In my view, the short answer is: dice. That is, not a number randomly chosen, but a pattern arising from probability theory when playing dice games.
In any casino deck, there are 52 cards, not including the 2 jokers (who arrived late on the scene historically and often fail to participate, the layabouts!). It's easy enough to link this number, 52, to the number of weeks in a year, then link the number of suits, 4, to the seasons, the number of colors, 2, to warm and cold seasons (or night and day, or male and female), and finally the ranks in each suit, 13, to the weeks in a season. Although some historians claim to debunk this as mere coincidence, we don't have a record of the pattern's genesis or the reasons behind it, nor can we ask the long-dead people who chose it over rival patterns. We can, however, posit that 52 has always been the number of weeks in a year (if weeks are 7 days, which they have been since later Roman times) and 4 always the number of seasons (if you divide the year at solstices and equinoxes). And as most card players in the last thousand years have known these facts, these could have contributed to the pattern "clicking" and feeling "somehow right." That is, the coincidence could be part of the reason the pattern survived and thrived even if the designer of the 52 card deck never saw or thought about a calendar.
One minor piece of evidence for this is that when the 48-card Portuguese deck arrived in Japan bearing its 4 suits of cups, staves, swords, and coins, each with 12 ranks, it was adopted in a slightly modified form. The Japanese players decided that they wanted to relabel the deck's structure so that it had 12 suits of 4 ranks each, the 12 suits corresponding to the 12 months of the year. There is actually quite a long history of people of different nations associating the calendar to cards, dominoes, dice, I Ching hexagrams, and so on. I haven't seen the 52-cards-to-52-weeks, 4-suits-to-4-seasons hypothesis convincingly debunked.
Either way, it turns out that for tarot cards there are especially sound reasons for the numbers 56 and 21, and, by extension, albeit to a lesser extent, to 22 and 78.
If you look back to around 1100 CE, when the first Chinese domino sets appear in the record, they have two suits of 11 ranks (give or take one). 11 is a non-random number. A suit of Chinese dominoes is marked to represent the 11 different outcomes you can get from rolling 2 ordinary (ie, cubic) dice and adding the faces: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. That's 11 different sums you can get. Now, in the most common Chinese domino set, the second suit is 10 dominoes. This is presumably because 10 is the number of fingers, is similar enough to 11, and when you add both, you get 21. And 21 is another special number.
Why is 21 special? Because this is the number of different outcomes you get when you roll two dice but don't add the faces, merely reporting them both, not caring about the order. This is by far the most natural way to think about a pair of dice you've just rolled. "I rolled two 6s" or "I rolled 3 and 7" the simplest way to read dice, possible even for those who don't know any arithmetic. Players had been using dice for millennia before the invention of die rolls on tiles (ie, dominoes). The numbers 11 and 21 showed up on dominoes because they were familiar to players who understood enough to strategize, and, more importantly, were familiar to the designers of the tiles.
Now, that's dominoes, but what about cards? First of all, cards derive from dominoes: the earliest cards were paper dominoes either drawn by hand or printed in woodblock presses. Consequently, the patterns of 11 and 21 in dominoes form the starting point for playing card decks. In the modern 52 card pattern, all suits have 13 ranks, not 11. Well, games evolve. The original idea of 11 was lost along the way, along with taking the cards literally as either paper dominoes or symbols of dice outcomes. You can still see the resemblance to dice in the array of, say, diamonds on the 6 of diamonds, or clover leaves in the 4 of clubs, or really the pattern on any number card. By some route or other, two Chinese domino suits eventually became four card suits. Now, similar multi-suit and different-rank-count ideas were tried with dominoes, and we can't say for sure that there weren't identical 52-domino sets first. But whatever account you believe, there was plenty of variation across the centuries in the empires that played these games. Card and domino suit patterns came and went. Some are mentioned in documents but lost, some exhibited in museums, some even still in play.
Tarot is interesting, not only because there are more tarot variants than any other category of card game, but also because the original, traditional tarot deck has 4 suits that are even bigger than in the casino deck (14 ranks, not 13 as in your favorite regular card game, nor 11 as in Chinese dominoes). And it also has this extra suit that goes up to 21. Now, contrary to popular belief, trump suits were not a new idea in 15th century Milan, when tarot was invented. But illustrated permanent trumps appear to have been. In most games, the trump suit changed on the fly; in tarot, it was always the fifth suit, the suit of 22 illustrated majors. The question is: Do we believe the 21 + 1 cards - the number of combinations a pair of dice can take on - plus The Fool for 0 - added to the deck are a coincidence?
We might believe it's a coincidence. Stranger things have happened.
Let's put that aside for a minute.
What about the 56, though? Does that mean something?
56 is to three dice as 21 is to two dice. Each different combination of 3 dice corresponds to a different, unique minor card, and all of the minor cards are given an ID this way. Just as you can pick any of the 21 majors with a roll of 2 dice, you can pick any of the tarot minors with a roll of 3 dice.
The same, again, goes for the 21 regular trumps. Each corresponds to a unique result of rolling two dice.
What about The Fool, though? Why is he there, and doesn't he break the scheme? Well, yes, sort of.
There are precedents for dominoes representing 0, not just 1-6. For example, the modern European-style set contains 28 dominoes, corresponding to all the rolls (combinations) of, well, a pair of mythical 7-sided dice with faces 0-6. There is no 7-sided die in existence, at least not in a regular shape with congruent faces. But the European dominoes pretend there is, to put 0 into the mix.
At this point, we should probably recall that 0 was not accepted as a number like all the others for quite some time. In fact, most Europeans didn't know about the number 0 before 1200 CE, about the same time we have our first clear written evidence of playing cards appearing in China. Even today, not everyone accepts that negative numbers are numbers, let alone complex numbers. We can safely assume that the average European didn't see 0 as quite the same as the other numbers for many centuries after 1200 CE. We may be justified in setting The Fool aside from the other 21 majors, even without the convenient factoid that the rules of tarot games treated him as unique, a kind of wild card.
Now, ok, let's summarize. What have we got? We have 56 majors (a familiar 52-card deck with one extra rank), all of which are IDed by the different patterns you get with 3 dice. We have 21 minors, which are IDed by the different patterns you get with 2 dice. In this sense, the 77 cards can be mapped to, or addressed by, if you will, 5 dice. And beyond all that, we have the weirdo wild man, The Fool, whose 0 means both high and low, and allows him to infiltrate any rank or suit.
Also, by the way, did you notice that 22 is 2 times 11? Another way to interpret the majors is as all 11 sums of a pair of dice, duplicated and put in a row. This is virtually identical to what ancient Chinese dominoes did with the original 11 sums, tossing in another suit of 10 new symbols to cover all 21 combinations. The 11 original sums and their symbols were then duplicated exactly to get 11 + 11 + 10 = 32 dominoes, presumably because this was a power of 2 and half of 64, the number of I Ching trigrams (as a result of the predominance of I Ching, the Chinese had a deep affinity and love for powers of 2). The point is that the 2x11 pattern existed in dominoes already, and yes, some of the dominoes or cards based on them were illustrated with scenes and ranked, much as tarot trumps would be later. There's a case to be made that when the 52-card deck became the 78-card deck, a set of Chinese dominoes or cards was reskinned and dropped in as a fancy new trump suit. This is actually the explanation I favor, though no clear historical evidence remains one way or the other.
Let's go back to the minors for a minute, remembering that we have still temporarily banished The Fool from the majors.
If you isolated the 56 minors and drew a card at random, that would be equivalent to rolling 3 dice and reading off the numbers the way anyone would around the world (ie, not caring about the order, which mathematically means you are reporting what's called the combination). Ok: not perfectly equivalent, because the probabilities of the 56 dice outcomes are not balanced. That is, snake eyes (1 and 1) is only half as likely as getting, say, 1 and 2. But if we ignore the unevenness of the probabilities, 3 dice will nevertheless map to the 56 minors, and so you can perfectly accurately see each minor card as symbolizing a unique outcome from a roll of 3 dice. (Forgive me for getting repetitive here.)
If you put the 21 majors back in the deck for a total of 77 cards, and then drew one, this would not, however, be equivalent to rolling 5 dice. It almost would, but it wouldn't. Why? Let's say you colored 2 of them blue and 3 of them green. When you roll all 5 dice, you get a pattern on the blue dice (one of the majors is thereby selected) and also a pattern on the green dice (one of the minors is thereby selected). From that roll of 5 dice, which card is chosen? The answer is: two different cards are chosen, a major and a minor. Just the die roll is not enough to say which of the two cards is the "right" one selected by rolling dice.
Still, we're getting pretty close to converting a tarot deck into the dice that gave birth to it centuries earlier.
Can we do any better? And what about The Fool? Can he come back to the tavern and join the revelry?
Let's use a trick. The Fool might like that (especially if he were teaming up with The Magician, but that's neither here nor there).
Notice that if a die roll needs to select either a major (from the 22) or a minor (from the 56), that means that you will be reading either from two dice or from three dice. So, actually, do we need all 5 dice at once? Or even all? We need either 2 dice or 3 dice, plus a method to decide whether we're going to use 2 or 3. Fortunately, if we only need 2 dice, it doesn't hurt to have rolled 3. So we can always go ahead and roll 3 dice, and read either 2 of them or all 3, depending on some other command.
Where could that command come from?
Could we, say, use dice?
Ok, that sounds believable. Now, how many majors are there? 22. How many minors? 56. What's the ratio? 22:56. Hmmmm, can't be reduced. What if we kick The Fool out of the tavern again, for a minute. 21:56. Can it be reduced? Yes!
It reduces by a common factor of 7, and you get 3:8. What does that mean? It means that when we draw a card, 3/11 of the time, we draw a major, and 8/11 of the time, we draw a minor. (That is, provided we've banned The Fool.) This is particularly handy, because, remember, 11 is one of the canonical numbers with a pair of ordinary, cubic dice. If you add the two faces, you get 11 different possible outcomes.
(If we put The Fool back and upscale the ratio for practicality, we get 21:78 or 7:26, 56:78 or 28:39, and 1:78.)
Ok. Let's try to use this trick.
We roll 3 dice, not knowing whether we will read 2 of them (and then draw a major card) or all 3 (and then draw a minor card). To answer that question, we roll another 2 dice, add the two faces, and look at the outcome. After 3 of the outcomes - say, sums of 2, 3, or 4 - we will read 2 of the other dice and draw a major. After the other 8 outcomes, we will read all 3 of the other dice and draw a minor.
As before, the probabilities are not equal. For example, an outcome of 7 is much more likely (6x more) than an outcome of 2. So in this current scheme, we will get a major card less often via the dice method than if we were simply drawing shuffled cards. However, it's still interesting to note that if we roll the dice repeatedly, we now have a method that will eventually get to every one of the cards. Except The Fool, of course, because we banished him.
It turns out that we needn't have banished him, really. When you draw from a pile of the 22 majors, 1/22 of the time, you will get The Fool. If we draw from the whole deck, it's 1/78 of the time. But we've already admitted that our probabilities are off in the dice method. So all we really need to do is attach a particular die outcome to The Fool and go on our way. Let's give The Fool 12. So, whenever the two special dice both come up as 6, that means that instead of consulting all 3 other dice, or 2 of them, we simply ignore them and choose The Fool. This does mean that The Fool is replacing one of the situations where we would have drawn a minor. But we already noticed that the minors were overrepresented in the probabilities. While there are 11 sums of two dice and 21 combinations, there are 36 permutations, and double-6 is exactly one of those permutations. This means that according to our current scheme, The Fool will be drawn 1/36 of the time, rather than 1/78, or about twice as often as he should be.
The neat thing, though, is that we now have a method for using a single roll of 5 dice to select potentially any tarot card. The probabilities are a bit off, but they could be tweaked. Interestingly, since we don't use one of the 3 initial dice about 3/11 of the time, we could perhaps ask that die to serve an extra role, and get ride of one of the 2 extra determining dice. So even though tarot corresponds closely to the probabilistic structures emanating from 2+3 dice, I think we could pull off a similar drawing-any-card-with-dice feat with only 4 dice. However, I have to think about this. I'm not sure whether that approach would preserve all 78 mapped cards.
There are other reasons 56 would have been an attractive number of minor cards, and it's possible that the alignment with 3 dice was never a factor. For example, it appears likely that two different deck types merged, and the resulting deck kept both queens and pages, rather than choosing between them, resulting in 4 court ranks rather than 3. Additionally, the woman for whom the earliest surviving deck was made, and who features in many of the card images, was the Duchess of Milan, not only an avid card player in a court of avid card players, but the daughter of the duke who had, we believe, commissioned the very first tarot prototype. Card games were played more by women than by men at the court, the Duchess was highly influential (her husband was a younger outsider, a marriage of convenience), and we have some reason to believe that equal representation in the ranks of the court cards was a key consideration. Finally, that first prototype of tarot had suits of 12 cards (1-10, queen, king) and a line of 16 trumps, 4 trumps loosely associated with each suit. So in that very court a few years earlier, and commissioned by the very same Duke, there was a deck containing 16 cards, 4 associated with each of 4 suits - exactly the eventual structure of the tarot courts. It isn't difficult to believe this had an influence by a minor transposition, merging those original trumps with the kings and queens for a new court of 16, and making room for a new line of 21 trumps, plus 0, The Fool.
But even though we can probably explain the alteration of the casino deck's 3 court ranks to the tarot deck's 4 ranks in these ways, this does not mean that probability theory and dice patterns played no role in this pattern succeeding where many other variations died out. And let's not forget: the court of Milan circa 1440 was not just a court of avid card players, but also a court of avid dice players.
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*(the Sola-Busca is the oldest complete deck that survives)
