[Outdated; Inaccurate] Overview -- Abilities and Effects

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Originally by John Carter:

Abilities are things that permanents or cards can do. The two most common ability types are activated and triggered, but there are several overall. The list of abilities includes:
I. Activated abilities
A. Regular activated abilities
B. Mana abilities
C. Delayed abilities
II. Triggered abilities
A. Zone-Change triggers
i. Comes into Play triggers
ii. Leaves Play triggers
B. Delayed triggered abilities
C. Mana abilities
D. State-Triggered abilities
III. Static abilities
A. Continuous effects
B. Replacement effects
C. Prevention effects

Non-mana activated and triggered abilities use the stack. Mana abilities are announced and resolved immediately. Static abilities are constantly working. Abilities generate effects. Delayed abilities are written “[person] may pay [do X] to [produce Y]”.

Triggered abilities may trigger at any time. Once an ability triggers, it waits until the next player receives priority and then all triggers go on the stack using APNAP. If an event that would cause a trigger is prevented or replaced, the trigger does not occur. Creatures with zero power do no deal any damage and therefore do not trigger anything that looks for dealing damage. When a triggered ability is put on the stack, it is announced following the same six steps used for playing spells; if targeting choices are required but cannot be made, the ability is immediately removed from the stack. Triggers with an if clause check for their if condition as part of triggering. Failing the if check means the ability will not trigger. The if check is repeated on resolution, and failing at this point makes the ability do nothing.

Unless otherwise specified, “comes into play” triggers will occur no matter what zone a permanent comes into play from. Because the permanent must enter play to trigger, that permanent may be targeted by its own ability if applicable even though the permanent might not be in play when the ability resolves. Unless otherwise specified, “leaves play” triggers will occur no matter what zone a permanent goes to after leaving play. When a group of cards leaves play together, all permanents in play prior to the mass migration check for leaves play triggers that involve the cards being transported (all the cards “see” each other as they’re moved).

Continuous effects apply constantly and based on timestamp. Continuous effects apply to permanents as they’re entering and leaving play. A creature that is a 1/1 and gives all creatures +1/+1 will enter play as a 2/2 and leave play as a 2/2. If two continuous effects conflict, the effects are applied oldest to most recent so long as there are no dependencies.

[CR 418.5b and c]
“418.5b An effect is said to “depend on” another if applying the other would change the text or the existence of the first effect, what it applies to, or what it does to any of the things it applies to. Otherwise, the effect is considered to be independent of the first effect.

418.5c Whenever one effect depends on another, the independent one is applied first. If several dependent effects form a loop, or if none depends on another, they’re applied in “timestamp order.””
If there are multiple dependencies, effects are applied from the most independent to the least independent.

State-triggered abilities operate like a triggered ability except instead of waiting for an event (such as coming into play) state-triggers look for a game state. The numbers of creatures in play, life total, control of a given permanent, and cards in hand are examples of game states. Instead of repeatedly triggering, a state-trigger occurs once and is put on the stack like a normal trigger (thus avoiding unbounded triggered abilities). After that ability has resolved, it may occur again if the conditions are met. Because state-triggers are usually worded “If X, then Y”, they do not fall under the regular provisions for targeting or “When X, if Y, then Z”, so once triggered state-triggers resolve without checking for their trigger state on resolution.