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The idea of the Deck is to use "Treeborn Frog", "Swap Frog" and "Ronintoadin" to make tribute fodder. Another purpose of "Swap Frog" is to send "Treeborn Frog" or "Ronintoadin" to the Graveyard and to return "Monarchs" to hand for later use. This Deck creates enough tribute fodder for duelists to have up to 15 monsters that require Tribute Summoning, while still managing to play smoothly. One can even take advantage of all the tribute based "spell" and "Frog" cards and try to pack a three tribute monster like "Beast King Barbaros" or "Destiny HERO - Plasma".
The September 2010 Lists slowed the deck down, thanks to "Substitoad" going straight from Unlimited to Forbidden. While there are still plenty of ways to search and dump "Treeborn Frog" into the graveyard, Frognarch players no longer enjoy the considerable deck-thinning abilities and easy "Dupe Frog" locks that "Substitoad" provided. However, the addition of "Formula Synchron" and the ease of which it can be summoned via "Treeborn Frog" plus "Fishborg Blaster" have helped offset the loss a bit. Due to the banning of Fishborg Blaster, Effect Veiler has been added commonly to the deck as a replacement tuner for Formula Synchron, and is also versatile because it can negate effects that begin OTKs.
Originally, this decktype rarely included Synchro Monsters, instead focusing solely on creating tribute fodder for the large numbers of tribute monsters they ran; but the aforementioned release of "Formula Synchron" and banning of "Substitoad" have resulted in the rise of an offshoot (typically referred to as "Formula Monarchs") of this deck that relies more heavily on Synchro Monsters. However, the September 2011 Lists has essentially rendered the synchro-orientated decks unplayable with the limitation of Formula Synchron, Pot of Avarice, and especially the ban of Fishborg Blaster, Formula Monarchs signature Tuner monster.
The idea of this deck is to Tribute Summon the "Monarchs" by using the "Frog" Monsters' ability to swarm the field with monsters when necessary. Thanks to "Treeborn Frog's" ability to come back to the field every turn, you don't have to worry about the Tribute materials for the "Monarchs".
Another strategy that can lead to clearing of the opponent's field and more fodder would be the use of "Enemy Controller". Because this card is a Quick-Play Spell Card, it can tribute "Treeborn Frog" during your Standby Phase after its summon, while still giving you the opportunity to summon it again.
With the help of cards such as "Level Eater" and "Ronintoadin", Tribute Summoning cards that requires multiple Tribute Materials (Like "Obelisk the Tormentor", or "Beast King Barbaros") is very easy to preform.
It is risky to use any Trap Cards in this deck as you will be unable to revive "Treeborn Frog". Occasionally, one "Treacherous Trap Hole" is used, because it can be activated at any time, or chainable Draw Power, such as "Legacy of Yata-Garasu" and "Jar of Greed"), because you can activate it before or during your Standby Phase.
- Note: This deck's main strategy revolves heavily around the card "Fishborg Blaster", and due to the September 2011 Lists it can only be used in the Traditional Format.
The Formula Monarch deck is based on the old Frognarch deck, adding 1-2 copies of "Fishborg Blaster" to Synchro Summon with "Treeborn Frog" to make "Formula Synchron" every turn. You cannot send "Fishborg Blaster" to your Graveyard for "Swap Frog"s effect as "Fishborg" is not an Aqua-Type monster. Ideally, you can discard "Fishborg Blaster" and Special Summon "Swap Frog" from your hand, then use its effect to send "Treeborn Frog" to the Graveyard; but you're not always going to have both "Swap Frog" and "Fishborg Blaster" in your hand to start with.
Because of that, a lot of players add "Genex Undine" (and, by extension, "Genex Controller"), which can send any WATER monster to the Graveyard. You can then use the "Genex Controller" you added to your hand as discard fodder for "Fishborg", or you can even summon it on a later turn for a Synchro Summon (you can tune it with "Caius the Shadow Monarch" to make "Locomotion R-Genex").
Frog Monarchs, whilst being a very control-oriented deck, do have several weaknesses, the first and most obvious being heavy reliance on tribute monsters which creates dependencies (leading to potentially bad hands) and makes it a dangerously slow archetype in the current fast paced metagame. "Zombie World" and "Mask of Restrict"--both of which will prevent Tribute Summons--can be extremely deadly if the Monarch player finds themselves with a hand full of tribute monsters and no spell/trap removal.
Perhaps even worse than the above are cards that lock out Special Summons entirely; like "Archlord Kristya", "Vanity's Fiend", and "Fossil Dyna Pachycephalo", which will shut down a "Monarch" deck completely until they can draw something like "Soul Exchange", "Dark Hole", or "Treacherous Trap Hole" to get rid of the threat.
Another weakness of the deck's main build is its requirement to have "Treeborn Frog" in the Graveyard. Cards that Banish monster such as "D.D. Crow" and "Chain Disappearance" work extremely well at neutralizing "Treeborn Frog". "Trap Stun" can neutralize most of these threats, but it's a good idea to have "Burial from a Different Dimension" as a backup.
As for the general play style of Frognarchs: even with the assistance of cards like "One for One" and "Formula Synchron" it's still a relatively slow deck. A deck with swift speed that can create a strong field presence can usually hold its own against this deck.
Alternatively, a deck that can consistently prevent the "Monarch" player from gaining field presence will also do quite well against them. Particularly difficult matchups for "Monarchs" in this respect are "Gladiator Beasts" (especially due to "Gladiator Beast Retiari") and "Machina Gadgets" (due to "Machina Fortress", whose effect allows them to gain advantage in exchange for "Monarch's" effects).
Also, since their power comes from high attack monsters, you can take control of them with Intercept!