While I explore this site, I occasionally see the phrase "GM fiat" (or "DM fiat", for D&D questions and answers), but I don't know the exact meaning of that. I want to know the meaning of that terminology.
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In a large number of RPGs, the GM is positioned as the controller of the world, its NPC inhabitants, the items in the world, and their essential natures. They are also often positioned as the final arbiter of rules, and thus hold considerable authority. Hopefully, a GM imbued with such power will remember: with great power comes great responsibility.
That said, a fiat is defined as:
So a GM fiat is when the GM says something is the case - because they have the authority to do that - and it becomes the case.
A GM fiat is produced independently by the GM. It is separate to decisions made by the group as a whole: a GM can declare a house rule as a GM fiat, but that's different to the group producing a house rule together.
Implicitly, the GM is not required to justify or explain their fiat - these things just happen because you're the GM and get to make them happen.
Because GM fiats are arbitrary and can involve major changes (like the changing of the rules themselves), the motto of "with great power comes great responsibility" is massively relevant. These changes could make the game more fun or extremely un-fun for players.
Some examples of usage of GM fiat
Fiat comes to English from the Latin Fiat, which is the third-person passive subjunctive of Fiere (to do), basically meaning "Let it be done".
It is used in English usually to mean a decree or judgement, so a "GM Fiat" is essentially a way of saying "The GM says this is the way it is, so this is the way it is, no arguments."
Fiat in Latin means "let it be" or "let it be done". It roughly means to make a decree.
DM/GM Fiat in particular is generally considered the act of a GM arbitrating things not covered by the rules, declaring house rules or creating a rules clarification that does not exist in the pre-written material.
Fiat: by decree.
In the context of gaming, GM Fiat means, literally, "because the GM says so."
Anything more is context dependent.
DM Fiat often goes along with what is also known as Rule Zero: The DM's judgement is final and supercedes all other officially documented rules. Essentially, they have the ultimate authority, and can make any decision they wish without being able to be overruled. As with any such dictator-like power, this can be used for either good or ill, but has become most famous for the worst of examples, such as with DMs making abusive or simply foolish decisions.
This rule can be considered inaccurate, however, and an additional term has come to represent this fact: Rule Negative One: What the gaming group as a whole agrees upon is final and supercedes even Rule Zero, because if everyone is unhappy, then they will leave and there simply is no game. It's useful to remember that a DM can not truly bully the players, because it is just a game, and everyone can just opt to not play with them; perhaps go play a new game with a new DM that doesn't make such abusive fiat decisions.