A creature that has been dealt lethal damage (damage marked on it equal to or greater than its toughness while that toughness is also greater than 0; 704.5g), or has been dealt damage from a source with deathtouch since the last time state based actions were checked (704.5h), or has its toughness reduced to 0 or less (704.5f), will die the next time state based actions are checked. This happens regularly every time right before a player would receive priority, even before any waiting triggers are put on the stack. Attacking or blocking creatures with first strike or double strike just make the combat phase have two combat damage steps rather than just one, though only those attacking/blocking creatures with either ability get to assign and deal combat damage during the first one. And just like in any other combat damage step, state based actions are checked right after the combat damage turn based action, and any creature suffering from any of the conditions I listed will die then.
In instances like first strike dealing lethal damage, the creature leaves the battlefield in the additional (first) combat damage step. The damage is dealt as that step begins, the creature is destroyed, then players receive priority.
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A creature will be destroyed for having lethal damage marked on them the next time statebase actions are checked. Such a check is performed before any player would receive priority.
In the case of first strike it would look like this
First-strike damage step, damage is dealt as a turn action.
State based actions are checked
Active player receives priority.
Assume they pass, there is another check.
Non active player gains priority.
Assume they do nothing we move to normal combat damage and normal combat damage is dealt as a turn based action and so on.
1. It's not damage, by itself, that destroys a creature, but rather a state-based action could do so (C.R. 119.5, 704.5g-h). This is true even though combat damage is dealt at the same time (C.R. 510.2).
2. All first strike and double strike do is give a combat phase two combat damage steps rather than one, and restrict which creatures assign combat damage during those steps (C.R. 702.4b, 702.7b). See also this thread.
510. Combat Damage Step
510.4. If at least one attacking or blocking creature has first strike (...) or double strike (...) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. (…)
510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. (…)
510.2. Second, all combat damage that’s been assigned is dealt simultaneously. (…)
510.3. Third, the active player gets priority. (See rule 117, “Timing and Priority.”)
117.5. Each time a player would get priority, the game first performs all applicable state-based actions as a single event (see rule 704, “State-Based Actions”)(…)
704.1. State-based actions are game actions that happen automatically whenever certain conditions (listed below) are met. (…)
704.5g If a creature has (…) total damage (…) greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed. (...)
704.5h If a creature has (…) been dealt damage by a source with deathtouch (…), that creature is destroyed. (…)
701.7a To destroy a permanent, move it from the battlefield to its owner’s graveyard.
704.3. (…) Once (…) state-based actions have been performed (…), the appropriate player gets priority.
510.4. If at least one attacking or blocking creature has first strike or double strike (…), instead of proceeding to the end of combat step, the phase gets a second combat damage step. (…)
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In the case of first strike it would look like this
First-strike damage step, damage is dealt as a turn action.
State based actions are checked
Active player receives priority.
Assume they pass, there is another check.
Non active player gains priority.
Assume they do nothing we move to normal combat damage and normal combat damage is dealt as a turn based action and so on.
1. It's not damage, by itself, that destroys a creature, but rather a state-based action could do so (C.R. 119.5, 704.5g-h). This is true even though combat damage is dealt at the same time (C.R. 510.2).
2. All first strike and double strike do is give a combat phase two combat damage steps rather than one, and restrict which creatures assign combat damage during those steps (C.R. 702.4b, 702.7b). See also this thread.
510.4. If at least one attacking or blocking creature has first strike (...) or double strike (...) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. (…)
510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. (…)
510.2. Second, all combat damage that’s been assigned is dealt simultaneously. (…)
510.3. Third, the active player gets priority. (See rule 117, “Timing and Priority.”)
117.5. Each time a player would get priority, the game first performs all applicable state-based actions as a single event (see rule 704, “State-Based Actions”)(…)
704.1. State-based actions are game actions that happen automatically whenever certain conditions (listed below) are met. (…)
704.5g If a creature has (…) total damage (…) greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed. (...)
704.5h If a creature has (…) been dealt damage by a source with deathtouch (…), that creature is destroyed. (…)
701.7a To destroy a permanent, move it from the battlefield to its owner’s graveyard.
704.3. (…) Once (…) state-based actions have been performed (…), the appropriate player gets priority.
510.4. If at least one attacking or blocking creature has first strike or double strike (…), instead of proceeding to the end of combat step, the phase gets a second combat damage step. (…)
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