True randomness can feel unfair
A fixed-chance roll is memoryless. Every attempt has the same probability, however many came before. That is statistically honest, but it produces streaks that players find frustrating and, on the other side, runs of success that feel excessive. In a competitive setting, a long unlucky run can decide a match, which is hard to accept when the event was pure chance.
Pseudo-random distribution, often abbreviated PRD, is a response. Instead of rolling the same chance every time, the game gives each failure a small boost to the next attempt’s chance, and resets the chance after a success. The sequence is still random, but extreme streaks become much less likely.
How the mechanism works
A simple version looks like this:
- Start with a low chance on the first attempt.
- Every time the attempt fails, raise the chance by a fixed increment.
- When an attempt succeeds, reset the chance to the starting value.
- Eventually the chance reaches 100 percent, so a long streak is impossible.
Games that use this approach usually describe the event with a nominal percentage, such as a 25 percent chance to trigger an effect. The real starting chance is lower than that, and it climbs so that, over many trials, the average success rate matches the nominal figure.
A worked example
To see how this changes things, consider a deliberately simple system. The first attempt has a 10 percent chance. Each failure adds 10 percentage points, so the chances are 10, 20, 30, up to 100 percent on the tenth attempt, then reset after a success.
The probability of still having no success before each attempt is:
- before attempt 1: 100 percent
- before attempt 2: 0.9, or 90 percent
- before attempt 3: 0.9 x 0.8 = 0.72
- before attempt 4: 0.72 x 0.7 = 0.504
- before attempt 5: 0.504 x 0.6 = 0.3024
- before attempt 6: 0.3024 x 0.5 = 0.1512
- before attempt 7: 0.1512 x 0.4 = 0.06048
- before attempt 8: 0.06048 x 0.3 = 0.018144
- before attempt 9: 0.018144 x 0.2 = 0.0036288
- before attempt 10: 0.0036288 x 0.1 = 0.00036288
The average number of attempts until a success is the sum of those probabilities, which is about 3.66. That means that in the long run one attempt in about 3.66 succeeds, or roughly 27.3 percent. So a system that “starts at 10 percent” is, in effect, close to a 27 percent proc chance.
Compare that with a fixed 27.3 percent chance. The odds of ten failures in a row would be about 0.727^10, around 4 percent. In the rising system that chance is exactly zero. The average rate is similar, but the extremes have been trimmed.
Why the extremes shrink both ways
Resetting after a success matters as much as the boost after a failure. Because the chance drops back to the low starting value, two successes in a row become less likely than under fixed odds. In the example, the chance of a success on the attempt right after a success is only 10 percent, not 27 percent.
That means PRD reduces both bad streaks and lucky streaks. Outcomes become more even, which is why designers use it for effects that are meant to feel reliable, such as a chance to trigger a special attack. The idea of designing randomness around player experience is a recurring theme in random mechanic design, and it is closely related to how critical hits are handled in some games.
What it changes for the player
- The stated percentage is not the per-attempt chance. The real chance on any given attempt depends on how many misses came before it.
- Past results do matter. After a miss, the next attempt really is more likely to succeed. This is the opposite of a memoryless system, and it is why the reasoning in the article on the gambler fallacy does not apply here.
- Streaks are bounded. There is a maximum number of failures, so the worst case is limited.
- Short-term variance falls. Over a handful of trials, results cluster more closely around the average than with fixed odds.
That last point means random clumping, the natural tendency of independent random sequences to produce runs, is deliberately suppressed.
Comparing with pity timers
PRD and pity timers share the idea of raising the chance after failures, but they usually sit in different places. PRD tends to be used for repeated in-combat events with a moderate chance. Pity timers are generally found in rare reward systems, where the aim is a guaranteed reward after a set number of misses. The distinction is covered in the article on pity timers: one is a streak limiter for frequent events, the other a safety net for rare ones.
How to evaluate such a system
If a game documents its constants, you can compute the effective rate and the distribution of streak lengths. If it does not, a large number of recorded trials can approximate the pattern, though you would need a sizeable sample before the pattern becomes visible. Short observation windows will show noise either way.
The main takeaway is that a percentage given for a PRD effect is a long-run average, not a roll you can assume is identical every time. Understanding which kind of randomness is in play is the first step to reasoning correctly about what to expect.