More invention ruminations

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Whoever invented the game of Triumphs had to have had a mathematical turn of mind. One seeks a balance when creating a game; it cannot be too fast, simple, and easy to win, nor can it be too long to play, complicated, and hard to win. To achieve this balance requires thought and testing, through several iterations, until such harmony is reached, and the game perfected.

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).
Image

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.

Re: More invention ruminations

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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 numIbers 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.
hm ...

the mathematical structure of 21 results with 2 dice appears also in the Sepher Yetzirah with its 22 letters and 10 numbers and its 32 (= 22+10) ways of wisdom, and in the I-Ching with its 64 hexagrams and 32 (= 64/2) hexagram pairs, from which 22 have a not balanced structure and 10 a balanced (3 yin and 3 yang ; 22+10=32).

The Sepher Yetzirah is clearly much older than Dante etc. and Tarot and the 'I-Ching is older than Sepher Yetzirah and anyway, mathematical structures don't need time to exist.

http://trionfi.com/tarot/new-themes/sepher-yetzirah/

Image


21 Dice results and 21 of 32 hexagram pairs (not balanced)

6 of this kind ...
1+1 ... 100000 and 011111
2+2 ... 010000 and 101111
3+3 ... 001000 and 110111
4+4 ... 000100 and 111011
5+5 ... 000010 and 111101
6+6 ... 000001 and 111110

3 of this kind ...
1+4 ... 100100 and 011011
2+5 ... 010010 and 101101
3+6 ... 001001 and 110110

12 of this kind
1+2 ... 110000 and 001111
1+3 ... 101000 and 010111
2+3 ... 011000 and 100111
2+4 ... 010100 and 101011
3+4 ... 001100 and 110011
3+5 ... 001010 and 110101
4+5 ... 000110 and 111001
4+6 ... 000101 and 111010
5+6 ... 000011 and 111100
5+1 ... 100010 and 011101
6+1 ... 100001 and 011110
6+2 ... 010001 and 101110

6+3+12 = 21

1 remaining not balanced hexagram pair
... 000000 and 111111

10 remaining balanced hexagram pairs
for instance .... 111000 and 000111
and 9 others
Huck
http://trionfi.com

Re: More invention ruminations

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Ross Caldwell wrote: 31 May 2022, 17:56 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.
I have difficulties to follow these arguments. In mathematics there may be 21 possible combinations of 2 dices, but in statistics there are 36 combinations. '4' + '1' is not the same as '1' + '4', even if both combinations have one '1' and one '4' for. As such, the change of getting a '1' and a '4' is twice has high as getting a '4' and a '4'. For me comparing Tarot with mathematics is just plain nonsense, they have nothing to do with each other. Tarot is much more than combining some hypothetial numbers. Originally, except for the pip cards, Tarot was not numbered, it was only ordered. So please, stop seeking for arguments where they simply do not exist.

Re: More invention ruminations

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Iolon wrote: 01 Jun 2022, 07:42
Ross Caldwell wrote: 31 May 2022, 17:56 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.
I have difficulties to follow these arguments. In mathematics there may be 21 possible combinations of 2 dices, but in statistics there are 36 combinations. '4' + '1' is not the same as '1' + '4', even if both combinations have one '1' and one '4' for. As such, the change of getting a '1' and a '4' is twice has high as getting a '4' and a '4'. For me comparing Tarot with mathematics is just plain nonsense, they have nothing to do with each other. Tarot is much more than combining some hypothetial numbers. Originally, except for the pip cards, Tarot was not numbered, it was only ordered. So please, stop seeking for arguments where they simply do not exist.
The game designers didn't consider combinations in the statistical way, they used the simple combinations as if 4+1 were the same as 1+4. Wibold's dice game in the 10th century used the 56 combinations of 3 dice; dominoes use 21 combinations, not 36. The 4+1 tile is the same as the 1+4 tile.

Marziano created his game first on a mathematical basis, based squarely on the number four.

I stated my position in my first sentence, and I've stated it many times before. The number of trumps was chosen to work in an elegant way with the game. The imagery was forced to conform. The trump sequence is not a piece of moral art independently conceived, then just stuck onto the regular deck, which miraculously worked as a game. It was conceived first in a mathematical way, in relation to the regular deck of 56 (which it must have been at the time). If we can bring in the likes of Brunelleschi and Toscanelli, then we can speak of architecture and geometry, too.

Re: More invention ruminations

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Huck wrote: 31 May 2022, 22:57
hm ...

the mathematical structure of 21 results with 2 dice appears also in the Sepher Yetzirah with its 22 letters and 10 numbers and its 32 (= 22+10) ways of wisdom, and in the I-Ching with its 64 hexagrams and 32 (= 64/2) hexagram pairs, from which 22 have a not balanced structure and 10 a balanced (3 yin and 3 yang ; 22+10=32).

The Sepher Yetzirah is clearly much older than Dante etc. and Tarot and the 'I-Ching is older than Sepher Yetzirah and anyway, mathematical structures don't need time to exist.
Sefer Yetzira and I Ching are irrelevant to the historical context of the trumps' creation. I'm not philosophizing about the transcendental numerology of 21, or mathematical ideas in general, I'm just trying to figure out why they chose that number. That means when, and who.

I would not permit myself to use something like the Pythagorean Theorem unless Brunelleschi, who was an engineer, architect, and was always thinking about measures, is in the picture. Now that he is, I've suggested perfectly plausible practical ways he may have come to the number. One way is the ratio of suit to trumps, 3:2, which is also that of Marziano's game. Another way is by analogy with dice rolls, which is an old suggestion. Wilkinson suggested it in relation to Chinese dominoes a century ago; Moakley got the suggestion from mathematician Maurice Kendall. Another way is by conceiving of the four-player game as four sides of a table, then dividing the table in two diagonally, which makes the right-angle triangles. This suggests the Pythagorean Theorem, which is an elegant way to relate the fourfold 56-card game to the new game they wanted to create. Instead of 14 tricks, the theorem requires 19 tricks, with an "imperfection" left over. This requires 20 new cards, and I can imagine that the remainder suggested the extra card. These three ways of generating 21 are not mutually exclusive, since one could have suggested the other and they could have seen that as elegant nod to Fortuna. But the Michelino deck 3:2 ratio, itself imperfect like Tarot's with the Fool, or the hypoteneuse of a 14x14 right-angle triangle, is the simplest explanation. The game was pleasant, so Brunelleschi noted that the number of trumps had to be more than the number of cards in a suit, and this was 3:2.

Re: More invention ruminations

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Ross Caldwell wrote: 01 Jun 2022, 09:43 I'm just trying to figure out why they chose that number [21;vh]. That means when, and who.

I would not permit myself to use something like the Pythagorean Theorem unless Brunelleschi, who was an engineer, architect, and was always thinking about measures, is in the picture.
I propose to see the zeitgeist of renaissance times which still builds upon medieaval understanding of biblical wisdom. Speaking about Wisdom, see there the respective book:
Wisdom 11,20

But you have arranged all things by measure and number and weight.
This citation is decisive for the understanding of how important numbers are for understanding the world in medieaval times, following Meyer, H., & Suntrup, R. (1987). Lexikon der mittelalterlichen Zahlenbedeutungen. Fink., there p. VII. This goes --at least-- back to Augustinus and Isidor.

Note that 21 is not an easy number for allegorization: as every number it can be interpreted in positive or negative direction ("ad malam partem", op. cit., p. XVII). Thereby the following is important, op. cit., p. XX:
8. Der Ort der Zahl in der Zahlenreihe und im Dezimalsystem

[..]
Ebenso ist das Überschreiten der Zehn in malam partem zu deuten, so daß die Zahl 11 zum Paradigma für diese Auslegung werden kann. Ihr Mangel an perfectio durch Überschreiten der Zehn läßt sich mit dem Mangel an perfectio durch Unterbieten der Zehn im Falle der Neunzahl vergleichen [...] Abweichungen von der Eins und den Grundzahlen des Dezimalsystems legen also Deutungen ad malam partem nahe, während sonst das Überschreiten im Sinne einer Steigerung verstanden wird: [...] -- Diese Methode der Deutung von Zahlen ist allen Exegeten von der christilichen Antike zum MIttelalter völlig vertraut.

[
8. The place of the number in the number sequence and in the decimal system

[..]
Likewise, the exceeding of the ten is to be interpreted in malam partem, so that the number 11 can become the paradigm for this interpretation. Its lack of perfectio by exceeding the ten can be compared to the lack of perfectio by undercutting the ten in the case of the number nine [...] Deviations from one and the basic numbers of the decimal system thus suggest interpretations ad malam partem, while otherwise the exceeding is understood in the sense of an increase. [...] -- This method of interpretation of numbers is completely familiar to all exegetes from Christian antiquity to the Middle Ages.
]
In this light, 21 is rather a negative number to be interpreted ad malam partem. This is justified by the positive interpretation of the 20, understanding 20 as the doubling of the perfect 10, hence the law of old and new testament (p. 670). The 21 breaks this.

In the dictionary, on p.675, 21 is however positively denoted for the old authors, since in the Bible there is a positive mentioning of 21 in
Daniel 10, 13

But the [angelic] prince of the Persian kingdom resisted me twenty-one days. Then Michael, one of the chief [angelic] princes, came to help me, because I was detained there with the king of Persia.
Note that 21 days are three weeks, it is a 3 times 7 structure. For medieval authors, it is the multiplication of the number of the trinity with the perfect number of the wisdom of the Holy Spirit.

I propose to read the 21 of the tarocch' in this light: Solomon, the wisest of all men, says in
Proverbs 9, 1

Wisdom has built her house,
She has hewn out her seven pillars
The architecture of the trumps is 3 times 7, stacked upon each other to form seven pillars of wisdom in the three domains of body, intellect, soul, which are to be dealt with by faith, hope and charity.

Re: More invention ruminations

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Addendum: in Meyer, H., & Suntrup, R. (1987). Lexikon der mittelalterlichen Zahlenbedeutungen. Fink., there is further information which might be helpful:
p. XVII
Kaum eine Rolle spielt die Subtraktion, bei der das Faktum der geringeren Größe sowie bisweilen auch der Subtrahend gedeutet werden. Aufgrund des Ansatzes beim Minus gegenüber einer anderen Zahl tendieren Auslegungen dieser Art ad malam partem.

[Subtraction, in which the fact of the smaller size and sometimes also the subtrahend are interpreted, plays hardly any role. Due to the approach to the minus compared to another number, interpretations of this kind tend ad malam partem.]
This is interesting w.r.t. Roman numerals in tarocch’ are additive: not only do they signify an ascending evolution, but they avoid the “ad malam partem” of the subtraction – every step to the next card is good and not evil (even if the devil appears on one later on).

On p. 650, the entry for the number 14 yields a positive interpretation, since it is interpreted as the doubling of the perfect number 7 (which stands for wisdom) and as 10 plus 4 (Dekalog of Old Testament plus 4 evangelia of new testament; wisdom of the old testament plus wisdom of the new testament)

So one needs a good argument for the 14 -> 21 (+0) transition. One might be, that in the cited
Daniel 10, 13

But the [angelic] prince of the Persian kingdom resisted me twenty-one days. Then Michael, one of the chief [angelic] princes, came to help me, because I was detained there with the king of Persia.
the Devil (i.e. the angelic prince of the Persian kingdom) is defeated by the archangel Michael. The devil is overcome in 3 * 7 as it is reintroduced in the ur-tarocch’ (the fourteen on trionfi.com does not contain the devil (anymore)).
Thereby it follows the 7 pillar –structure of the temple of wisdom: 14 = 2 *7 -> 21 = 3*7. The temple of wisdom is then crowned by the tetramorph and the cupola of the firmament, architecturally spoken.
Then: the 3 *7-structure provides the possibility to structure after faith – hope – charity (which are not displayed in tarocch’), hence they may be or are implicit.
In this case, the fire of charity is in the mystic tradition a gift, given by God, in a movement from top to down, contrary to its nature – in an enlightenment, as in lightning. Note that the whole mystic tradition is (Neo)Platonian; Dyonisos Areapagitus, Boethius, Master Eckart, Albert the Great, Bonaventura. In this light godly lightning becomes really important, resulting in a burning tree stump: tarocch’.

Re: More invention ruminations

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Ross Caldwell wrote: 01 Jun 2022, 09:43 Sefer Yetzira and I Ching are irrelevant to the historical context of the trumps' creation. I'm not philosophizing about the transcendental numerology of 21, or mathematical ideas in general, I'm just trying to figure out why they chose that number. That means when, and who.
I've spend a lot of energy for this German lot book system with a 22x22x22x22-scheme.

It consisted of 22 "animals" or "humans", which also also appeared in a system with 32 figures, which appeared somewhere in Bohemia and also in a text in Heidelberg. The Bohemian object had somehow a "1327" in the document, I remember, so rather early.

The earliest "sure 22" in the " historical context of the trumps' creation" is still the Boiardo Tarocchi poem, later than the 22 pictures of the Fränkische Losbuch and of the Bollstatter version.
Recently we got a new 22-phantasy of an Imperatori-genesis with the name "14+8". Phantasies are not facts. 6 cards produced for the Bon family ca. 1470 also are not 22.

There is not everywhere a trump/suits relation of 3:2. Minchiate has 40 trumps and 14 cards in each suit. In Doppelkopf there are sometimes 48 cards (26 trumps and 6 or 8 cards for each suit) or 40 cards (22 trumps and 18 cards in 3 suits of 6). For Doppelkopf I know, that it is defintely an interesting game. Minchiate I can't judge, not enough opportunity to play such games.
The fact, that Dummett had presented this 3:2-idea doesn't make it a correct idea. There are a lot of shortened Tarot- or Tarockversions, with which players play with enthusiasm. The trump/suits of 3:2 suffers naturally under such conditions.
Huck
http://trionfi.com

Re: More invention ruminations

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Huck wrote: 02 Jun 2022, 00:40 The earliest "sure 22" in the " historical context of the trumps' creation" is still the Boiardo Tarocchi poem, later than the 22 pictures of the Fränkische Losbuch and of the Bollstatter version.
Recently we got a new 22-phantasy of an Imperatori-genesis with the name "14+8". Phantasies are not facts. 6 cards produced for the Bon family ca. 1470 also are not 22.
We've been having this argument for 18 years. Neither of us has moved. Unless we discover either the Original Carte da TrionfiTM or its gamebook describing the explicit composition of the deck, it is unlikely either of us ever will.

3:2 was Dummett's offhand suggestion, when he realized that the same ratio would apply to the Visconti di Modrone if it had all of the standard trumps plus the three Theological Virtues. It's a coincidence, so there was no reason to take it seriously.

He didn't notice that the same ratio worked out for Marziano, if a suit had 11 cards. Still a coincidence.

Then comes a possible meeting of Brunelleschi with the game, and the spark of an idea. If the game were pleasant, he would have noted the ratio. So now there is the basis of a theory of how the two games are connected.

Interestingly, the ratio works the other way, too (approximately). Trumps to the regular deck is 2:5.5 for Marziano and 2:5 for Tarot. So, either ratio may have been the spark, in this theory. Along with the related themes, deification and triumph.
There is not everywhere a trump/suits relation of 3:2. Minchiate has 40 trumps and 14 cards in each suit. In Doppelkopf there are sometimes 48 cards (26 trumps and 6 or 8 cards for each suit) or 40 cards (22 trumps and 18 cards in 3 suits of 6). For Doppelkopf I know, that it is defintely an interesting game. Minchiate I can't judge, not enough opportunity to play such games.
The fact, that Dummett had presented this 3:2-idea doesn't make it a correct idea. There are a lot of shortened Tarot- or Tarockversions, with which players play ith enthusiasm. The trump/suits of 3:2 suffers naturally under such conditions.
Nobody said 3:2 was objectively the best ratio. I have no idea how to figure something like that out, or if it even exists. All I'm suggesting is that this is that, in this theory, the two Filippos played Marziano's game, it was enjoyable, and that either 3:2 or 2:5 is the ratio that Brunelleschi noted as making the novel game enjoyable, an idea he then brought back to his friends in Florence.

Re: More invention ruminations

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Ross Caldwell wrote: 02 Jun 2022, 07:37 Then comes a possible meeting of Brunelleschi with the game, and the spark of an idea. If the game were pleasant, he would have noted the ratio. So now there is the basis of a theory of how the two games are connected.

Interestingly, the ratio works the other way, too (approximately). Trumps to the regular deck is 2:5.5 for Marziano and 2:5 for Tarot. So, either ratio may have been the spark, in this theory. Along with the related themes, deification and triumph.
I don't understand that. What is the regular deck? 52? 16/52 (30.7 %) is not 2:5.5 (36.4 %) for the Marziano. 2:5 for Tarot (21/52) is okay, but why should this be of any relevance?
There is not everywhere a trump/suits relation of 3:2. Minchiate has 40 trumps and 14 cards in each suit. In Doppelkopf there are sometimes 48 cards (26 trumps and 6 or 8 cards for each suit) or 40 cards (22 trumps and 18 cards in 3 suits of 6). For Doppelkopf I know, that it is defintely an interesting game. Minchiate I can't judge, not enough opportunity to play such games.
The fact, that Dummett had presented this 3:2-idea doesn't make it a correct idea. There are a lot of shortened Tarot- or Tarockversions, with which players play ith enthusiasm. The trump/suits of 3:2 suffers naturally under such conditions.
Nobody said 3:2 was objectively the best ratio. I have no idea how to figure something like that out, or if it even exists. All I'm suggesting is that this is that, in this theory, the two Filippos played Marziano's game, it was enjoyable, and that either 3:2 or 2:5 is the ratio that Brunelleschi noted as making the novel game enjoyable, an idea he then brought back to his friends in Florence.
Brunelleschi had an understanding of cranes and this would have made him to a master for flying actors during triumphal processions. Has this something to do with card playing?

The most logical idea for the Michelino deck is, that the 60 card deck with 10 numbers and 5 courts stood at the beginning, and 4 of the 5 courts positions were replaced by 4x4=16 Greek-Roman gods. Which in a second step were declared as trumps.
But possibly already queen-virgin-ober-unter were used as trumps before in the 60 cards deck, so that the step to 16 gods as trumps was simply logical.

A suit with 10 numbers cards and one King is a rare sensation in the playing card world (I don't remember having seen this feature elsewhere). Court cards, which are declared by rule to trumps appear very often. That's a standard in games with trumps.

Ober and Unter were called marshalls and in the basic deck with 13 cards they were the only court cards beside the kings. They have a military name and it is easy to imagine, that trumping was interpreted as a military action. And the numbers were interpreted as the population. It seems natural, that Ober and Unter were used as trumps.
Huck
http://trionfi.com