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Randomness is sometimes rejected from competitive gaming since it can decide over loss and defeat without reflecting the actual skill level. However, coping with the unexpected is an aspect of skill. Nonetheless there are a couple of random events within Dota 2, that keep the game less predictable and static. To limit the influence of huge streaks, pseudo-random distribution replaces the true random distribution where it made sense for the developers.

The effects of PRD on the number of attacks until the next proc.

Proc chance of PRD effects

The probability of an effect to occur (or proc) on the N-th 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.

Technically, if corresponds to the event occurring on trial and is the inverse of that event, pseudo-random distribution enforces that for all . Also, when , which occurs on the first trial where , the event is guaranteed if it has not already happened. This results in a distribution where .

On melee heroes, ‘s Bash has a 25% chance to stun the target. On the first attack, however, it only has an ~8.5% probability to bash. Each subsequent attack without a bash 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 bash occurs, the probability resets to ~8.5% for the next attack. These probabilities average out so that, over a moderate period of time, Bash effect 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 abilities in Dota 2. Gameplay wise, PRD is difficult to exploit. It is theoretically possible to increase your chance to bash or critical strike on the next attack by attacking creeps 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 a hero with critical strike attacking buildings does not increase its chance to critical strike on its next attack, since critical strike does not work against buildings. The chance is not reset/increased as long as the ability is on cooldown as well (e.g. Bash).

Some mechanics roll a random value between 0 and 1 and scale it along the minimum / maximum gradient. This includes

A couple of random events have discrete states that have similar probability.

Along with the listed abilities, all Evasion sources and the drop chance of neutral items use pseudo-random distribution as well.

1 Requires talent.

2a Requires .

2b Requires .

### Hero and Unit Abilities

Other Hero and Unit Abilities