Basic Trope: The villain unwittingly gives the hero an advantage.
Straight: Emperor Evulz kidnaps and holds the hero's sister ransom. Unknowingly, the hero's sister was holding the hero hostage to get an artifact of evil to offer to Evulz.
Exaggerated: Emperor Evulz turns on a light-switch.It turns out to also cut enough power from the hero's binds to allow them to escape.
Downplayed: Evulz holds the hero's sister ransom. The sister was looking for a way to get close to Evulz but didn't know how.
Hey, how was Evulz supposed to know?
Evulz actually wants to help Albert, possibly because Albert isn't actually a threat to his goals or there is a looming Bigger Bad, but being seen doing it would cause too many problems, so he appears to be "accidentally" helping.
Enforced: "Oh, shit... Evulz is gonna win at this rate, and it's too late to change it! Oh! Make him accidentally give Albert an advantage!"
"Nice job helping him, Evulz!"
"You know, I really thought that would end with you dying horribly and me not feeling like a complete idiot..."
Invoked: Evulz is a powerful manipulator but weak in combat, so after so long he starts to relax and make plans that leave him more open.
Exploited: Carly, The Starscream, looks everything over, and realizes how many things are on the needles edge of aid to the hero. After giving some suggestions to Evulz that seem like a good idea, she causes his death and take his place, planning a much better job.
Defied: Evulz refuses to do anything that isn't on a strict and controlled plan unless the risk is needed or worth it, that way he minimizes his self-harm.
Evulz: I have to be careful, who knows what might help the heroes, I'm pretty sure my beast has seen them before.
Conversed: "Oh, dear, Evulz just released the beast that the heroes helped, the beast won't be happy".
Deconstructed: Evulz becomes rather paranoid about how much he does that helps the heroes. Soon enough he goes on a rampage that ignores both Evulz's main objective and kills many people on all sides.
Reconstructed: Before breaking down, Evulz starts to think, and realizes that the heroes do this for him as well. Soon enough he has an ever better plot that uses the heroes to his advantage.