What is the ruling on someone who vowed to completely abandon the sin of masturbation, then returned to it, knowing that he did not specify anything in particular like fasting or charity?

A vow (nadhr) that a person utters in the form of an oath (yamin) to urge himself to do something or to refrain from it, without intending it as a vow or an act of drawing closer to Allah, takes the ruling of an oath. If he does not fulfill it, an expiation for an oath (kaffarat yamin) becomes obligatory upon him. This is called a vow of obstinacy and anger (nadhr al-lajaj wal-ghadab). If the vow is ambiguous, such as when one says, "A vow is incumbent upon me for Allah," without specifying anything, then an expiation for an oath becomes obligatory according to the majority of scholars, due to the saying of the Messenger of Allah, peace and blessings be upon him: "The expiation for a vow when nothing is specified is the expiation for an oath."