Double strike does not work at all with equipped creatures
If a creature is supposed to gain double strike through an effect that grants double strike specifically to equipped creatures (e.g. blacksmith's talent, cloud planet protector), if the creature is blocked, it will only deal first strike damage and will not deal damage in the normal damage step. Unblocked creatures granted double strike through the same effect (e.g. blacksmith's talent) will deal damage in both steps.
Khalid#08921
shared this idea
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Rezzahan#77802
commented
A blocked attacker that has no blockers left when it comes to assign combat damage, assigns NO combat damage. Unless it has trample or a similar ability allowing it to do so despite being blocked. Just because all blockers are gone does not make a blocked attacker unblocked.
509.1h An attacking creature with one or more creatures declared as blockers for it becomes a
blocked creature; one with no creatures declared as blockers for it becomes an unblocked
creature. This remains unchanged until the creature is removed from combat, an effect says that
it becomes blocked or unblocked, or the combat phase ends, whichever comes first. A creature
remains blocked even if all the creatures blocking it are removed from combat.510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are
currently blocking it (if, for example, they were destroyed or removed from combat), it assigns
no combat damage. If exactly one creature is blocking it, it assigns all its combat damage to that
creature. If two or more creatures are blocking it, it assigns its combat damage to those creatures
divided as its controller chooses among them.