D&D 5E - How exactly does a Paladin break it's Oath?

Well, typically you pick an alignment within one step of your god. IE: Pelor doesn't have evil paladins. Gods of chaos and destruction tend to not be overly fond of people who support the rule of law and the growth of stable civilization. But in 5E it's largely thematic unless your DM is enforcing more specific rules.

But you're asking about how you break your oath, okay, and you're an Oath of the Crown paladin, so good or evil, you support law, order and civilization. You probably follow a King of some kind. So if your oath is to serve the causes of an evil king you are probably doing stuff like killing his enemies, scaring people in submission, all to preserve the law, order and civilization of your land as your King sees it.

So to break you oath you would probably have to do chaotic, unlawful things, like killing loyal supporters of the King when the King has not ordered it, and they have violated now laws. You could also be assisting rebel groups, as those people would most likely be attempting to overthrow the King you pledged your loyalty to.

Keep in mind: breaking your oath doesn't make you an oathbreaker paladin. It is not a shortcut into the class out of the DMG; which was intended to be for good paladins who have turned evil, not evil paladins who want to be more evil.

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