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This always struck me as odd in the Deathly Hallows. Yes, Voldemort was wrong in the end thinking that one becomes the master by killing the previous owner. But even acting according to his own theory, he seems to be rather illogical and inconsistent.
This all boils down to his decision to kill Severus Snape (spoilers) in order to, in his mind, become the master of the Elder Wand. So he basically thought Snape was the master because he killed Dumbledore, and by killing Snape he himself would become the new master. But according to his logic, wouldn't every single previous master had to been killed by the next one?
So in order for Dumbledore to become the master, he should have had killed Grindelwald. But Voldemort was perfectly aware that he didn't, Grindelwald was still alive when Dumbledore died. Wouldn't this raise a question in Voldemort's head, that if Dumbledore really were a master of the Elder Wand, shouldn't there be another way to become one? And even more so, even Girndelwald didn't kill the previous master, Gregorovitch.
Then what he thought he was going to benefit from killing Snape? Because, according to his own logic, that one becomes the master of the Elder Wand by killing the previous master, neither Snape, Dumbledore, nor Grindelwald were ever its masters. According to his own logic, Voldemort should have been the master at the moment he killed Gregorovitch himself, yes?
Voldemort doesn't seem to be that stupid to make this kind of logical mistake but this all makes me think that he would have needed a bit of help from Professor Quirrell to get them past the potion riddle during their pursuit of the Philosopher's Stone.