Quiz: which is the least common M10 common?
Brian Kowal has completed the jigsaw to compute the M10 Commons print run. It is published at Bill Stark's excellent site http://www.thestarkingtonpost.com/?p=1042. Brian's lists have not been independently confirmed, but look plausible (although I think that one Stampeding Rhino must be missing from Good Run B).
He identifies 4 runs:
- Good Run A: length 66: 2 copies of each of 33 different cards
Good Run B: length 66: 3x22 cards (adding one more Rhino)
Bad Run A: length 55: 2x27 cards + 1xTerramorphic Expanse
Bad Run B: length 55: 3x18 cards + 1xTerramorphic Expanse
Brian wrote in the Starkington Post:
The purpose of this posting is to speculatively explain some of Brian's observations, and come up with some nice algebra.Each pack has 9 or 10 commons. The first 5 or 6 are from one of the first two runs. The last 4-5 are from one of the second two runs. Most of the good cards are in the first 5 or 6 cards, so I named the first run the “Good Run” and the second run the “Bad Run.” The runs are all loops, so the last card in the run is listed as the same as the first one.
There is something else going on with the runs too: in Run A each card shows up twice while in Run B each card shows up three times.
Initially, I had thought that the 101 commons might be combined with the 20 basic lands on a single sheet. of 11x11=121 cards. However, this hypothesis is very unsatisfactory for at least three reasons:
- (1) Commons runs are too obvious - each card will always have the same neighbours.
(2) Commons and basic lands are not needed in this specific frequency.
(3) It would be inconvenient to separate the commons from the lands, because 20 is not a multiple of 11, so can't just "split by column".
Let's say that WotC are aiming to print all the common cards with approximately the same frequency, which seems a desirable goal, particularly for a basic set.
Sheet A could contain:
- Good Run A: length 66: 2x33 cards
Bad Run A: length 55: 2x27 cards + 1xTerramorphic Expanse
- Good Run B: length 66: 3x22 cards
Bad Run B: length 55: 3x18 cards + 1xTerramorphic Expanse
Suppose we have 5 common sheets: 3xA and 2xB. That makes 5x121 = 605 cards. But 6 common sets would be 6x101 = 606. What's happened to the missing card? Terramorphic Expanse is the only card to appear on both sheets and it appears just 1x3+1x2=5 times in total, while all the other cards appear 2x3 or 3x2 = 6 times.
Note that this card is the only non-coloured card in the commons, so missing one does not upset the colour balance. (Again, this consideration is probably viewed as more important in a Core Set than in an expansion.)
It isn't enough to ensure that each common card is printed approximately the same number of times. It's also important that each run must be inserted into boosters in the same proportion. Otherwise after a million boosters are packaged, there might be a thousand cards left in one feed queue. I.e. the good cards and bad cards must be allocated in the ratio 6:5. But we don't have 11 common cards in a booster - we have 9 or 10. What to do?
Wizards' solution is ingenious. They define three possibilities:
- (1) The pack has a foil. Then the non-foil commons must be 5 Good and 4 Bad. Say this happens with probability f.
(2) The pack has no foil. Then the commons can be 5 Good and 5 Bad. Say this happens with probability (1-f)p.
(3) The pack has no foil. Then the commons can be 6 Good and 4 Bad. Say this happens with probability (1-f)(1-p).
- p = 5/11 + 1/[11(1-f)].
But as it is, we are told on each booster that approximately 1/67 cards is premium. A booster contains 16 cards (according to the text on the wrapper), although one is just a tip or token and can't be foil. So f = approximately 16/67, then:
- p = 5/11 + 67/(11(67-16)) = 322/561 = approx 0.574.
I don't know why WotC have chosen the value of f that they did, though.
Brian made two other interesting comments:
Sometimes a common will hop one spot or something weird (this seemed to happen most with Griffin Sentinel).
I've noticed this before with other sets. E.g. in Champions of Kamigawa, I saw transpositions where the 11 cards from one strip of a sheet met the 11 cards from an adjacent strip. Occasionally the first card of a strip seemed to overtake the last card from the preceding strip. Here though the overtaking seems to be associated with a single card Griffin Sentinel, but I wonder if this is just because the sample size for this feature is small.
There are two levels of split going on. First the split between Good and Bad ensures some level of balance between boosters. Then printing a Good card with 3 different sets of neghbours makes it harder for drafters to spot that it has been taken. Particularly in a set where players are only able to play two colours, the unbalancing impact on sealed of giving a player additional removal across other colours is reduced. I am not claiming this is perfect, but I think I can see what WotC are trying to do here.Interestingly, one of the Good runs seems to be much better than the other. Almost all of the removal is in Good Run B. That doesn’t make me feel so good about this Sealed format.
Anyway, I'd better wrap up. I enjoy this kind of analysis, and if anyone has similar ideas about other sets, or indeed other rarities with M10, please post here.
Thanks,
Andy.
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