1) That these particular blocks were used sometimes to print, from the first two blocks only, 48-card ordinary (non-trionfi) decks for sale.

2) From this, he concludes that probably 48 cards was the size of non-trionfi decks in general in XV century Italy. Pratesi himself partially withdraws from this conclusion in 2014, based on the 1424 sermons against cards by San Bernardino of Siena. The saint denounced four face cards including the Queen, by name.

3) That we can tell something about the decks that players played with, because a deck that would be highly inconvenient for printers to print, would probably not be made.

When a sheet is also printed from the third block, which has all 21 trumps, plus three queens, we get close to a tarocchi deck, but not quite. As Pratesi says: "With respect to a standard tarot of 78 cards, with all three sheets with their 72 cards we are still lacking 6 cards: the four 10s, the Queen of Batons, and the Matto." Pratesi imagines a fourth sheet printed with just these six cards, and that indeed seems ridiculous. Think of a printer wasting so much paper!

**2. The paper:**

Pratesi says about the paper:

Leinfelden is the location name one of two extant copies printed from the third block, the other sheet 3 ( https://www.nga.gov/collection/art-obje ... 41321.html ) is located in Washington D.C. That sheet has stated dimensions of 291x435 mm. Sheet 1 ( https://www.nga.gov/collection/art-obje ... 41319.html ) in Washington is 291x436 mm, and sheet 2 ( https://www.nga.gov/collection/art-obje ... 41320.html ) is 300x441 mm. The larger sizes are due to margins; the Leinfelden sheet either has them trimmed off, or the size quoted is for the printing, not the paper. The Washington image of sheet 3 shows not much margin, exactly, but a strangely heavy black line around the whole sheet. I do not understand this black line. I gather we have no image of Leinfelden.The sheet shape, to begin with, is 280x435 mm (Leinfelden), which corresponds to a rather common kind at the time.

Fat black line on Washington sheet 3.

This fat black line goes all around Washington Rosenwald sheet 3, like a frame; It would not help, but rather be a problem for, the card-making process. Could it be hand-drawn? Sheet 2 has a thinner black line frame, and sheet one has none at all.

Here is the upper corner of sheet 2 showing the thinner (and uneven) black frame. You can see here a brown area like a coffee stain, but on the card in the corner, which should be the female Page of Coins, you can see that where the stain stops, the image does too. But on the other hand the card frame lines continue beyond the brown stain. A little bit of the other images, such as the page's sword, and the tops of two heads, also continues beyond the brown stain. But the tie ribbon of the Page of Sword's sleeve, stops at the stain edge. It seems that the everything beyond the brown was lost, and was filled in by hand in ink at some point. But I don't understand this, unless the brown part is old paper mounted on a newer backing sheet.

I suppose these facts about the Rosenwald sheets must be well known.

I do know enough about handmade paper to know that no one ever made 290x440 mm paper. The dimensions of these sheets are half a sheet of the size called "medium" (444.5 x 571.5 mm) in old English paper sizes: the overwhelmingly most common size. The size match is nearly perfect: half of English medium would be 286x444 mm. Paper sizes are based on the arm length of the paper maker. If there were ever any 280x435 mm sheets of paper sold, they were made in a size like English medium size and then cut in half. It does not make sense to cut paper in half before printing if you can help it. Even if the blocks you have are half the size of the paper you have, it is easy enough to bolt two blocks together.

Pratesi says this was a common size at the time: I would like to know what sheets of that size were used for. A full sheet cut in half is fine for hand-writing a document. Whether bambagina paper was made in half or regular sizes could be found out by a visit to the factory in Amalfi (it's still running), or no doubt from some source, but the Wikipedia article does not say.

My claim about paper size and printing is certainly true of movable type printing. If a book is size 8vo, it is always printed on full sheets and folded in eight, never on half sheets (as these are) folded in four. But the woodcut printing process is different, so I don't know for sure that woodcut printers would never print on cut sheets of paper. Also, although I'm pretty sure no one would make half-size sheets of paper, card stock may be different. The tray of slurry which the paper maker has to lift, would be heavier for thicker paper. Cards were pasted to backs (and a middle layer too, maybe) so I don't know whether the printed layer was card-stock thickness. Are the Rosenwald sheets bambagina paper? A microscope can tell.

Washington sheet 1, has a bottom margin which is rather skinny: Sheet 2 has a rather skinny top margin. A printer's devil who put paper on the blocks as lopsided as this, would get sent to bed without his supper. I think the paper was a standard size and shape, very close to English medium (paper was an internationally traded commodity); it is more likely the blocks for sheets 1 and 2 were bolted together, than that the paper was cut in half before printing. When a sheet was printed on the bolted blocks, the result was three upper rows and three lower rows, with a channel between them: the channel is because you wouldn't want the ink-taking raised areas of the blocks to run to the very edge of the wood. Our sheets result from cutting a size medium sheet along that channel, after printing. I expect that in normal production of cards, printed sheets were pasted to backs first, then cut. To cut an unpasted sheet in half along the central channel would not therefore be a step in manufacturing, but you would likely do it to keep a record of the output of these blocks.

If the brown stain does indeed mean the surviving paper is pasted to a backing, then my conclusions drawn from the margins of the backing sheet are not very strong.

Pratesi says: "With respect to a standard tarot of 78 cards, with all three sheets with their 72 cards we are still lacking 6 cards: the four 10s, the Queen of Batons, and the Matto." Printing a 4th block with only six cards seems strange, but without them, the three blocks don't make a tarocchi that makes any sense. A game without tens is possible, and a game without a fool is possible, but how could anyone ever sell a game with queens for only three of the four suits? No tens, no fool, and three of the four queens, is three unlikelies multiplied together, and the third one is just silly. This can't be the truth. If we had a story that worked, we could say: here are blocks, and the first two were used to print regular decks, and all three to print tarocchi decks. If we had that story, we could say: and therefore the regular deck was 48 cards. But we don't have that story, or any story, yet. Therefore the three sheets we have are no evidence at all that a 48 card deck was ever printed and sold from these blocks. If you wanted to claim that the first two blocks were used to print a 48 card game, then what was the third block used for? To print a "tarocchi" game that would get the shopkeeper a sock in the nose from the customer who finds there's a Queen missing?

Perhaps, there was indeed a fourth block with only six cards on it. Later, we shall look for a solution to this mystery, one that doesn't require throwing away most of the fourth sheet. But meanwhile, we shall take a detour to a world of slightly skinnier cards.

**Printing 9 cards across the width of the paper.**

If what we want to know is, what would be a good system for printing some regular and some tarocchi decks, we can answer that. First, use a 3x9 layout rather than a 3x8 one, which is an 11% reduction in the card width. The size of the paper is pretty much a given, and while fitting 9 cards across may be OK, that is already cutting it close. So 10 across would probably be just too skinny. With a 3x9 layout, each block at can print 27 cards, and that number is pretty much a fixed maximum given the card size and the paper technology of the day. You need three blocks: call them the Pips block, the Faces block, and the Trumps block. (The Faces block has some pips cards on it). The blocks are bolted together two at a time, and you print using size medium (445x571 mm) paper, not half-sheets of it. So the printer who needs R regular and T tarocchi decks, does this:

* He prints X sheets using the Pips and Faces blocks bolted together.

* He prints Y sheets using the Pips and Trumps blocks bolted together.

* He prints Y sheets using the Trumps and Faces blocks bolted together.

What X and Y are, will be revealed shortly. So from that printing, he has made:

* X+Y printings of the Pips block,

* X+Y printings of the Faces block, and

* Y+Y printings of the Trumps block.

He needs T tarocchi and R regular decks. Then here are the formulas for Y and X:

* Y = T/2, or in other words, T = Y+Y

* X = R+Y, or in other words, R = X-Y

The T tarocchi decks will need T Pips, T Faces, and T Trumps printings, and the R regular decks will need R Pips and R Faces printings. So for R regular and T tarocchi decks he needs:

* R+T printings of the Pips block, which is (X-Y) + (Y+Y) printings, which is X+Y printings, which is just what he has.

* R+T printings of the Faces block, which is (X-Y) + (Y+Y) printings, which is X+Y printings, which is just what he has.

* T printings of Trumps block, which is Y+Y printings, which is just what he has.

Thus, however many regular and tarocchi decks he needs, he can strike the right number of printings off the bolted blocks, to make those decks, with none left over. The only restriction is he must make an even number of tarocchi decks.

Each block has 27 slots. If the regular deck is 52 cards, then Pips and Faces block each have 26 cards on them, leaving one space on each block which could perhaps be used for printing a religious picture, or something. Even if those 2 out of 54 spaces were just wasted, that is only 3.7% of the paper wasted. As for Trumps block, it has 27 spaces. If one is left blank, like the other two blocks, and then four are used for the fourth face card (which tarocchi needs but the 52-card regular deck does not have), and then one space is used for the Fool card, there are 21 spaces for the trump cards. 21 is an interesting number. However, you could put one more trump in the empty space in Trumps block, and for that matter, two further trumps in the empty spaces in the Pips and Faces blocks. Thus the printing process constraints don't lead to 21 trumps for certain, they would allow up to 24 trumps.

So that's the story if you allow 9 cards across the c. 440mm side of the paper. If I'm wrong about woodcut printers using full sheets, rather than half sheets, of paper, then the printer does not need to bolt his blocks together, nor do so much algebra. He just prints R+T of Pips and Faces block, plus T of Trumps block, to make R regular and T tarocchi decks.

**4. Printing 8 cards across the width of the paper, as the Rosenwald sheets do**

Can we do something clever if the cards must be wider, so only 8 cards can fit across the sheets, not 9? With only 8 cards across, each full sheet of paper has room for 6x8 cards, that is 48 cards. Half sheets have room for 24. As Pratesi found, the Pips and Faces blocks can print a 48 card deck, but the Rosenwald Pips, Faces, and Trumps blocks together don't print anything that makes sense. Six more cards are needed to make the 78 card standard tarocchi. So we need a fourth block, and it must have:

* The fourth queen, the Queen of Batons,

* The Fool card, and

* Four Tens cards.

Perhaps it also needs two more boy Page cards, if tarocchi, which has four queens, had four boy Pages rather than two of each sex. What clever thing can we do with the 18 blank spaces? I suggest the fourth block should contain,

* The fourth queen, the Queen of Batons,

* The Fool card, and

* Twenty Tens cards, 5 sets of one of each suit,

* and perhaps two boy pages ; total 24.

Then every time a tarocchi deck is printed, a sheet with sixteen tens cards on it is left over, and the sheet is put on a pile. Every time regular decks are wanted, that is 52-card decks, one sheet is taken from the pile for each four regular decks. Unless you want fewer than one tarocchi deck for each four regular decks you want, you will always have plenty of tens in the pile, so a printing of the Pips and Faces blocks (which is one sheet of paper) will be enough for a 52 card regular deck. This is an explanation of a workable business plan that could have produced the three existing Rosenwald sheets. This explanation does not imply a 48-card regular deck; it is fine with a 52-card deck.

If my proposal of a fourth block with twenty tens cards on it seems too bizarre, the other options are:

* These Rosenwald sheets were printed on blocks which were never used for commercial production and sale,

* OR, only 48-card regular decks were ever made, and the third sheet was struck off a block with trumps on it that was never used commercially,

* OR, someone tried to make a living selling tarocchi decks with three but not four queens,

* OR, a fourth sheet was printed with only 6 out of 24 spaces filled, and most of that sheet of bambagina paper was used to start the morning fire.

**5. The 1477 contract in Bologna.**

A Pratesi article about this contract is translated here: viewtopic.php?f=11&t=1128

The section of the contract which was transcribed, translated, and posted reads:

I think it unlikely that Master Pietro could arrive with 125,000 decks of cards and walk away with 18,000 soldi. I rather assume the idea is 125 decks per month, or if not per month then per some other set period, already established by custom. This is the normal sort of arrangement that a dealer makes with a manufacturer.Item that the aforesaid Mr. Roberto is obligated to give and pay to the aforesaid Master Pietro or his son in his name eighteen soldi of money for each 125 packs of cards, or true triumphs sufficiently less than for 125 packs, in so far as the number of the cards is more of Triumphs than of cards.

The 1908 report of the contract said:

Pratesi says the original of the contract makes no mention of the numbers 40 and 60; they are only in the 1908 description of the contract. In 1908 I believe, ordinary decks of playing cards had 52 cards, and tarocchi or tarot decks had 78, and 52/78 = 40/60. I think the mention of 40 and 60 in 1908, is the ratio between the number of cards in the regular decks and the number of cards in the tarocchi decks, which ratio was 40 to 60 in 1908. Why did he say 40 to 60 rather than 2 to 3? No idea. Perhaps he thought it sounded more scientific, like the people who say 50% when they mean one-half.* 1) both cards and triumphs were used for playing [giocare];

* 2) cards were only 40, triumphs 60;

* 3a) production occurred in groups of 125 decks of cards, or in the case of a smaller number of groups also including packs of triumphs, in an "equivalent" manner, ie, with a same total number of cards.

* 3b) each card, whether belonging to cards or triumphs, required roughly the same commitment to work and the same raw materials, so that differences in price thus did not exist (a rasone de carta per carta debba essere pagato come de le carte e non più [because card for card should be paid as cards and no more].)

This contract will work smoothly provided the ratio in 1477 between the deck sizes was a ratio of small integers. For example if the regular deck was 52 cards and the tarocchi deck was 79 cards rather than 78, then since 52 and 79 are not connected as a ratio of small integers, there are only two ways to fulfill this contract:

* either Master Pietro provides 125 regular decks and no tarocchi decks,

* or he provides 46 regular and 52 tarocchi decks.

So if Mr. Roberto wants more than zero tarocchi decks, his only option is to take 52 of them! That is obviously impractical. No one would sign such a contract. So the deck sizes in 1477, in Bologna, must have been linked by a ratio of small integers. We must therefore propose a regular deck size, and a tarocchi deck size, such that each is at least a little bit plausible, and the two are linked by a small-integer ratio. There aren't too many cases to check. For example if the smaller deck is 52 cards, then the only ratios to check are1:2, 2:3, 4:5, and 4:7. All other ratios give non-integer sizes for the larger deck. These four ratios imply deck sizes for the larger deck of 104, 78, 65, and 91. Tarocchi decks of 91 or 104 have never been proposed. 65 might work for the game of 8 Emperors, but that game had not been heard of for a long time before 1477.

In fact, 52 and 78 is the only pair of sizes I found, linked by a small integer ratio, with both of them plausible. 40 and 60, suggested to me by mikeh, is barely plausible, since Bologna in particular is known for playing with truncated decks, such as decks without 8s, 9s, and 10s. But while there may have been one game played with a 40 card deck, it is hard to believe that only that one game was ever played in Bologna, or that every game they played used a deck truncated in the same way. That would have to be true if you could say "deck of cards" and in Bologna it always meant 40 cards with no ambiguity. If even legal contracts could say "deck of cards" and have it mean 40 cards, that would imply that no one in Bologna ever played or even thought of playing any game but that one game. (Of course, if the 1477 Bologna contract mentions 40 and 60 card decks after all, all bets are off). So when Master Pietro signed a contract to supply 125 decks of cards, he didn't think he needed to specify that they were 40-card decks: it was a given, in Bologna, that a deck of cards was 40 cards. That seems to me unlikely. Even more unlikely is that "trionfi deck" meant 60 cards with no ambiguity, since that assumes a tarocchi game with the truncated base deck, plus no fourth face card, plus 19 trumps, a number for which there is no independent support. That both 40 and 60 are true, seems very unlikely.

Anyway, the only point I need to make here is that a small-integer ratio, between the regular and the trionfi deck, is a convenience for commerce. If it is 2:3, a shop keeper can remember that the price of three regular decks is the price of two trionfi decks.

**6. An explanation of 21 trumps.**

It is not at all clear that the regular deck had 52 cards when the first trionfi decks came into existence. If the regular decks had already lost one of the four face cards before trionfi started, it's not clear why trionfi would have four. But if the regular decks had 52 cards, then there were reasons, not strong ones, but still some reasons, to make the new larger game have just one and a half times as many cards, that is, 78 cards. This was for the printer's convenience, and for the distributor and shopkeeper's convenience, as well. Given 26 new slots to fill in the larger decks, the designer has the luxury to put back in the queens that the regular deck had dropped. (If we can take Rosenwald sheets as a guide to which face card the regular decks did not have.) The new game will have a Fool (Matto). So if the new deck is to have 78 cards, and have the four queens back, and have a Fool, that leaves just 21 spaces to fill with trumps. That 21 is one and a half times the number of cards in each of the new deck's regular suits, is just coincidence.

As I said, the technical advantages (to the printer) and the business advantages to the mercer, of a 2:3 ratio are not huge, but still, they are reasons. I can see no reason at all why you would want the number of trumps to be in a 2:3 ratio to the number of cards in each trionfi suit. There may be a certain elegance to doing it that way, but it is technical and business reasons that make things happen in the world. So the 2:3 ratio to 52, seems to me the best explanation I've seen for 78 cards, and therefore, the best for 21 trumps.