Freeform magic and Gadgeteering are the most common tabletop RPG versions of this.
A variation on this is the concept of "reflavoring" or "reskinning", rewriting a spell, weapon, or ability into something completely different while retaining the same mechanics (or making minor changes, such as turning a fireball into an iceball).
Compare Ascended Fanon.
Named after Schrödinger's Cat.
- The short-lived City of Heroes trading card game had a proxying mechanic allowing players owning the right base card to print a tournament-legal card representing one of their MMO characters, with a website app provided to design said card. The actual allowed variation in game-mechanic terms was character archetype (which determined hit points), travel power (form of mobility), and available primary and secondary power sets. To balance not having the custom innate powers made for the official hero cards, proxied heroes started with three powers in play instead of two.
- Space 1889 there are rules for inventions, players can come up with their own.
- Unknown Armies has this with players creating adept schools, avatar archetypes and tilt ritual types. It has this within adept schools as well, called "random magick" as opposed to formalised spells, with rules for creating spells of one's own. For instance Dipsomancy, alcohol-based magic, features spells that enable characters to glimpse the future, throw objects around and make people drunk among other things, but it's mentioned that it can also be used to do things like reduce falling damage and bend natural law "in a short sighted sort of way" (one player interpretation being the ability to heal himself until he sobered up).
- Houses of the Blooded has mechanics that allowed players to do this to the game setting.
- Nobilis is all about doing anything you can logically infer from control over a word/concept and everything it represents.
- GURPS has a few possible examples, most notably, probably, the Gizmos advantage, but also Modular Abilities, and, heck, Syntactic Magic. Pretty much any advantage can have a series of enhancements or limitations applied to it to make it just the way you want it.
- The Powers supplement describes in detail how to do this with any advantage or disadvantage, allowing the creation of almost any power imaginable in any genre (I say "almost" because it's remotely possible there's one that can't be described).
- Mage: The Ascension, Mage: The Awakening and Ars Magica allow making up magic spells on the spot—the main limit being the number of different "types" of magic the character is skilled with.
- The HERO System has the "Variable Power Pool", which is a set of points that can be used to temporarily buy any power that has that cost or less. It's often bought with assorted limitations to make it less of a Green Lantern Ring Game-Breaker.
- Exalted characters can build their own charms and spells. Of course, the "Storyteller" has to make sure they stay within their archetype i.e. no Gigeresque special effects for Solars (at least at low Essence; there are ways to go transhuman later on), just Ancient Greece-style badass superhumans.
- Spirit of the Century seems to like this sort of thing.
- First you have the "universal gadgets" and "rare artifacts", which can be more-or-less made up on the spot, to whatever specs you need to solve the problem at hand. On the other hand, they're weaker than the alternatives
- "Personal gadgets" and "personal artifacts", which are made up ahead of time, though one of the three improvements might be kept secret to be decided later.
- Finally, if you choose to go in for character creation on the fly, your background and skills can be kept secret and decided later.
- Basically, there are lots of ways you can keep your character's awesomeness under your hat, typically in the interest of drama, or just getting to the fun quickly.
- Variable Energy Pools in Mekton Zeta allow you to build multiple energy weapons and shields into a single component.
- The original Mayfair DC Heroes RPG (later republished by a third party as Blood Of Heroes) was downright RIDDLED with this trope, including:
- Force Manipulation, which could simulate any 'Physical' power, as well as create solid objects of force
- Omni-Power, which could simulate all but the most expensive powers for a small in-game fee
- Sorcery, which could simulate ANY power, but if used at too high a level could potentially wear out the caster (aka Spirit damage)
- Omni-Connection, where the character can pay a small fee during gameplay and say, "Say, I happen to know someone who works there!" or the like.
- Omni-Gadget, where a character simply pays a points cost before hand to have a certain number of Schroedinger's Gadgets that just happen to be what he brought with him, like the Bat Shark Repellent Spray on the day he happens to be attacked by an exploding Great White Shark.
- In the Hong Kong Action role playing game Feng Shui, even minor scene details can be made up on the spot by the player. That punch bowl you threw in the face of the guy you were fighting wasn't there until you said it was.
- The Dragonlance: Fifth Age Dramatic Adventure Game has a freeform spellcasting system for the most part. The limitation is that the character can only know a certain number of schools or spheres of magic, such as Pyromancy or Animism. They can do anything within the confines of the schools or spheres they know and that they have enough spell points for (And succeed at the card draw!).
- Risus. The players get to, essentially, create their own character classes from scratch.
- World Tree gives players access to divine Nouns and Verbs, which can be combined to produce virtually any magical effects imaginable.
- TOON offers Gizmos, "placeholder" items that can be anything the player wants (the example given is a mouse just happening to have an electric pencil sharpener handy to shove a cat's tail into). Once a Gizmo's nature is revealed, it's stuck that way for the rest of the cartoon.
- The Star Trek: The Next Generation RPG by Last Unicorn Games uses this for minor items that are common enough on Starfleet ships that it would be impractical for a GM to track the location of every last one of them, like phasers, medical kits, and tricorders. Instead, unless a player specifically declared that they were equipping themselves with one before getting into their current situation, a player can make a search roll. If they score high enough, it turns out there was a phaser there the whole time. Of course if the PC leaves the ship, then there seem to be a lot fewer phasers and tricorders just lying around.
- This is used frequently used by Ben (who role-plays Obi-Wan) on Darths & Droids, usually in response to Jim (Qui-Gon, Padmé) declaring some bizarre use of an object or something to that effect. Two major examples are when Jim tries to use his Laser Sword to deflect the Battle Droids' bullets and when he tries to make Anakin a Jedi with his blood. Ben is one clever guy.