Probabilistic event

All main entries and most side entries in the Final Fantasy series feature events whose outcomes are probabilistic. Probability values are either hardcoded, or derived by composing various parameters and stats.

Probabilistic events must not be confused with pure randomness, which is the result of generating of a random value for use in formulas (e.g. variance in damage formulas, or purely random damage rolls), rather than for comparison with probability values.

Mechanics

Whenever an outcome X has a probability of P/Q of being triggered, the game selects a value N from a [0..Q-1] uniform random distribution. Then, it compares N and P:

• If $N<P$, then X is triggered.
• If $N\geq P$, then X is not triggered.

This is a standard way for software to simulate probabilistic events. The main discriminating factor between different systems is the implementation of the random number generator (RNG or rng for short).

Percentages

Sometimes, the probability of X is expressed as P% for human readability. As P% is equivalent to P/100, the game simply uses a [0..99] uniform random distribution.

Somewhat confusingly, certain games express probabilities as percentages using values greater than 100% (for example, 150%). In these cases, the calculation is often based on a Q value larger than 100, such as 127 or 255. In other situations, the "%" symbol does not indicate a true percentage, but represents a parameter used within a more complex formula (for example, the Hit stat in Final Fantasy VIII).

100+%

Sometimes, due to game mechanics, real probabilities higher than 100% are involved (i.e. expressed as improper fractions, unlike the cases described in the previous section). Usually, the game does not automatically rescale them to 100%, because they may be required in their original form for basic arithmetic (e.g. the computation of status affliction probability in Final Fantasy X).

Outcome determination does not change when the probability of X is expressed as an improper fraction. However, it trivially descends that N < P for all possible values of N (i.e., X is always triggered).

Appearances

Final Fantasy

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Final Fantasy II

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Final Fantasy III

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Final Fantasy IV

Stat bonuses tied to leveling up past level 70 are probabilistic. Each character has a table of available stat boosts (or penalties) from which an outcome is randomly selected and applied.

Final Fantasy V

Most physical and magical actions can hit or miss their target(s) according to a sequence of probabilistic checks, including, but not limited to the Catcher special property, hit rate, evasion, and magic evasion.

Some commands have multiple probabilistic outcomes:

• !Steal
• !Mug
• !Call
• !Animals
• !Gaia
• !Dance

Some spells across most spell classes have probabilistic outcomes (other than the aforementioned hit or miss probability):

• !Time: each targetable opponent has the same probability of being targeted by each hit of Meteor.
• !Blue: each targetable unit on the field has the same probability of being targeted by Roulette.
• !Summon: both Chocobo and Odin have alternate outcomes that, at least partially, depend on probability.
• !Mix: one of the three Dud Potion mixes (Turtle Shell + Elixir) can either inflict sap on a vulnerable target (75% probability), or reduce a non-heavy target's HP to a single digit value (25% probability).

Some enemy abilities have probabilistic outcomes:

• Blaster
• Grand Cross

Added abilities and added statuses have a predetermined probability of being triggered.

Each targetable opponent has the same probability of being targeted by a reflected spell.

In any given area (including the world map) where it is possible to run into random encounters, there are 4 possible random battle formations (some of which may coincide), each with its own probability of appearing.

Stolen and dropped items are received according to fixed probabilities.

Final Fantasy VI

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Final Fantasy VII

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Final Fantasy VIII

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Final Fantasy IX

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Final Fantasy X

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Final Fantasy XII

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Final Fantasy XIII

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Final Fantasy XV

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Final Fantasy XVI

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