There is a broad understanding in modern carnival, that "11" is connected to carnival (carnival starts at 11.11. at 11.11 a.m. each year, at least in specific regions as for instance the lower Rhineland). However, there is reseach, that it is difficult to prove, that this was already in use in very early times.
However, at the 12.11. 1381 an knightly order of the fools was founded (called a "first" carnival organization), in the lower Rhine region. It was considered to last 12 years, which it did (then it was changed to another order). The members had a fool made of silver as sign. The founder, Adolf of Cleve, was listed as 11th member. The facts are not totally secure and occasionally disputed, but there are documents etc.
The Under in 1377 (very near to 1381) in the favoured deck of Johannes of Rheinfelden was numbered "11". From documents at the Brabant we've the impression that playing cards entered in 1379 the region, at least then we've the first document there.
The under is in the iconography of normal cards the card, which is most designed "foolish".
There is an old Roman custom of funny activities at the date 1.1.
There is a medieval "feast of the fools" at the 1.1., which likely relates to the old Roman custom. Prohibited, but still living in renaissance, likely transmuting in 15th/16th century to more modern carnival customs. It was also connected to games and gambling.
http://trionfi.com/0/d/91/
There is evidence at some occasions (between them the Tarot relevant court of Galeazzo Maria Sforza in Milan),
http://trionfi.com/0/g/71/ (in development)
that the 1.1. was connected to festivities, which allowed games and also gambling. Also connected to games seems to have been 1.1. 1441, when Bianca Maria Visconti was guest in Milan.
http://trionfi.com/0/d/
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there is the consideration, that "Tarot as a game" was already played, when "special cards" didn't exist.
Assuming this, then one needs for specific functions in the game cards, which carry the following positions: "highest card", "lowest trump" and "fool-function", cards, which were honoured by a higher worth (4-5 points).
Taking a normal card game, then naturally King is the highest card, Ace the lowest and the function of the fool would have the under.
With that we would have defined the cards 1 + 11 + 14 in a 4x14-deck. With the "1" we would have the magician, who has the suits on his table - so it is designed towards the card game. With 11 and 14 we would have the cards which fell "out of the row" in the 14 Bembo cards.
The number
111111111110110000010
desribes with 1 and 0 the existence of the 14 Bembo trumps on a background of 22 trumps in the Tarot-de-Marseille order.
There are about 4 million other numbers possible, when you part 22 cards in "existant and not existant" with "1 and 0"
... but "just this" good argumentable sorting "happened as a fact".
How much other combinations of 22 "1's and 0's" would have a similar good argumentable sorting?
Even when you find a few 100, let's say 400, and you've 4 000 000 possibilities, then you still would have a probability of 1:10000 against "finding a good argumentable sorting" accidently. Even when you conclude, that there are 4000, you would end with a probability against 1:1000. And when you decide, that there are 40.000 similar good, the accident still would demand a lucky opprtunity of 1:100.
You don't find 40.000, you don't find 4000, and likely you don't find even 400, and likely you've difficulties to find more than 40.
In historical matters you've always difficulties to reach high probabililties for something being true or false. A 99:100 relation already speaks: "it's almost true", at least it is very, very probable. And in research you've decide, if you put your energy in 99:100 probababilities or 1:100 probabilities.
A 99:100 probability turns almost true, when you search in this direction and find more ... as we did.
In research you behave as in an almost unknown city. City have logical rules, after which they are build. When you know the church, you mostly you know, where the shops are ... When you know the station, you mostly know, that they're build a little outside of the old center of the city, before the old city walls. This is not always right, but mostly.
... and so on. You follow such rules in your orientation, sometimes you're wrong, but mostly right. And research is similar. Stupid research is not successful - you go in the wrong direction.
When 100's of researchers say, that the Tarot had 22 trumps before 1450 and search and search and find nothing, then it means, that one has to look in the other direction.When 100's researchers say, that the Mantegna Tarocchi was made around 1465 and search and search and cannot become confident with their findings, then you've to turn the table and look at another place and on the basic premise, if this is really correct.
It's simply probable, that there are wrong somewhere.
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(Later added)
### Just as example:
The Mantegna Tarocchi was likely not readily composed still in the year 1474, and the most likely production date is 1475. Just following that, what is "likely".
The production location was (likely) Rome, the organizing poet (likely) Ludovico Lazzarelli, the engraver (likely) a German printer with the name Sweynheim and the commissioner was (likely) from papal circles and the whole object was (likely) to have a good article to sell it to pilgrim touists for the jubilee year 1475.
(Likely) most individual paintings existed before, not as engraving, but in other forms and compositions. Most relecvant earlier composition: Lazzarelli's poem with 27 illustrations produced (likely) ca. 1470 - 1474, from which 23 pictures have strong similarity to the Mantegna Tarocchi.
Logically it was (likely) Lazzarelli, who developed a further model with 50 pictures - nobody else had more relationship to the Mantegna Tarocchi as he.
And generally (likely): Most engravings are the copies of paintings, which existed before. The engraving process needs more time than painting. So if an engraver worked originally himself, he first made a painting and then engraved. But (likely) usually he took the painting from somewhere and then he engraved.
So there is nothing unsual in the considered process of the Mantegna Tarocchi.
Hind's suggestion, when he found similar pictures (dated 1467/68) to the Mantegna Tarocchi, to suggest that the Mantegna Tarocchi existed before was a blind shot, not more and actually pointing in the wrong direction. He couldn't state that, for logical reasons. Artist A could have copied from artist B, or artist B could have copied from artist A. Still both was possible ... and considering the usual engraving processes, it was likely, that the engravings came later. Hind was an engraving specialist - he should have known that, actually.
Hind himself argumented, that the engravings in style looks most similar to the producer of the Ptolemy book of 1478. What Hind doesn't knew: It was already stated in German dictionaries at his time, that the engraver of this product was Sweynheim.
Sweynheim was in Rome and Lazzarelli was also in Rome. But Lazzarelli was before in Venice and there he collected the pictures. So the product got a Venetian and a Ferrarese style, which everybody recognized and made everybody look in Ferrara and in Venice look for the relevant artist.
But Sweynheim only copied. Likely he hadn't too much own opinions about that, what he copied. He was a printer usually, and printers patiently print that, what other persons have said and, if demanded, they similar patiently engrave that, what other people painted. No problem: the technican has no "content-problem". He's simply good in his own job.
"Content problems" were usually solved by the "creative jobs" ... these were poets usually.
Still around 1480 a major painter in Urbino mourns, that the painters (the technican's) get less reputation (and likely less money) than the poets.
Lazzarelli was a poet. Naturally poets influenced Trionfi games - like Boiardo for instance. Like Martiano da Tortona influenced the production of Michelino da Besozzo.
As Luigi Pulci (likely) influenced the early Minchiate.
Lazzarelli speaks of his unknown painter for the manuscript which finally was in Urbino in his poem ... he calls him his own "Apelles" and leaves it with that ... the Apelles is only a nameless "somebody" - just the technican.
... but not only the technican was forgotten as producer of the Mantegna Tarocchi, but also more or less the poet.