Pseudo-Random Distribution (PRD)

Excessive randomness usually generates wild behavior that, although consistent with mathematical models, clash with players' perception of fairness, which is integral to good game design.

Relic Hunters Legend uses considerable amounts of Random Number Generation (RNG) in a lot of different systems such as Loot Drops, Critical Hits and Dodge Projectile%. To keep things fair and more predictable, without huge streaks of either positive or negative events, "true" RNG is replaced by Pseudo-Random Distribution (PRD) in some particular situations, as noted throughout this Wiki.

The contents of this page have been sourced from the Dota2 Gamepedia Wiki article with the same name.

## Definition

The uniform or "true" random distribution describes the probability of a random event that underlies no manipulation of the chance depending on earlier outcomes. This means that every "roll" operates independently.

Pseudo-random distribution (PRD) refers to a statistical mechanic of how certain probability-based items and abilities work. In this implementation the event's chance increases every time it does not occur, but is lower in the first place as compensation. This results in the effects occurring more consistently.

The probability of an effect to occur ("proc") on the Nth test since the last successful proc is given by

For each instance which could trigger the effect but does not, the PRD augments the probability of the effect happening for the next instance by a constant C. This constant, which is also the initial probability, is lower than the listed probability of the effect it is shadowing. Once the effect occurs, the counter is reset.

*On the first attack, however, the Condition only has an ~8.5% probability to proc.*
*Each subsequent attack without a proc increases the probability by ~8.5%.*
*So on the second attack, the chance is ~17%, on the third it is ~25.5%, etc.*
*After a proc occurs, the probability resets to ~8.5% for the next attack.*
*These probabilities average out so that, over a moderate period of time, it procs nearly 25% of the time.*

Effects based on PRD rarely proc many times in a row, or go a long time without happening. This makes the game less luck-based and adds a great deal of consistency to many probability-based Skills.

Gameplay-wise, PRD is difficult to exploit. It is theoretically possible to increase your chance to Critical Hit on the next attack by attacking enemies several times without the effect happening, but in practice this is nearly impossible to do.

Note that for instances that would not trigger the effect, the probability counter does not increase, so you can't increase your Critical Hit Chance by shooting at a box (that is immune to Critical Hits) and then shooting an enemy.

## Percentages

The probabilities listed in the game are theoretical percentages, which are slightly higher than the actual probabilities.

**P(T)** is the theoretical probability;

**P(A)** is the actual average;

**C** is the PRD constant;

**Max N** is the minimum number of rolls that would result in C × N becoming greater than 1 (i.e. guaranteed proc);

**Average N** is the expected value of N: the sum of the products of N and probabilities;