[Outdated; Inaccurate] Overview -- The Stack

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Originally by John Carter:

“The Stack” is the theoretical zone through which all spells and non-static abilities pass. The only things found on the Stack are spells and pseudospells. A Pseudospell is the representation of an ability while it is on the stack, much like a placeholder. When a spell or pseudospell resolves, a permanent is put into play or an effect is generated. Some effects may do nothing. If a spell or ability is countered it is removed from the Stack immediately, and no part of its instructions is carried out. Countered spells are put directly into the graveyard. Countered pseudospells (the representation of an ability on the stack) cease to exist.

Players may add spells or abilities to the Stack whenever they have priority. When both players pass priority, the next spell or ability on the Stack resolves. If the Stack is empty at this time that step or phase ends, and the game continues as required. With the introduction of 6th Edition and the Comprehensive Rules, the Stack became a more fluid device as well. When both players pass on a non-empty Stack, the top item of the Stack resolves-- not everything on the Stack. After resolving that one spell, each player will have the chance to add to the Stack before resolving any remaining items. Thus the Stack can go up several times, down a little, up again, and finally all the way down. There is no requirement that the whole Stack resolve just because one item has resolved.

Some things avoid the Stack altogether:
1. Effects generated while resolving a spell or ability
2. Continuous effects generated by static abilities
3. State-based effects
4. Playing a land
5. Mana abilities
6. Game actions (untapping, mana burn, turning a creature face up etc.)