Visions Collation

Visions is a small set with 62 commons, 55 uncommons, and 50 rares. This is a new size for small sets. The set was printed in the USA and Belgium.

Visions was sold in 15 card booster packs. Booster boxes have 36 packs.

There are also Visions preview packs that have different booster art. The collation of such packs is excepted to be different than ordinary Visions.

US Pack Anatomy

The US printing uses sequential collation with 10 × 11 sheets. Packs are back-facing and contain 11 commons, 1 rare, and 3 uncommons (in that order).

11 Commons1 Rare3 Uncommons

There are three common runs, A, B, and C. Runs A and B contain 30 and 25 cards respectively. (Cards appear twice in each run, so these are probably the top and bottom halves of a full sheet.) Run C contains 7 cards. Two different pack formats have been observed. Most packs have 5 cards from A, 5 cards from B, then 1 card from C. A few packs have 8 cards from A and 3 cards from C. (Note, this kind of pack has only been observed once so far, but something like this is also required by the math.) Assuming these are the only pack types, we can calculate the rate of each based on the ratio of A and B cards (since the printing rate of C cards is somewhat uncertain). Mathematially, the rate of the packs with no B cards should be 1/9. If this is correct, C cards would get 11/9 cards per pack on average. However, I believe this is probably not correct.

If we take the Belgian printing as a clue, we can hypothesize that the C run is printed on the top half of the rare sheet. But, unlike the Belgian printing, there is more than one C card per pack, so we can guess that the sheet actually has 110 cards instead of 100 cards like the Belgian printing. If this is true, then C should get 6/5 cards per pack (which is slightly less than the 11/9 number). To achieve this ratio, we need to introduce a new pack type. My guess is 9 cards from A and 2 cards from C. (This is far from certain.) Under this hypothesis, packs with 8 A cards appear 1/11 of the time and packs with 9 A cards appear 1/55 of the time.

Given that A and B cards are equally rare (which should be true if they are printed on the same sheet), and that C cards appear at a 6/5 rate, it turns out C commons are slightly more rare than A and B commons. (This does not depend on the exact pack configuration that gives 6/5.) On average, C commons will be 330/343 as common as A and B commons. However, C commons are probably not equally likely, as seven does not go evenly into likely sizes of the C run. Given my guess of a length 60 C run, there will probably be 3 cards that appear 8 times and 4 cards that appear 9 times. Then, compared to A and B commons, these will be 44/49 and 99/98 as likely, respectively. (This means C commons that appear 9 times in the run should be slightly more common than A and B commons.)

Common Runs

Run A contains 30 cards each twice. Cards are in a repeating color pattern of white, black, red, green, blue. The choice of first card is mostly arbitrary.

Fallen AskariSolfataraGiant CaterpillarMan-o'-WarHope CharmCoercionRock SlideQuirion RangerBreezekeeperParapet
Infernal HarvestSuq'Ata LancerSpider ClimbVision CharmKnight of ValorDeath WatchSong of BloodFeral InstinctMan-o'-WarFreewind Falcon
Funeral CharmKeeper of KookusBull ElephantVision CharmKnight of ValorWicked RewardSuq'Ata LancerFeral InstinctKnight of the MistsResistance Fighter
Death WatchRock SlideEmerald CharmVanishingJamuraan LionCoercionTremorQuirion RangerMystic VeilFreewind Falcon
Infernal HarvestSolfataraBull ElephantVanishingHope CharmFallen AskariKeeper of KookusGiant CaterpillarMystic VeilJamuraan Lion
Wicked RewardTremorEmerald CharmKnight of the MistsParapetFuneral CharmSong of BloodSpider ClimbBreezekeeperResistance Fighter

Run B contains 30 cards each twice. Cards are in a repeating color pattern of white, blue, black, red, green. The choice of first card is mostly arbitrary.

Crypt RatsHearth CharmPanther WarriorsWarrior's HonorImpulseTar Pit WarriorRaging GorillaElven CacheRemedyShrieking Drake
Dark PrivilegeDwarven VigilantesRiver BoaRemedyBetrayalCrypt RatsRaging GorillaPanther WarriorsSun ClaspBetrayal
Wake of VulturesHearth CharmRiver BoaWarrior's HonorCloud ElementalUrborg MindsuckerFireblastMortal WoundGossamer ChainsUndo
Wake of VulturesTalruum ChampionKing CheetahRighteous AuraCloud ElementalTar Pit WarriorDwarven VigilantesElven CacheSun ClaspImpulse
Urborg MindsuckerFireblastKing CheetahGossamer ChainsShrieking DrakeDark PrivilegeTalruum ChampionMortal WoundRighteous AuraUndo

The layout of run C is not known, but it contains Python, Goblin Swine-Rider, Warthog, Infantry Veteran, Inspiration, Phyrexian Walker, and Sisay's Ring.

Belgian Pack Anatomy

The Belgian printing uses striped collation with 10 × 11 sheets and 10 × 10 sheets. Packs are back-facing and contain 3 uncommons, 1 rare, and 11 commons (in that order).

3 Uncommons1 Rare11 Commons

There are two groups of commons. Most commons are in group B which consists of 55 commons, each printed twice on a 10 × 11 sheet. The remaining 7 commons are in group A. The first common in every pack is from group A, and the rest are from group B.

It is very unlikely that (excluding errors) any pack contains more or less than one A common. This is because A commons are printed on the top half of a 10 × 10 rare sheet. This mean they are printed at the same rate as rares which also appear one per pack. However, this means that A and B commons do not have the same rarity. Overall, A commons that appear 7 times on the sheet are 77/100 as common as B commons, and the common that appears 8 times (Sisay's Ring) is 88/100 as common.

There are pictures of all three sheets. [1]

Common Sheets

Group A is printed on the top half of the rare sheet. (See below for the bottom half containing the rares.) It contains 6 cards each seven times plus Sisay's Ring eight times. Note that the cards that appear in this group are not exactly the same as the cards that appear in run C from the US printing.

Urborg MindsuckerMan-o'-WarResistance FighterSisay's RingKing CheetahKeeper of KookusPhyrexian WalkerUrborg MindsuckerMan-o'-WarResistance Fighter
Phyrexian WalkerKing CheetahKeeper of KookusSisay's RingUrborg MindsuckerMan-o'-WarResistance FighterSisay's RingKing CheetahKeeper of Kookus
Sisay's RingUrborg MindsuckerMan-o'-WarResistance FighterPhyrexian WalkerKing CheetahKeeper of KookusPhyrexian WalkerUrborg MindsuckerMan-o'-War
Resistance FighterSisay's RingKing CheetahKeeper of KookusPhyrexian WalkerUrborg MindsuckerMan-o'-WarResistance FighterPhyrexian WalkerKing Cheetah
Keeper of KookusPhyrexian WalkerUrborg MindsuckerSisay's RingMan-o'-WarResistance FighterSisay's RingKing CheetahKeeper of KookusSisay's Ring

Group B consists of 55 cards each appearing twice on a sheet.

Fallen AskariParapetSong of BloodMystic VeilWarthogCrypt RatsParapetRock SlideVision CharmBull Elephant
Hearth CharmBreezekeeperPanther WarriorsDeath WatchWarrior's HonorTremorShrieking DrakeMortal WoundInfernal HarvestInfantry Veteran
Elven CacheCoercionFreewind FalconFireblastImpulseEmerald CharmDark PrivilegeJamuraan LionRaging GorillaImpulse
Sun ClaspGoblin Swine-RiderKnight of the MistsFeral InstinctPythonKnight of ValorSong of BloodBetrayalQuirion RangerCrypt Rats
Cloud ElementalEmerald CharmWicked RewardHope CharmRaging GorillaInspirationBull ElephantWake of VulturesHope CharmSolfatara
Fallen AskariRighteous AuraDwarven VigilantesShrieking DrakePanther WarriorsDeath WatchInfantry VeteranTremorBreezekeeperMortal Wound
Talruum ChampionUndoRiver BoaFuneral CharmSun ClaspFireblastUndoGiant CaterpillarTar Pit WarriorRemedy
Spider ClimbInfernal HarvestJamuraan LionHearth CharmCloud ElementalFeral InstinctDark PrivilegeGossamer ChainsTalruum ChampionVanishing
Warrior's HonorSuq'Ata LancerInspirationGiant CaterpillarCoercionKnight of ValorSuq'Ata LancerBetrayalSpider ClimbWake of Vultures
Mystic VeilWarthogPythonRighteous AuraGoblin Swine-RiderVanishingElven CacheFuneral CharmFreewind FalconDwarven Vigilantes
Rock SlideVision CharmQuirion RangerTar Pit WarriorRemedySolfataraKnight of the MistsRiver BoaWicked RewardGossamer Chains

Uncommon Sheet

Each of the 55 uncommon cards appears twice on the sheet.

Tin-Wing ChimeraWind ShearProsperityDormant VolcanoHonorable PassageNecromancyKyscu DrakeMundunguHeat WaveTeferi's Honor Guard
Time and TideLead-Belly ChimeraTeferi's Honor GuardBrood of CockroachesUktabi OrangutanBrass-Talon ChimeraMagma MineMiraculous RecoveryIron-Heart ChimeraSummer Bloom
Magma MineNekrataalMatopi GolemDream TidesSpitting DrakePeace TalksDesolationSummer BloomWaterspout DjinnHulking Cyclops
Kyscu DrakeDream TidesMob MentalityMatopi GolemSuq'Ata AssassinScalebane's EliteWaterspout DjinnScalebane's EliteRelic WardQuicksand
Goblin RecruiterEvergladesNecromancyCreeping MoldCoral AtollMob MentalityHelm of AwakeningBlanket of NightDragon MaskTime and Tide
SimoonStampeding WildebeestsLead-Belly ChimeraJungle BasinLongbow ArcherDragon MaskUktabi OrangutanEvergladesViashino SandstalkerLongbow Archer
Shimmering EfreetJungle BasinHonorable PassageBrood of CockroachesElephant GrassBrass-Talon ChimeraHulking CyclopsDaraja GriffinVampirismSimoon
Relic WardVampirismDormant VolcanoForeshadowTalruum PiperPeace TalksDesolationJuju BubbleOvinomancerGoblin Recruiter
Tin-Wing ChimeraShimmering EfreetViashino SandstalkerKarooJuju BubbleWind ShearTempest DrakeTalruum PiperCoral AtollNekrataal
Spitting DrakeMundunguArmy AntsStampeding WildebeestsOvinomancerArmy AntsMiraculous RecoveryBlanket of NightElephant GrassForeshadow
Helm of AwakeningHeat WaveQuicksandSuq'Ata AssassinCreeping MoldProsperityIron-Heart ChimeraDaraja GriffinTempest DrakeKaroo

Rare Sheet

Each of the 50 rares appears once on the sheet. Note that the top half of this 10 × 10 sheet consists of the commons from group A.

Phyrexian MarauderThree WishesSquandered ResourcesNatural OrderGuiding SpiritVampiric TutorDiamond KaleidoscopeEye of SingularityViashivan DragonOgre Enforcer
Kaervek's SpiteChronatogSands of TimeKatabatic WindsFemeref EnchantressForbidden RitualTeferi's RealmTitheSnake BasketBogardan Phoenix
CorrosionDesertionTeferi's Puzzle BoxLichenthropeTriangle of WarAku DjinnRighteous WarZhalfirin CrusaderFirestorm HellkiteElkin Lair
Anvil of BogardanFlooded ShorelineEquipoiseQuirion DruidKookusPillar Tombs of AkuWand of DenialArchangelCity of SolitudeRelentless Assault
Breathstealer's CryptRainbow EfreetUndiscovered ParadiseRowenSuleiman's LegacyNecrosavantPygmy HippoRetribution of the MeekGriffin CanyonLightning Cloud

[1] The Gamepedia wiki has pictures of the Belgian common, uncommon, and rare sheets.