A decklist inspired by Evan Vargas, a little WorldGoneMaad, and revised with help from my buddy pkx and the users of the GoatFormat.com Discord server, especially Levi and LongKun. Let's cut to the chase:
(06/14/2022) EDIT: Trade one Mobius in main for the Jinzo in side: https://www.duelingbook.com/deck?id=10866046
At time of writing, June 2022, two of the most popular decks are Chaos Warrior and Chaos Turbo. Goat Control has recently topped again, and did so maining Royal Decree. Panda Burn is all the rage and also topped recently. What this says to me is: let's play some tribute monsters!
Warrior is extremely vulnerable to Brain Control and Creature Swap, so we know all of our theft spells will go off, and it has difficulty climbing over anything bigger than 2000 ATK (or DEF) as Black Luster Soldier - Envoy of the Beginning is their only way to do so via battle. D.D. Warrior Lady and D.D. Assailant remain somewhat problematic but not enough to matter, as we can use more tribute monsters than they have D.D.s. Our Royal Decree, if played proactively, can completely shut off 25% or more of their deck. We also don't play monsters face-down by default, so their Nobleman of Crossout and Mystic Swordsman LV2 are also potentially blank. Scapegoat slows down Warriors significantly as well.
Chaos Turbo is fairly vulnerable to Brain Control, and would be more vulnerable to Creature Swap if we had our own Gravekeeper's Spy, though you are still fairly likely to steal a Magician of Faith or Dekoichi the Battlechanted Locomotive. Chaos Turbo's best monsters, BLS and 2-3 Chaos Sorcerer, are all killable with Snatch Steal or Brain Control and Monarchs can run over more than half of them. Soul Exchange is battle position-agnostic and will remove a GK Spy as easily as a BLS. Creature Swap can backfire, as can Flying Kamakiri #1 somewhat as Chaos Turbo will occasionally run recruiters of their own like Mystic Tomato. Turbo decks have also recently been playing Solemn Judgments in their 55 cards if not battle traps and Trap Dustshoots, so Decree will put in work here as well. Thestalos the Firestorm Monarch can hit Chaos monsters that tend to linger in the hand but is equally likely to hit a Thunder Dragon. Kycoo the Ghost Destroyer gives Chaos decks a hard time no matter what so we have two in the sideboard to improve this matchup. Our Warrior toolbox, which I will go into below, also helps against Chaos Turbo.
Goat Control is a somewhat tough matchup because they run one more Metamorphosis than we do and they also pack the Monarch's nemesis, Tsukuyomi. Swords of Revealing Light, Mirror Force, and Ring of Destruction are in our sideboard almost entirely because of this vulnerability. Our Warrior toolbox can carry us pretty far in the Goat Control matchup since it loves Royal Decree and doesn't particularly fear Tsukuyomi. It does feel bad when a Sasuke #4 loses the coin flip to an attack mode Dekoichi, so be mindful of that play and try to save a Kamakiri for when that happens.
Panda Burn is hopefully an easier fight, as they depend on Traps to lock down your field and burn you. Sasuke #4 can get a lot done by itself, should you find yourself with only one monster zone available, but the Ojama Trio lock is generally weaker against decks that main Decree and Swap. While your field is locked down though, your other theft spells will be dead draws. Tribute monsters also allow one to make the most of what few monster zones one has--Mobius and Jinzo are particularly good here. Two copies of Mystik Wok appear in the sideboard to help with this matchup, as Monarchs can provide serious life gain opportunities and can also do a lot with just one freed monster zone. Scapegoat is obviously very bad here, and thusly Metamorphosis becomes a brick, so it's best to side those out in game 2 and 3 (though Metamorphosis on a Monarch gets you Ryu Senshi, a mini-Jinzo). Additional battle traps were heavily considered for the 55 to deal with Gyaku-Gire Panda, but the SoRL/Mirror Force/Ring package can help.
This is a non-standard Warrior toolbox package, consisting of only four Warriors and one Reinforcement of the Army. Because we want to use our normal summons to bring out tribute monsters or set up tribute monsters, staples like Exiled Force and D.D. Warrior Lady didn't fit with the game plan. However we still needed to handle threats like a Warrior toolbox should.
Flying Kamakiri #1 is the primary enabler of this toolbox--a recruiter that can special summon all Warriors in the deck makes up for the low RotA count. Kamakiri also fetches two other useful monsters we'll discuss further below.
Sasuke Samurai fills the role that Mystic Swordsman LV2 would, removing facedown monsters. A single copy is enough since it has some redundancy with Sasuke Samurai #4.
Sasuke Samurai #4 appears in triplicate here because its effect performs similar functions to Blade Knight, MS LV 2 and Ninja Grandmaster Sasuke combined, while having a DEF that Tsukuyomi cannot overcome and an ATK that allows it to be special summoned by Kamakiri. Because we're running Soul Exchange at three copies, we're not always going to be able to do things on our own Battle Phase, that's why it's important that our monsters can do things on the opponent's turn. Sasuke Samurai #4 can defend itself 50% of the time from any attacker and that's valuable. Opponents see the card as genuinely threatening and will use removal on it.
Every monster in the deck is meant to be playable face-up, potentially blanking opposing Nobleman of Crossout like in Warrior builds. Unlike most Monarch builds which prioritize using FLIP monsters like Dekoichi or Gravekeeper's Spy, the monster lineup can apply pressure consistently while maintaining board presence and 50% of the time it can do so while outclassed.
Now we're starting to get into the classic Vargas Soul Control element of the monster line-up.
Hand of Nephthys, which was traditionally tutored out via Apprentice Magician, has found a new ally in the Creature Swap-friendly Flying Kamakiri #1. Hand of Nephthys can, with a normal summon and a Soul Exchange or Brain Control or sheep token, summon Sacred Phoenix of Nephthys from the hand or deck. Otherwise it's Creature Swap bait.
Twin-Headed Behemoth is a more recent innovation, appearing in a Monarch build designed by Richard Zapp. Behemoth plays excellently versus Asura Priest, reviving during the End Phase and providing you with a body to tribute for a Monarch or Hand of Nephthys. Behemoth's 1500 ATK beats over rival recruiters, Dekoichis, and Don Zaloogs. Plays nicely with Creature Swap.
The monarchy is intact from Vargas' original build, with a second Mobius The Frost Monarch added to the original tribute lineup. (EDIT: Jinzo is better here than a second Mobius is, you won't always draw Decree). Three Thestalos the Firestorm Monarch keep your opponent committing cards to the field while two Mobius and a Phoenix almost guarantee you'll be able to punish them for doing so. Sacred Phoenix applies pressure to aggro decks, whose monsters don't usually reach 2400 ATK, and who often depend on battle traps to make up for this--battle traps that of course trigger Phoenix. Phoenix, like Vampire Lord, revives after being negated by Solemn Judgment as well.
The Spell lineup is creature focused and fairly straightforward. Three copies of Soul Exchange are maindecked, along with two copies each of Creature Swap, Scapegoat, Metamorphosis, and Brain Control. The deck revolves around power plays where advantage is gained through theft of opposing creatures, tributing them for your Monarchs, while taking away cards from their hand or backrow.
Thousand-Eyes Restrict, Ryu Senshi, Dark Blade the Dragon Knight, and Gatling Dragon will be the most common Fusion monsters you will summon with Metamorphosis though it is important to have a fully stocked Fusion Deck as you never know what monster your opponents may have.
Other cards worth mentioning include the playset of Royal Decree which is necessary to keep your recruiters and monarchs alive, and the single copy of Silpheed which can be used as tribute fodder, Creature Swap fodder, or just an extra beater. With as many WIND monsters as we're running, paying for a Silpheed is easy.
Much has already been said about many of the cards in the sideboard, so I'll just focus now on the ones we haven't discussed yet.
Solemn Judgment appears as a three-of to swap with the Decrees in the event you're fighting a rogue deck and need a general purpose answer, or you're succumbing to a strategy whose Traps you already address with Mobius. Helps stay on top of the field against Goat Control where your Decrees will probably be redundant. It warrants further testing but it's such a powerful card in terms of Trap economy that is seemed foolish not to include it.
Lightning Vortex is there to help against aggro decks that might swarm faster than you can steal, but in practice it's been mainly to clear sheep tokens or recruiters so you can hit home with a 2400 ATK tribute monster. Asura Priest may be a valid replacement.
A third copy of Brain Control exists to support an increased Monarch count, should you decide to side out the Phoenix package, and is also good against Warrior.
Breaker the Magical Warrior is a fifth Mobius, the fourth being Jinzo.
Monsters: Zaborg the Thunder Monarch, Granmarg the Rock Monarch, Dark Dust Spirit, Blowback Dragon, Airknight Parshath, Asura Priest, D.D. Warrior Lady, D.D. Assailant, Zombyra the Dark, Goblin Attack Force, Big Shield Gardna, Kycoo the Ghost Destroyer, Bazoo the Soul Eater.
Spells: Nobleman of Crossout, Scapegoat, Mystical Space Typhoon, Giant Trunade, Enemy Controller, Book of Moon, Smashing Ground, Messenger of Peace, Mystik Wok, My Body as a Shield.
Traps: Torrential Tribute, Call of the Haunted, Sakuretsu Armor, Widespread Ruin, Magic Cylinder, Draining Shield, Jar of Greed, Dust Tornado, Fairy Box.
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