So, this is a Muldrotha deck I built for my budget meta (no card costing more than $1 TCGPlayer mid, except the commander). It's your basic Muldrotha value engine deck, with the major exception being that the budget restriction excludes some of the more obvious card choices (Spore Frog, Eternal Witness, Sidisi, Undead Vizier).
Obviously it's not meant for the 100% hyper-tuned super competitive metas, but it can carry its weight. You mostly feel the budget in the mana base, with a very limited amount of lands that tap for multiple colours and enter the battlefield untapped. Still, once it gets going it's quite resilient.
Cycling lands (Barren Moor, Lonely Sandbar, Tranquil Thicket): Replace themselves early for a relatively low cost, and can get brought back from the yard later in the game. I opted for the Onslaught cycling lands rather than the original Urza's Saga cyclers or the Amonkhet deserts because these cycle for the cheapest, and I already run way too many lands that enter the battlefield tapped.
Blighted Cataract: I originally had Memorial to Genius here, but the fact that the Cataract enters the battlefield untapped and can be cracked immediately beats out the fact that it taps for colourless and costs one more to activate.
Drownyard Temple: Taps for colourless, but can be brought back easily, especially useful as pseudo-ramp in turns four to six.
Gargoyle Castle: This deck likes its games long and grindy. Generating a 3/4 flyer every turn fits that strategy.
Myriad Landscape: Recently became budget with its M25 printing. This will dig up two forests 95% of the time, but it's reusable and it thins your deck.
Elephant Grass: Propaganda isn't budget. This is. You can easily skip the cumulative upkeep, then recast it with Muldrotha out. If you need to cast another enchantment that time, the cumulative upkeep isn't so punitive that it can't be paid for two or three turns.
Hope of Ghirapur: Once it connects, it can easily lock that pesky spellslinger or superfriends player out of the game entirely. On top of that, you get some extra versatility because it can be cast off of Muldrotha as either an artifact or a creature.
Evolutionary Leap: Lets us find new creatures to (ab)use while recycling enter the battlefield triggers, at almost no cost.
Wood Sage: Occasionally I'll tap this naming something like Sakura-Tribe Elder, but mostly it's there to make sure I have a nice and juicy graveyard waiting when Muldrotha makes her dramatic entrance.
Zur's Weirding: Hooo boy, when this card sticks around things get weird. Muldrotha lets you play around the drawback (other than when your instants and sorceries get dropped, but we have recursion for that), but it will make games very chaotic.
Nihil Spellbomb: Even if there's no relevant graveyards to eat, it's still drawing a card every turn for 1B.
Loaming Shaman: Can shuffle back stuff from your own graveyard if necessary, or an opponent's graveyard if you don't have access to the spellbomb.
Horizon Spellbomb: It's repeatable colour fixing with optional card draw stapled on.
Khalni Heart Expedition: Surprisingly repeatable, there's several cards in this deck that can drop multiple lands in a single turn.
Splendid Reclamation: When you get this in your opening hand you can easily create situations where you suddenly untap with eight to ten lands available when you're ready to cast Muldrotha for the first time, meaning you can start generating value the moment she comes down.
Dreamborn Muse: In long, grindy games, this can help speed an opponent along to death by milling, and it fills your own graveyard. It's also a creature, meaning it can be quite hard to get rid of.
The Umbras (Crab Umbra, Spider Umbra): Cheap protection against the most common forms of removal. Can also easily be repeated.
Siren Stormtamer: Not only protects Muldrotha from targeted removal, but also your graveyard from getting exiled, as the majority of effects like Tormod's Crypt require the player to be targeted. Also, re: the deck's budget, this was at $0.96 in the first draft, but it more than doubled in price since then.
Jarad, Golgari Lich Lord: Comes down late in the game as a big body that can take large chunks out of your opponents' life totals.
Xathrid Demon: Risky, but it's a large evasive body that does the same as Jarad late game.
Torgaar, Famine Incarnate: Can repeatedly set you back to 20 life when you're being focused by the table, or it can put that pesky Oloro player into a manageable state.
Sinister Concoction: Repeatable removal for a negligible cost. Three quarters of the cost of activating it are things that Muldrotha actually wants to happen.
Nevinyrral's Disk: When paired with an umbra this can pretty much lock opponents out of developing any kind of serious board state.
Gaze of Granite is an excellent suggestion. I mostly tossed Forced March in there because I had it laying around (and because running just four swamps makes Mutilate kind of meh.)
And yes, in the long run, Tatyova generates a lot of incremental value, even if you just play a random basic from your graveyard each turn.
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Obviously it's not meant for the 100% hyper-tuned super competitive metas, but it can carry its weight. You mostly feel the budget in the mana base, with a very limited amount of lands that tap for multiple colours and enter the battlefield untapped. Still, once it gets going it's quite resilient.
1x Muldrotha, the Gravetide
Land (38)
1x Barren Moor
1x Blighted Cataract
1x Dimir Guildgate
1x Dismal Backwater
1x Drownyard Temple
1x Evolving Wilds
10x Forest
1x Gargoyle Castle
1x Golgari Guildgate
5x Island
1x Jungle Hollow
1x Jwar Isle Refuge
1x Llanowar Wastes
1x Lonely Sandbar
1x Myriad Landscape
1x Simic Guildgate
4x Swamp
1x Tainted Wood
1x Temple of the False God
1x Terramorphic Expanse
1x Thornwood Falls
1x Tranquil Thicket
Shenanigans (6)
1x Elephant Grass
1x Hope of Ghirapur
1x Evolutionary Leap
1x Wood Sage
1x Sultai Ascendancy
1x Zur's Weirding
1x Nihil Spellbomb
1x Loaming Shaman
Ramp (13)
1x Horizon Spellbomb
1x Coiling Oracle
1x Golgari Signet
1x Khalni Heart Expedition
1x Sakura-Tribe Elder
1x Simic Signet
1x Burnished Hart
1x Commander's Sphere
1x Cultivate
1x Farhaven Elf
1x Harrow
1x Sultai Banner
1x Splendid Reclamation
Digging (10)
1x Epiphany at the Drownyard
1x Vessel of Nascency
1x Commune with the Gods
1x Gather the Pack
1x Grisly Salvage
1x Mulch
1x Satyr Wayfinder
1x Tracker's Instincts
1x Forbidden Alchemy
1x Dreamborn Muse
Protection (4)
1x Crab Umbra
1x Siren Stormtamer
1x Spider Umbra
1x Swiftfoot Boots
1x Jarad, Golgari Lich Lord
1x Xathrid Demon
1x Torgaar, Famine Incarnate
Removal (11)
1x Caustic Caterpillar
1x Sinister Concoction
1x Seal of Primordium
1x Fleshbag Marauder
1x Forced March
1x Putrefy
1x Reclamation Sage
1x Languish
1x Nevinyrral's Disk
1x Ravenous Chupacabra
1x Acidic Slime
Draw (6)
1x Implement of Examination
1x Secrets of the Dead
1x Windfall
1x Fact or Fiction
1x Slithermuse
1x Tatyova, Benthic Druid
Recursion (4)
1x Codex Shredder
1x Den Protector
1x Victimize
1x Creeping Renaissance
Tutor (2)
1x Jarad's Orders
1x Final Parting
(Non-obvious) card choices
Blighted Cataract: I originally had Memorial to Genius here, but the fact that the Cataract enters the battlefield untapped and can be cracked immediately beats out the fact that it taps for colourless and costs one more to activate.
Drownyard Temple: Taps for colourless, but can be brought back easily, especially useful as pseudo-ramp in turns four to six.
Gargoyle Castle: This deck likes its games long and grindy. Generating a 3/4 flyer every turn fits that strategy.
Myriad Landscape: Recently became budget with its M25 printing. This will dig up two forests 95% of the time, but it's reusable and it thins your deck.
Hope of Ghirapur: Once it connects, it can easily lock that pesky spellslinger or superfriends player out of the game entirely. On top of that, you get some extra versatility because it can be cast off of Muldrotha as either an artifact or a creature.
Evolutionary Leap: Lets us find new creatures to (ab)use while recycling enter the battlefield triggers, at almost no cost.
Wood Sage: Occasionally I'll tap this naming something like Sakura-Tribe Elder, but mostly it's there to make sure I have a nice and juicy graveyard waiting when Muldrotha makes her dramatic entrance.
Sultai Ascendancy: It smooths out your draws, and under the right circumstances it can be a onesided Howling Mine.
Zur's Weirding: Hooo boy, when this card sticks around things get weird. Muldrotha lets you play around the drawback (other than when your instants and sorceries get dropped, but we have recursion for that), but it will make games very chaotic.
Loaming Shaman: Can shuffle back stuff from your own graveyard if necessary, or an opponent's graveyard if you don't have access to the spellbomb.
Khalni Heart Expedition: Surprisingly repeatable, there's several cards in this deck that can drop multiple lands in a single turn.
Splendid Reclamation: When you get this in your opening hand you can easily create situations where you suddenly untap with eight to ten lands available when you're ready to cast Muldrotha for the first time, meaning you can start generating value the moment she comes down.
Vessel of Nascency: Repeatable self-mill.
Dreamborn Muse: In long, grindy games, this can help speed an opponent along to death by milling, and it fills your own graveyard. It's also a creature, meaning it can be quite hard to get rid of.
Siren Stormtamer: Not only protects Muldrotha from targeted removal, but also your graveyard from getting exiled, as the majority of effects like Tormod's Crypt require the player to be targeted. Also, re: the deck's budget, this was at $0.96 in the first draft, but it more than doubled in price since then.
Xathrid Demon: Risky, but it's a large evasive body that does the same as Jarad late game.
Torgaar, Famine Incarnate: Can repeatedly set you back to 20 life when you're being focused by the table, or it can put that pesky Oloro player into a manageable state.
Nevinyrral's Disk: When paired with an umbra this can pretty much lock opponents out of developing any kind of serious board state.
Slithermuse: Can be Evoked from the graveyard for repeatable refills on your hand.
Tatyova, Benthic Druid: Generates great value off of cards like Splendid Reclamation and Myriad Landscape
Den Protector: It's mostly there to get back any instant or sorcery for [cost]4G[/cost].
Sultai Ascendancy seems like a hidden gem, I'll have to add that to my deck. Also Tatyova and budget fetches seems underrated and powerful.
(W/U)(B/R)GForm of Progenitus, Shape of a Scrubland
BRGJund Tokens with Prossh, the Magic Dragon Foil
URGAnimar, the RUG CleanerFoil
RRRFeldon of the Third Path 2.0 Foil
BG(B/G)Not Another Meren DeckFoil
UR(U/R)Mizzix, Y Control and X Burn Spells
(W/U)(B/R)GHarold Ramos - The 35 Foot Long Twinkie (In +1/+1 counters)
UB(U/B)Dragonlord Silumgar
And yes, in the long run, Tatyova generates a lot of incremental value, even if you just play a random basic from your graveyard each turn.