This is why the nucleus of Toscanelli-Brunelleschi is attractive to me. Designing a better card game is exactly the kind of problem they might spend their leisure time on. They bring the arithmetical and geometrical aspect to the problem, as well as the iconographic element, an allegorical triumphal procession, in which they and their friends and colleagues had practical experience, along with the underlying interest in the exploration of literary symbolism, even theological contemplation. Brunelleschi himself brings the popular touch which I believe the trump sequence has, especially the presence of the Fool and Bagatto, and the Traitor

*pittura infamante*. These are figures you'd see on the street, and Brunelleschi was a man of the street.

The conception of the game was at first mathematical. Unfortunately for me, I'm not of a mathematical turn of mind. I'm good with intuitive geometry and proportions, but with things like figuring out odds I'm hopeless. Brunelleschi and Toscanelli lived entirely in this mathematical world, probably thinking like Gerolamo Cardano in matters of gambling and chess (as well as his mechanical abilities), where we can study his thought intimately, unlike theirs.

So my mind is probably too dull to reverse-engineer the underlying mathematical conception of the game. But it doesn't stop me from trying.

If Brunelleschi had played

*Deification*with Filippo Maria, he may have noticed immediately that the ratio of trumps to a suit was essentially 3:2 (plausibly assuming that there were ten numbers and a king in each suit); if it were an enjoyable and satisfying game, this ratio may have stuck with him as the proper number for an enjoyable game. The ratio is replicated in Tarot. This is one way to imagine how the number of 21 trumps was chosen.

Other methods don't require the inspiration of Marziano's game.

The 21 possible combinations of two dice corresponds well with the image of the Wheel of Fortune at the heart of the sequence, if we imagine that morality and mathematical aspects were conceived at the same time. It is a game of chance, but also skill, with the possibility that skill, symbolized by the virtues, can change a poor chance into a winning one if you play your cards right.

Or it could be a symbolic expression of the Pythagorean Theorem in relation to the game, trying to find an “ideal” ratio of trumps to suit cards. It would follow the reasoning that a 56-card game for four players gives each player 14 cards and thus a round of 14 tricks. If the game is conceived as a square, with each side measuring 14, and the new part, the trumps, as laying on top of it, then it may be thought of as the diagonal line making the square into two right-angle triangles (also suggesting two partnerships in play).

This hypoteneuse measures 19.8 units. In order to deal 19 cards and tricks to each of four people requires that there be 20 trumps (76/4 = 19). But the remainder of 0.8 is not accounted for, so another whole number, a card, must be added for the symbolic completeness, making 21. Thus the Pythagorean Theorem applied to the fourfold game results in 21 Trionfi.

In all of these scenarios, the Fool, although conceptually paired with the Bagatto at the lowest end of the trump sequence, has no ordinal position and is considered also to be outside of the sequence of 21. He can pop up anywhere, as an “excuse” from playing what would be a losing trick, and as a wild card, a substitute for a missing card in combinations.

Now that the number is accounted for, the iconographic programme must be explained. Because of the triumphal theme, which appears in several genres beginning with

*naibi a trionfi*in 1440, it is tempting to connect it to a triumphal mood in Florence. It seems that this must be associated with the Florentine victory over the Visconti forces under Niccolò Piccinino at Anghiari on 29 June, 1440. Can the game of Triumphs have been created only ten weeks or so before the earliest notice of it? This is hard for me to believe, given the time it takes to design and perfect a game. Rules aside, however, the only practical difficulty would be in the physical creation of the 22 new cards. Carving a plate for printing, or painting cards (both of which the versatile artist Lo Scheggia could have done), could be done in two or three weeks at the most.

Another coincidence makes this date attractive: Andrea del Castagno's shame paintings of Rinaldo and Ormanno degli Albizzi and six accomplices on the walls of the Bargello begun on 13 July, soon after the battle. They were famous, depicted hanging by a foot, and they suggest the

*Traditore*of the Triumphs immediately. But if their fame is what brought the image into the sequence, this shortens up the period before 16 September 1440 to only 65 days or nine weeks two days for the game to have been invented, perfected, and published. If we allow two weeks for Giusto Giusti's luxury commission to have been produced, the time is only seven weeks.

The chronology seems too tight for me. For some breathing room, I'd suggest that the “triumphal mood” was related to the events of the preceeding year, 1439, and that the abundance of spectacles and the continuous procession of dignitaries local and foreign into and out of the city that year inspired the fashion for depictions of triumphs. For the inclusion of the shame painting in the sequence, while Andrea del Castagno's were a peak moment for the subject and manner of depiction, such paintings were never absent from the public places of the city.

It is notable that Eva Mori's 2014 doctoral thesis

*Lo spettacolo nella Firenze oligarchica durante l'egemonia degli Albizzi (1382-1434)*, which, despite the title, actually tabulates every known civic spectacle up to 1439 (pages 259-305; thus past the Albizzis' exile, and including, in the following documentation, events up to 1454), does not know of a single such spectacle in the years 1437 and 1438. We can assume that only the annual religious festivals went on as normal in those years. Thus between the celebrations surrounding the consecration of Santa Maria del Fiore and the completion of the dome, and Francesco Sforza's arrival to grand festivities in July/August 1436, and the ceremonial entrance of Eugene IV in preparation for the Council of Union in January 1439, the Florentines were treated to no unusual or exotic spectacles. In 1439, of course, the city erupted into worldwide prominence, and the exotic became commonplace.

To my mind, this is when the triumphal mood and the fashion for triumphal subjects in art began.

A new wrench in the machinery of this elegant vision is the precocious dating of the Rothschild cards. If, as they appear to be, they are entirely the work of Giovanni dal Ponte, they must date at the very latest to the last months of his life, which, with very little uncertainty, was before March, 1438. Thus, by the 1439 triumphal theme scenario, they cannot be carte da trionfi. They could be a single emperor-trump game, like that later designed by Fernando de la Torre. In this case a dating to years before Giovanni's death is plausible. I don't find the suggestion that they formed part of an Imperatori deck persuasive, since I believe it must have been altogether different from the Italian cards. Another possibility is that the game of Triumphs itself was invented earlier than 1438, and even that Giovanni dal Ponte painted the first pack of carte da trionfi, modelled after a game released only weeks or months previously. At best, these speculations force me to consider that the triumphal genre fashion arose not in reaction to any particular event, but from more abstract imaginings on the part of the inventive and creative men in Filippo Brunelleschi's circle. It could be; the absence of a triumphal cart filled civic procession in Florentine records of 1437 and 1438 does not mean that something like it did not occur; it certainly does not mean that the groups responsible for creating such processions were not imagining them.