Random resolution, also called stochastic resolution, is a type of resolution in which the game mechanics use randomness, generally to introduce an element of risk or uncertainty. Random resolution is referred to as fortune in the terminology of GNS Theory and the Big Model.
Random resolution is rarely wholly random, and the odds of success (or other relevant outcome) are usually affected by character traits or statistics or by the fictional positioning of the situation, or both. These may be built into the resolution mechanic by means of modifiers, target numbers, adjustments to dice pools before rolling, or other means. For example, Dungeons & Dragons 5th edition's core resolution mechanic uses both character statistics and fictional positioning, applying a modifier based on statistics (primarily abilities) and adjusting the target number based on the situation (which may itself depend on the statistics of another character). A certain amount of judgement may be applied to determine these where they are not set explicitly by the rules of the game, particularly by the GM, but the resolution method is still random resolution (not judgemental resolution) as long as procedures determine the outcome based at least partly on randomness.
Random resolution relies on the use of randomisers. The most commonly used randomisers used in role-playing games are dice, but playing cards are also common. Others that have been used include non-standard playing cards (e.g. Tarot cards), random number generators on devices, picking tokens out of bags, etc.
Applying randomness "in the Middle" or "at the End"Edit
Something that is unique to random resolution is the timing of the random elements within the overall resolution mechanic. If the random element is the final step of the mechanic and absolutely determines the outcome, this is called Fortune at the End (FatE). However, if there can be further non-random resolution after the random element is performed, e.g. negotiation or spending player resources to affect the outcome, this is called Fortune in the Middle (FitM). (In both cases, the word "Fortune" refers to random resolution using the terminology of GNS Theory and the Big Model.) The mechanical parts that take place after the random input are usually similar to different types of resolution, i.e. deterministic or judgemental resolution.
These terms are somewhat confusing and have been widely misunderstood outside the culture of The Forge in which they were created (see also: Forgespeak). In particular, the terms do not indicate the timing of the resolution mechanic within the overall resolution process (e.g. whether dice are rolled before or after the action is described), but only the timing of the random element within the mechanic itself. Nor does the presence of a "Middle" and "End" imply a third category of Fortune at the Beginning, because this is covered in the definition of "in the Middle". (More descriptive terms could be "randomness at the end" and "randomness before the end".)
Fortune-in-the-Middle mechanics in which the part of the mechanics that takes place after the randomised element can alter the overall outcome (e.g. from a success to a failure or vice versa) are sometimes said to have "teeth" or be "with teeth". FitM mechanics in which the part of the mechanics after randomness can modify the effect without changing the overall outcome are sometimes said to be "without teeth".