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Random number generator
- "RNG" redirects here; for the stat abbreviated as "Rng", see range.
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The random number generator (or RNG) is a system that randomly generates numbers. Randomness is present in almost every game in the Fire Emblem series, primarily in the results of combat. As with most computer systems, random numbers in Fire Emblem are not truly random but pseudorandom—they simulate randomness with a deterministic series of numbers. When and how random numbers are generated changes from game to game.
Events that use random numbers include:
- Attacking or being attacked
- Leveling up
- Creating a unit with randomly leveled-up stats
- Creating one of several possible "diagonal" paths
Generation
In the first three games, random numbers are "burned", and change each frame; while in later games they only change once they are used. In most cases, only a single random number is used to determine the outcome of a random event. However, in games that use true hit—The Binding Blade being the first of which—two random numbers are used and averaged to determine whether an attack hits.
Shadow Dragon & the Blade of Light, Gaiden, and Mystery of the Emblem
Random numbers are saved as an eight-bit integer (ranging 0–255) that increments by 55 each time it is used, including when it is burned.[1] In Fire Emblem: Shadow Dragon & the Blade of Light, the eight-bit integer is multiplied by 10 and divided by 25, then truncated—this allows for numbers ranging from 0–102, but all numbers above 100 are reduced to it; in Gaiden and Mystery of the Emblem, the integer is multiplied by 100 and divided by 256, then truncated, allowing for a range of 0–99.[1]
Thracia 776
Random numbers are stored as eight-bit integers (ranging 0–99). In many occasions like at the start of a chapter or when closing a unit stats screen, the game will generate a new sequence of random numbers using the Knuth's substractive generator. The 55 first numbers are generated with an initial seed equal to a RAM value increasing by 1 every frame, looping from 1 to 64, and the following values are generated with the formula:
RN[N] = (RN[N-55] - RN[N-24]) modulo 100
One consequence of these rules is that there are only 64 different sets of stats for units generated at the start of a chapter. Also, the randomness is not perfect and some of the numbers can be predicted, for example the 35th random number will always be equal to 94 regardless of the seed.[clarification needed]
For the purpose of random events calculations, random numbers 0 are treated as 100.
The Binding Blade, The Blazing Blade, The Sacred Stones, and Path of Radiance
Random numbers are stored as sixteen-bit integers (ranging 0–65535). The three initial random numbers are generated at startup, and are always the same for the GBA games. For Path of Radiance, based on the GameCube internal clock, the three initial random number are chosen between 7 different sets of 3 numbers, and up to around 30 extra numbers can be burned after that.[clarification needed]
The following random numbers are generated with the bitwise operation:
RN[N] = ((RN[N-1] >> 5) XOR (RN[N-2] << 11) XOR (RN[N-3] << 1) XOR (RN[N-2] >> 15)) modulo 65536
For the purpose of random events calculations like battles or leveling up, these numbers are divided and truncated. In The Binding Blade, the integer is divided by 655, allowing for numbers 0–100; in the other games, the integer is multiplied by 100 and divided by 65536, allowing for numbers 0–99.[2]
This oversight in The Binding Blade means that it is possible to miss 100% accurate attacks; a 1RN value, such as a staff with 100 displayed hit, may miss 0.055% of the time, and a 2RN value with 100 displayed hit, such as a regular attack, may miss .00006% of the time.[3]
New Mystery of the Emblem
Random numbers are stored as sixteen-bit integers (ranging 0–65535). The four initial random numbers are generated at startup with two Mersenne Twister algorithms in a row, with the first seed based on the DS internal clock.[4]
The following random numbers are generated with the bitwise operation:
RN[N] = ((RN[N-4]) XOR (RN[N-4] >> 8) XOR (RN[N-4] << 3) XOR (RN[N-4] << 11) XOR (RN[N-1]) XOR (RN[N-4] >> 19)) modulo 65536
Like the previous games, the integer is multiplied by 100 and divided by 65536, allowing for numbers 0–99.
Attacking or being attacked
Depending on whether the game uses true hit or not, either one or two random numbers are expended to determine whether an attack hits or misses. If the attack hits, another random number is spent to determine whether the attack is critical or not. Certain games expend additional random numbers for additional effects. In The Blazing Blade and The Sacred Stones, for example, there is a probability for an Assassin's critical hit to activate Silencer, and so an additional random number is spent if an attack is critical in those games, even if the attacker is not an Assassin.
Leveling up
- Main article:
Growth rate
When a unit levels up, random numbers are used to determine whether each stat increases or not. The odds of a stat increase for a specific unit are determined by the unit's personal growth rates, and—when applicable—their class. Some games also provide items and skills that boost a unit's growth rates, such as the Starsphere in Fire Emblem: Mystery of the Emblem or the Aptitude skill.
In the GBA games, each level-up uses seven RNs to determine whether or not HP, strength/magic, skill, speed, defense, resistance, and luck increase, in that order.
Additionally, in Thracia 776, enemy stats are treated as though they had leveled up, and can therefore vary between playthroughs and resets. As a side effect of the way RNs are generated, every enemy present at the start of a chapter will only have 64 possible stat layouts. The GBA games also have enemy stats based on their growths with added randomness, though they are calculated in a manner that results in far less variance than in Thracia.
Some games have mechanics to prevent a level-up from not increasing any stats and therefore limiting randomness:
- In The Binding Blade, The Blazing Blade, and The Sacred Stones, if a level-up would not increase any stat, the level-up will be re-rolled up to two times. If a level-up would increase an already capped stat, it is considered a stat increase and will not be re-rolled. If both re-rolls fail to increase a stat, the level-up will not grant any stat increases.
- In Fire Emblem: Radiant Dawn, level-ups always increase at least one stat unless the unit in question already has all of their stats capped. If all of a unit's growth rates are modified to be 0% through hacking, the game will force a stat increase in HP. Additionally, level-ups through bonus experience always increase exactly three stats unless the unit has less than three un-capped stats.
- In Fire Emblem: Shadow Dragon, a unit's odds of increasing a stat through level-ups increases after it fails to increase on a level-up.
- In Fire Emblem Echoes: Shadows of Valentia, blank level-ups are forced to increase HP. However, if the HP cap of 52 is reached, blank level-ups are possible.
- In Fire Emblem: Three Houses, Byleth, Flayn, Cyril, and all members of the four houses are guaranteed to increase at least two stats on level-up. If a level-up hits a capped stat, it is counted as a stat increase. If a level-up would increase only one stat, that stat will not be rerolled.
In Fire Emblem Fates's Lunatic difficulty, a unit's level-ups are determined when they are first recruited, and therefore cannot be rerolled through resetting.
Fire Emblem: Path of Radiance and Fire Emblem Engage have an optional, fixed mode where level-ups are not determined by randomness. In both games, Fixed Mode is unlocked after completing the game once; in Engage, Maddening difficulty defaults to Fixed Mode.
Creating a unit
Random numbers are used to determine the stats of most enemies as they spawn. This is most evident for enemies in Arena battles. In the GBA games, for example, level 1 unpromoted enemies do not receive bonuses to their stat levels, but level 2 or higher enemies and promoted enemies do; thus the former do not use up as many random numbers as the latter.
Creating a path
When the game is forced to create one of several possible paths (usually by moving a unit to a point that is at a diagonal to its original position), it uses the RNG to determine which path to take. This can also be done by the player, if one controls a unit with odd-numbered movement.
In the GBA games, paths are drawn backwards from the unit's destination to its original position, and when either horizontal or vertical movement is possible, a low RN (between 0 and 49) will generate a horizontal path, while a high RN (between 50 and 100) will generate a vertical path. For example, if a the game is forced to generate a diagonal path one space up and to the right, a low RN will result in a path leading to the left from the unit's destination, then down to the unit; a high RN will result in a path leading down from the unit's destination, then left to the unit. The second of these two steps does not use an RN because there is only one possible way to create the path from that point.
Miscellaneous
In Fire Emblem: Thracia 776, every time the Combat Info window is opened, the game will simulate a round of combat, burning RNs as if the units entered combat. This will also happen every time a button on the directional pad is pressed to change the target, even if there is only one possible target.
