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In an open ended tabletop RPG, game balance is sometimes hard to achieve and, with an unlimited number of choices available to the players, a Game Breaker is inevitable, especially if you have a Rules Lawyer at your table. For this reason, most games mention some version of Rule Zero: The Game Master is always right.
Rule Zero is simply a reminder to the players that the Game Master has to exercise some common sense and is permitted to supersede the rules when the rules would ruin enjoyment and fair play. While a Game Master has fiat to exercise Rule Zero at their table at will, they are reminded that excessive arbitrary use of this rule will eventually lead to an empty game table.
Railroading is an example of excessive use of Rule Zero.
- Mutants and Masterminds is notable for having a game mechanic for rule zero called "gamemaster fiat." The gamemaster is permitted to arbitrarily create setbacks to keep his story on track (such as having a hero slip and fall if he's about to catch the bad guy long before the adventure says he should) but requires that the Gamemaster award the hero a hero point (which players can spend later on to perform impressive feats normally beyond their abilities.)
- Players can go a step further with "complications" which are specific recurring dramatic setbacks that a GM can use on a player that fit the player's character concept. A common example is the secret identity.
- Paranoia is notable in that it's one of the few Tabletop Games in which arbitrary use of Rule Zero is encouraged. The DM is allowed to fudge rolls, to let other plays fudge their rolls or fudge each other's rolls, and generally discard the rules as long as Rule of Fun is observed. The justifying reason for this caveat? Any player who tried to call the DM out on it would be acknowledging they have read the rules, which are above their security clearance. 
- B.A. From Knights of the Dinner Table averts this. He plays every rule for better or for worse. He eventually seized control of his game through the use of a GMPC and his control over non mechanical story elements (even in the PC's backstories.)
- To a degree, this is true of almost every GM in the Knights of the Dinner Table universe. A HackMaster GM is accredited by a national association before being allowed to run an "official" campaign. Years' worth of legal precedent have gone towards removing the concept of Rule Zero from accredited, tournament legal campaigns. After all, since tournaments usually involve opposing groups and characters competing against one another, it makes sense to ensure that they're all playing on the same page. This has evolved into the "Rules of Fair Play" doctrine, where all rules introduced into the campaign apply to both characters and NPCs without bias or discrimination, effectively removing a GM's judgment from the equation. This environment makes B.A., and other GMs, extremely creative umpires who arbitrate how invoked rules play out within their games.
- Weird Pete is the opposite extreme enforcing Rule Zero through demerits that can result in level loss and can only be undone by working them off in his gameshop unpaid.
- Averted hard in World of Synnibar, which actually imposes limits on what the GM can and cannot do:
"Fate [the GM] has absolute control during the game regarding rolls and interpretation of the rules. Fate may not, however, deviate from the rules as they are written, for if he or she does and the players find out, then the adventure can be declared null, and the characters must be restored to their original condition, as they were before the game began."
- For reference, the rules are Ultraviolet-level, the top of the ladder, whereas most players are Red, just one rank above the bottom. Possessing knowledge above your security clearance is punishable by summary execution.