture the last trick. Here for instance from Danish Tarock: "The prime focus of the game is on the last trick. In general, the winner of a hand is the player who takes the last trick. Five cards, i.e., the four kings and the pagat, are designated as Ultimo cards. There is a considerable bonus for winning the last trick with an Ultimo card; this is known as "winning Ultimo") and the Fool (also called Excuse) has the condition, that he can't be captured, but stays at the hand (with its high point value) of the owner of the card (by this the lucky owner just gets a present; French rules: "If you hold the excuse you may play it to any trick you choose - irrespective of what was led and whether you have that suit or not. With one rare exception, the excuse can never win the trick - the trick is won as usual by the highest trump, or in the absence of trumps by the highest card of the suit led." ).
If we assume the same or a similar set of rules already for the Michelino deck, we must assume, that Jupiter (= highest card), Daphne (= second lowest card) and Amor (= lowest card or Fool) would be the appropriate counter objects. We've already analysed, that the Daphne myth is the centered object of the deck and that in the myth Daphne and Amor are the most important figures. It doesn't seem unlikely, that the above mentioned rules existed already in the Michelino deck.
Additionally to that: We could observe, that in the year 1423 (or near around the time, the correct dating is in dispute) the painter Pisanello got the commission from Filippo Visconti to paint decorative hunting themes in guest rooms in the castle of Pavia. As it seems, these decorations were done for the famous visitor and guest in 1424, Emperor John Palaiologus, just that man, from whom we do assume, that his presence in Pavia/Milan caused a specific Greek interest at Filippo Maria Visconti's side, which indirectly did lead to the motifs of the Michelino deck and the interest to experiment with themes of Greek mythology. Pisanello is called the pupil of Gentile de Fabbriano, but also said to have taken influences from Michelino da Besozzo. A shortliving cooperation of the two artists can't be excluded, perhaps Pisanello already presented Daphne as "hunting-motif", which was further developed by Michelino as playing card motif.
Pisanello's frescoes at Pavia are lost. From 1422 - 1442 other frescoes of Pisanello are dated (other dating: 1447), redetected in fragments under other paintings after WWII in the sala del Pisanello in the Palazzo Ducale in Mantua ( here). The main theme was then "Lancelot", centered in another favoured love story of the time (had been also a theme to Bonifacio Bembo, the Tarocchi painter of Milano). A later duke of Mantua focussed on love themes near to pornographic scenes in early 16th century (in which naked young men prefer to hunt naked young women mainly) and didn't forget the Psyche theme, another Amor-related story of Ovid. Pisanello himself later did meet the Emperor John Palaiologos at the council in Ferrara 1438 (perhaps he knew him already from 1423/1424), the latter meeting did lead to a medal with portrait of the emperor, and some belief, that this was the first of Pisanello's many famous medals, which would mean, that the occasion created a later rather popular and much imitated genre.
In other contemporary card decks (known from German sources) the "hunting theme" was generally dominating, various examples are known (for instance the "oldest" surviving Stuttgarter hunting deck, the Ambras deck, Flemish hunting deck). We've no positive evidence for the following assumption, but the appearance of so much "hunting" and "animals" in the old playing card decks might be expression of a general and farspread association between "card playing" and "hunting cards". Chess was played in a metaphorical picture as a "battle between kings", card playing seems to have had metaphorically the meaning "hunting the animals" (the animals appeared usually on the lower number cards, the higher court cards seem to have played the role of hunters.