The earliest known use of the name "Trionfi" can be dated to 16 September 1440 in the records of a Florentine merchant, Giusto Giusti. He recorded a transaction where he transferred two expensive personalized decks to Sigismondo Pandolfo Malatesta.
A letter from November 1449 from the Venetian Antonio Jacopo Marcello used the expression for a deck that was produced 1425 or earlier. It was commissioned by the duke of Milan, Filippo Maria Visconti, painted by Michelino da Besozzo and described in an accompanying text by Martiano da Tortona. The deck itself is lost, but da Tortona's description offers details about the deck. It likely had a total of 60 cards (four kings, forty number cards and sixteen trumps). The forty four-suited cards used birds as suit signs and the trumps presented sixteen Roman gods.
The names Taraux and Tarocchi appear for the first time in the year 1505 in parallel in Avignon (France) and Ferrara. Around this time, the name Trionfi seems to modify its character in a playing card context; it appears as a game of its own (Rabelais knows a Taraux and a Trionfi game) and seems no longer connected to the specific allegorical cards. This is most likely due to the popularity of Triomphe which usurped the old name. The general English expression "trump card" and the German "trumpfen" (in card games) have developed from the Italian "Trionfi".
The term Trionfi- or any similar term -first appeared in the 15th century. The Tarot cards that are popular today seem to be a version of Trionfi, with motifs and deck structure that vary in some ways. A Ferrarese document from 1457, for example, seems to be a receipt for the production of 2 decks, each of 70 cards - the modern Tarot deck typically has 78.
The first appearance of a deck with 78 cards was in the Boiardo poem Tarocchi, with the first deck thought to have been created between 1461-1494. The deck structure was created according to the Tarot-standard, but the motifs and suits signs of the Boiardo deck are totally different.
Other examples of Trionfi: