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So I just want to make sure I understand the following two things about Activated Abilities and Mana Abilities correctly.

  1. An Activated Ability is any ability a card has that is written as "[Cost]: [Effect]".

  2. Mana Abilities are special types of Activated Abilities that don't use the stack and can't be reacted to and spells like "Quash" and "Stifle" can't be used to counter these effects either.

So if I am correct on my understanding of the two points above, then am I correct in thinking that if you combo Karn, the Great Creator (KTGC) and Mycosynth Lattice (ML) then you would effectively prevent your opponents from being able to tap for mana as the passive of KTGC states that "Activated abilities of artifacts your opponents control can't be activated." and the first ability of ML states "All Permanents are artifacts in addition to their other types." or am misunderstanding something here?

  • Congratulations, you have found out how to efficiently make everyone on your game table hate you. – Erik Jul 12 at 7:33
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Yes, this is all essentially correct.

First, the format of activated abilities is defined in rule 602.1:

Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] [Activation instructions (if any).]”

Then rule 501 and its subrules describe what counts as mana abilites:

  • 605.1. Some activated abilities and some triggered abilities are mana abilities, which are subject to special rules. Only abilities that meet either of the following two sets of criteria are mana abilities, regardless of what other effects they may generate or what timing restrictions (such as “Activate this ability only any time you could cast an instant”) they may have.
    • 605.1a An activated ability is a mana ability if it meets all of the following criteria: it doesn’t require a target (see rule 115.6), it could add mana to a player’s mana pool when it resolves, and it’s not a loyalty ability. (See rule 606, “Loyalty Abilities.”)
    • 605.1b A triggered ability is a mana ability if it meets all of the following criteria: it doesn’t require a target (see rule 115.6), it triggers from the resolution of an activated mana ability (see rule 605.1a) or from mana being added to a player’s mana pool, and it could add mana to a player’s mana pool when it resolves.

Mana abilities can be either activated abilities or triggered abilities that trigger from the activation of activated mana abilities. The activated mana abilities are like other activated abilities in most ways, and there is no reason that Karn's ability would not affect them. So you are correct, Karn, the Great Creator and Mycosynth Lattice together prevent your opponents from activating any mana abilities.

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This is a well-known combo that has been tried extensively. See for example this article which was written before WAR was even released:

There’s also the new most popular combo on the block to consider—Karn, the Great Creator + Mycosynth Lattice. If you have both of these in play, your opponent is locked out of playing spells for the rest of the game, since all their permanents are artifacts and they cannot tap any lands to generate mana. The best part is that you don’t even have to play Mycosynth Lattice in your main deck, since Karn can just search for it from the sideboard, so all you’re using up is one sideboard slot. This combo may seem like a meme, but it could also just have competitive applications, especially in decks like Tron that can assemble both pieces in play by turn 3 relatively easily (all you need is Karn on turn 3 and Tron, or Karn + Tron + Tower on turn 4).

Or this one:

One of the reasons Karn's static ability is so strong is that, much like Stony Silence before it, it stops mana abilities. On its own, this hampers the ability of Mox Opal / Darksteel Citadel decks to cast anything under the Great Creator's watchful eye. However, it also has some interesting implications with Mycosynth Lattice.

Mycosynth Lattice turns all of the opposing lands into artifacts, rendering them inert while Karn is on the battlefield. In other words, this prevents your opponent from casting any spells for the rest of the game. Because Lattice is a six-mana card that is utterly blank on its own, this combo would normally have no shot of seeing competitive play. But Karn's Wish ability changes the equation. It gives you access to the combo without any risk of drawing a six-mana paperweight. In addition, it means that you have no need for card selection to help with assembly. Any time you untap with Karn and six mana sources, you will have the ability to prevent your opponent from ever casting another spell.

Do note that the combo only prevents opponents from tapping for mana. Both these authors say opponent is prevented from casting spells, which is almost but not quite the same - opponent can still cast spells that don't cost mana, such as Surgical Extraction and the flashback on Lava Dart, or if they cast something "without paying its mana cost", e.g. via an already in-play Omniscience.

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