The first collectible card game of the modern era, which is also still in active production, is Magic: the Gathering. It was devised by Dr. Richard Garfield, a mathematician, and includes many features that help to provide a challenging and balanced game. For example, most cards require mana to play; mana is normally produced by land cards, only one of which may be played in a turn, and there are five different types (or colors) of mana. Cards which principally require any one of these five colors of mana are inclined to favor different specialized ways of winning the game, and so deck design balances versatility, by using cards which rely on different colors of mana, and having enough mana of the right kind available early enough, by keeping the number of different colors of mana in use to a minimum.
The first Magic: the Gathering cards were printed by Cartamundi, a noted firm in the business of supplying customized playing cards, but Wizards of the Coast later switched to other suppliers. However, it has been claimed that regardless of who printed the cards for Magic: the Gathering, cards for it have always been printed on sheets of 11 cards by 11 cards.
And this page is concerned with the triviality of just how they manage that.
The Fourth Edition of the Core Set of Magic: the Gathering consisted of 5 basic lands with three different versions of artwork each, for a total of 15 cards of this type, 121 cards at the common level of rarity, 121 cards at the uncommon level of rarity, and 121 cards at the rare level of rarity.
So one puts the 121 rare cards on one rare sheet, printing as many of those as desired, the 121 uncommon cards on one uncommon sheet, and the 121 common cards on one common sheet. Finally, 15 times 8 is 120, so we have one unused card left over on the sheet used for printing basic lands.
The Tenth Edition of the Core Set had four different versions of the artwork for the five basic lands, so this time 20 times 6 is 120; it again had 121 cards in each of the three rarity levels. The Ice Age expansion set had the same composition.
As well, the Alpha, Beta, Unlimited and Revised editions of the Core Set also had three sheets of 121 cards with no mixing of rarities of normal cards across sheets.
Revised Edition had 75 commons, 95 uncommons, and 121 rares; the remaining spaces on the common and uncommon sheets contained basic lands. Beta and Unlimited edition contained 75 commons, 95 uncommons, and 117 rares, and so there were also basic lands on the rare sheet. Alpha contained 74 commons, 95 uncommons, and 116 rares, as two cards were omitted due to last-minute errors.
In the early years of Magic: the Gathering, expansion sets, which supplemented the original game, were sold in the form of booster packs which contained only 8 cards, instead of the usual number of 15 cards that has been used both for the Core Set and the later expansions that were organized into blocks.
There were two exceptions to this; Legends was sold in the form of standard 15-card booster packs, and Chronicles was sold in 12-card booster packs.
Also, the second set from the Ice Age block, Alliances, was sold in 12-card booster packs, and also had a limited number of cards with a different rarity due to the number of times they were printed on the sheet.
Instead of the cards having rarities of "rare", "uncommon", and "common", card rarities are often indicated for these sets by codes such as U1, U3, C1 and C3. The letter indicates whether the card was printed on the uncommon sheet or the common sheet, and the number indicates the number of times it occurred there.
In the booster packs with 8 cards, two were from the uncommon sheet, and six from the common sheet; in those for Chronicles, three were from the uncommon sheet, and nine from the common sheet, so in both cases, exactly three times as many copies of the common sheet were printed as of the uncommon sheet.
The distribution of rarities for these sets is:
C11 C6 C5 C4 C3 C2 U4 C1 U3 U2 U1 R1
Arabian Nights 1 9 15 2 1 1 17 33
4 + 51 + 66 = 121
11 + 45+ 60 + 4 + 1 = 121
Antiquities 25 5 11 29 4 26
87 + 8 + 26 = 121
100 + 10 + 11 = 121
Legends 45 30 8 105 121
121 = 121
16+ 105 = 121
90 + 30 = 120
The Dark 40 1 43 35
86 + 35 = 121
120 + 1 = 121
Fallen Empires 15 20 1 25 5 36
75 + 10 + 36 = 121
60 + 60 + 1 = 121
Homelands 50 20 25 45
75 + 45 = 120
100 + 20 = 120
Chronicles 30 7 17 25 46
75 + 46 = 121
90 + 14 + 17 = 121
C3 C2 U6 U2 R6 R2
Alliances 10 40 5 40 3 46
30 + 80 = 110
30 + 80 = 110
18 + 92 = 110
This table is actually somewhat fudged in two places; the numbers for Arabian Nights have been, I hope, corrected, and in the case of Homelands, one card has been moved from U3 to C1 to make things balance.
In any case, based on this history, it seems reasonable to accept the claim that Magic: the Gathering cards were printed on sheets with 121 cards on them, with the Alliances set as one exception. As the Alliances set was the first Magic: the Gathering set of cards printed at a different company instead of Carta Mundi, their original supplier, it makes sense that a different size of sheet might be used, at least initially.
But given that, there really is no reason to suppose that the sets from Mirage block at least through Onslaught block weren't printed on 110-card sheets, if that's the size used by WotC's new supplier.
Apparently, the return to 121-card sheets took place at the time of Dissension, with the preceding member of Ravnica block, Guildpact, being produced with 110-card sheets. That would coincide with the Ninth Edition of the Core Set being printed on 110-card sheets, and the Tenth Edition being printed again on 121-card sheets.
A typical pack of playing cards contains the normal 52-card deck, two jokers, and one extra card, which might, for example, contain bridge scoring values. This makes 55 cards, for which a 110-card sheet would be highly suited.
In fact, it's so well suited to that, one might well ask what Carta Mundi, the company that made the original Magic: the Gathering cards prior to Alliances, was doing with 121-card sheets. However, this does have a simple explanation. In many European countries, the most common decks of cards might contain simply Ace, 2, 3, 4, 5, 6, 7, Jack, Queen, King or Ace, for a 40-card deck, which could appear three times, with one card left over, on a 121-card sheet, but a 32-card deck, such as Ace, 7, 8, 9, 10, Jack, Queen, King in each suit, or a 36-card deck with Ace, 6, 7, 8, 9, 10, Jack, Queen, King in each suit are even more common.
If the 36-card deck comes with jokers and informational cards, like the 52-card deck usually does, printing it three times on a 121-card sheet would not involve too much waste.
Rather than making a third size of sheet for Tarot card decks, using two different 121-card sheets to print half the deck three times on each would be the simplest solution. Also, decks made for such games as Austrian Tarock have 54 cards in them, the 22 trump cards (including the Fool) and only 32 additional suit cards, Ace, 7, 8, 9, 10, Jack, Queen, King in each suit.
There is a bit more to this than that, though. Playing cards come in different sizes. Magic: the Gathering cards are the same size as Poker-size playing cards, 2 1/2 inches wide and just under 3 1/2 inches tall. There are also Bridge-size playing cards, slightly over 2 1/4 inches wide, and the same height as Poker-size cards. Putting 110 of them on a sheet designed for 110 Poker-size cards would be a level of waste not likely to be tolerated in a large print run.
The ratio of widths is about 9 to 10. So a 110-card sheet for Poker-size cards could be used to print 121 Bridge-size cards, and a 121-card sheet for Poker size cards could be used to print 132 Bridge-size cards, assuming the widths of both types of sheet are the same, and equal 11 card heights plus the necessary spacing between the cards for cutting.
Neither of these sizes is well-suited to printing 55-card decks in Bridge size, so I think it reasonable to suspect that firms which make a lot of such decks will have a third size of sheet, suited to printing 110 Bridge-size cards or 99 Poker-size cards.
And the 40-card deck is usually used in Italy with cards of different sizes entirely; Trevigane style cards are about 1 15/16 inches wide and 4 1/8 inches high, Sicilian style cards are about 2 1/16 inches wide and 3 1/4 inches high. And Tarot cards are often oversized.
In some cases, it isn't too difficult to figure out how the cards for a Magic: the Gathering expansion might have been printed on 121 card sheets.
The Eventide expansion consisted of 60 commons, 60 uncommons, and 60 rares. Thus, a sheet for each rarity level would have two copies of each card, with only one card wasted. The Future Sight set had a similar structure, with each rarity being divided into 33 normal cards and 27 cards with a different design representing creatures and spells - and card designs - that came from the future.
The Lorwyn and Shadowmoor sets had 121 common cards, 80 uncommons, and 80 rares. The simplest way to deal with this would have been to have one sheet for the common cards, and two sheets for each of the other two rarity levels, with 40 cards repeated three times.
The Darksteel, Fifth Dawn, Betrayers of Kamigawa, Saviors of Kamigawa, and Guildpact expansions all had 55 commons, 55 uncommons, and 55 rares. As 55 is divisible by 11, it suggests it should be possible to harmonize this with card sheets having 121 cards.
These cards were distributed in booster packs which contained one rare card, three uncommon cards, and eleven common cards. This tells us how much of each type of card we need.
One possible solution to this would be:
Since 11 is equal to 5 plus 6, and 6 is divisible by 3, we could begin by having a rare sheet that contains one copy of the 55 rare cards, plus three copies each of 22 of the uncommon cards. This would print those cards in the proportions required.
There are 33 uncommon cards left to be printed. We want three copies of each of these cards to 11 copies of each of the 55 common cards. One obvious way to proceed is this:
On the next sheet, print one copy of each of the 33 remaining uncommon cards, and two copies each of 44 of the common cards (3+8=11). When we print enough of those sheets to have all the uncommon cards we need, we will also have most, but not all, of those 44 common cards that we need: we would have as many as we needed if booster packs had only 6 commons instead of 11 in them.
On the next sheet, print two copies of each of these same 44 cards, and three copies of each of the remaining 11 cards. When we print enough copies of this sheet for what we need for booster packs with 11 commons in them - 5 more than the 6 we've already dealt with - we will have enough of the remaining 11 cards for booster packs with 7 1/2 commons in them, so we won't have printed too many.
Finally, we seem to need a fourth sheet, with those last 11 cards printed 11 times over, which we can print as many times as we like to make up the last deficiency.
The expansions Mirage, Tempest, Urza's Saga, Mercadian Masques, Invasion, and Odyssey each had 110 cards at each rarity level, as well as 20 artwork versions of the five basic lands (four each) (which we've already seen how to deal with), and so they could be handled the same way. This is also true of the Sixth, Seventh, Eighth, and Ninth editions of the Core Set.
Given the experience with Alliances, however, it could well be that these sets were simply printed on 110 card sheets.
The Stronghold, Exodus, Urza's Legacy, Urza's Destiny, Nemesis, Prophecy, Planeshift, Apocalypse, and Scourge expansions all consisted of 55 common cards, 44 uncommon cards, and 44 rare cards. Can these be handled by a similar strategy to that used for the case above?
One way to start would be to make a rare sheet consisting of two copies of each of the 44 rare cards, plus three copies of 11 of the uncommon cards. Printing all the rare cards this way would give us half as many copies of these 11 uncommon cards as we need.
This suggests as the obvious next step an uncommon sheet with one copy of each of those 11 uncommon cards, and two copies of each of the remaining 33 uncommon cards. This leaves us with 44 spaces on the sheet. It turns out that the easiest way to come up with a workable solution is to place two copies of 22 of the common cards on the sheet as well.
The 55 common cards are now divided into two groups; one of 33 cards of which none have been printed, and one of 22 cards of which enough have been printed for booster packs with only three common cards in them.
So for every 11 cards in the group of 33 cards that we print, we need to print 8 cards in the group of 22 cards of which some have already been printed.
We could have one common sheet that is made up of three copies of each of the 33 cards not in the uncommon sheet, and one copy of each of the 22 cards in the uncommon sheet. The ratio 3 to 1 is, of course, greater than 11 to 8.
And we could have another common sheet that is made up of one copy of each of the 33 cards not in the uncommon sheet, and four copies of each of the 22 cards in the uncommon sheet. Printing these two sheets in the right proportion would allow us to have exactly the cards we need.
The expansions Mirrodin, Champions of Kamigawa, and Ravnica all had 20 basic land cards, 110 commons, 88 uncommons, and 88 rares in the set, so they could have been produced by a similar method.
If 110-card sheets are used, two copies of each common would be printed on one of those sheets. Another sheet could contain the 44 rare cards once, and 22 of the uncommon cards repeated three times. The remaining 22 of the uncommon cards could be repeated five times on another sheet.
The largest Magic: the Gathering set was the Fifth Edition of the Core Set. It came with 20 basic land cards, 165 commons, 132 uncommons, and 132 rares.
Booster packs in this set had 1 rare, 3 uncommons, 10 commons, and one basic land.
The obvious starting point is to have a rare sheet with 121 of the rares, and an uncommon sheet with 121 of the uncommons.
Let us have an uncommon sheet with the remaining 11 of the uncommons, and a rare sheet with the remaining 11 of the rares.
On the uncommon sheet, if we print 3 copies of 11 of the commons, we can print one copy of these same 11 commons on the rare sheet to have the right amount of those 11 commons. If we only print 2 copies of 11 of the commons, then we will need 4 copies of these same 11 commons on the rare sheet. As it happens, both 3+2 and 1+4 equal 5, and there are 110 cards left on the two sheets.
So on the second rare sheet, we have four copies of 22 of the common cards, and one copy of another 22 of the common cards.
On the second uncommon sheet, we have two copies of the first 22 of the common cards, and three copies each of the other 22 of the common cards.
This takes care of printing as many as are needed of 44 of the common cards, and so when a common sheet is printed with the other 121 commons, a set with 165 commons, 132 uncommons, and 132 rares is achieved.
When the Coldsnap expansion, the third member of the Ice Age block, was printed after a lapse of years, it had 60 commons, 55 uncommons, and 40 rares.
The 60 commons could be each printed twice on a sheet of 121 cards with one left over.
If only one copy of each of the 40 rares is printed on a sheet of 121 cards, there are 81 cards left, enough to print three copies each of 27 uncommons.
This leaves 28 uncommons; printing them four times over on a sheet of 121 cards would leave nine cards unused on each sheet, enough to add another two uncommons to the set, but perhaps two designs were rejected at the last minute.
The Morningtide expansion had 50 cards of each rarity.
The obvious way to proceed, would be simply to have six sheets, two for each rarity; one with 30 cards repeated four times over, one with 20 cards repeated six times over.
An intermediate solution requires five sheets. Since the number of commons required does not have a simple ratio to the number of rares and uncommons, use two sheets for them, one with 30 cards repeated four times over, one with 20 cards repeated six times over.
The rare sheet can consist of all 50 rares once, with 23 uncommons printed three times over, and two blank spaces.
The number of uncommons remaining is 27; they could be handled with two sheets, one containing 12 uncommons printed ten times over, and one containing 15 uncommons printed eight times over.
Recently, a new rarity level was introduced to Magic: the Gathering, the Mythic Rare. These cards are half as frequent as normal rare cards.
The Conflux and Alara Reborn expansions have 60 commons, 40 uncommons, 35 rares, and 10 mythic rares.
Since a mythic rare is half as frequent as a rare, combining 35 rares printed twice with the 10 mythic rares to produce 80 cards is an obvious way to proceed. One could repeat this three times to fill two sheets of cards. One sheet of cards can handle the 40 uncommons repeated three times, and one can handle the 60 commons repeated three times.
The Shards of Alara expansion included 101 common cards, 60 uncommon cards, 53 rare cards, and 15 mythic rares.
60 uncommon cards repeated twice will make a sheet with one card left over.
53 rare cards repeated twice, with 15 mythic rare cards occurring once, fill a sheet of 121 cards exactly.
How does one then handle the 101 common cards?
One way would be to print a sheet with the 101 common cards and the 20 basic lands. This would make about twice as many basic lands as were needed, but they could be stockpiled for use in the two later expansions and in other products.
100 equals 60 plus 40, so one could print one sheet with 60 of the common cards repeated twice, and another sheet with 40 of the common cards repeated three times each.
If the remaining blank position in both of those sheets was filled with the one left-over common, the result would be that 5/6ths of the required supply of that common would be printed.
But there's also a blank position on the uncommon sheet. Each of the 60 uncommons is repeated twice there, however, so the additional supply will be at half the frequency of an uncommon; as many as would be needed if a booster pack contained 1 1/2 commons. Six times that is nine, so this is slightly less than the required number of this one card, since a booster pack may have either nine or ten commons, most often ten.
However, the rare sheet also has a blank space; filling it with a copy of that card as well allows us to slightly exceed the required supply.
I have noted above, though, that a printer of cards would likely need to be able to print cards both on sheets of 121 cards and on sheets of 110 cards, and normally on a sheet with room for 110 bridge-size cards as well. Such a sheet might be able to hold 99 poker-size cards, although, if it is not normally used for that purpose, a size might be chosen that is just slightly too small to allow that.
Could it be, though, that the sheet used to print 110 bridge-size cards actually has a bit of extra room on the margins, and, say if one prints poker-size cards on it in the other possible orientation, rotated by 90 degrees, one could actually fit 101 of them on a sheet? While the idea is tempting, 101 is a prime number. 102 cards could form a rectangle of 17 cards by 6; could they fit that way? No, as 17 card widths are a bit more than 12 card heights rather than a bit more than 11 card heights; turning the cards through 90 degrees appears only to be likely to decrease the number of cards that could be printed.
The Visions and Weatherlight expansions each had 62 common cards, 55 uncommon cards, and 50 rare cards. For these early expansion (rather than core) sets, a booster pack contained 1 rare, 3 uncommons, and 11 commons.
To begin, one could have a common sheet with two copies of each of 60 of the 62 common cards, and one blank space; and a rare sheet with two copies each of the 50 rare cards, and six copies each of three of the uncommon cards, leaving three blank spaces.
An uncommon sheet with two copies each of the remaining 52 uncommon cards would have 17 spaces left.
If we added eight copies of one of the remaining common cards to the uncommon sheet, we would have enough of those common cards for booster packs with twelve common cards, so there is enough space to handle both remaining common cards.
Magic: the Gathering, and the names of the expansion sets referenced here, as well as the card names, the mana symbols, and the pentagon of colors, are trademarks of Wizards of the Coast LLC, a subsidiary of Hasbro, Inc..