Does double strike apply both first strike and regular combat damage?

Double strike is a keyword ability defined in CR 702.4b. A creature with double strike assigns and deals combat damage in both the first strike combat damage step (if it or any other creature has first strike or double strike) and the normal combat damage step. This means it effectively strikes twice per combat.

This is handled by CR 510, which governs combat damage steps. CR 510.1 specifies that if any attacking or blocking creature has first strike or double strike, a first strike combat damage step occurs before the regular step. CR 510.4 then clarifies that a second combat damage step follows for creatures with double strike, and for any creatures without first strike that survived the first step.

A practical consequence is that a double strike creature can potentially kill a blocker in the first strike damage step and then deal its damage again — either to a new blocker or directly to the opponent — in the regular damage step, though in practice the damage in the regular step still goes to the original assignment unless the blocker is removed from combat.

Concrete example: You attack with a 2/2 creature that has double strike. Your opponent blocks with a 2/2. In the first strike damage step, your creature deals 2 damage, killing the blocker. In the regular combat damage step, your creature deals 2 damage again — but since the blocker is now dead, that damage goes to the defending player.

Note that double strike is different from two separate instances of first strike. It is a single keyword (CR 702.4) that grants participation in both damage steps, and effects that remove first strike do not automatically affect double strike unless they specifically reference double strike as well.