The Problem Streaks Create
In a pure random system with a 25% chance, each attempt is a fresh draw. That means long streaks are normal. The chance of ten failures in a row is 0.75 raised to the 10th power, about 0.056, so roughly one in eighteen sequences of ten attempts. Streaks of successes also happen. A player who sees a run of ten misses can reasonably feel that something is wrong, even though the system is behaving as stated.
Designers who want players to feel that chance is fair, and who want fights to stay interesting, sometimes use mechanics that smooth out streaks. The most discussed of these is often called pseudo-random distribution, or PRD, though the name is used loosely.
How a Rising Chance Works
The basic mechanism is a counter. Each time an attempt fails, the probability used on the next attempt increases by a fixed amount. When an attempt succeeds, the counter resets and the probability returns to its starting value.
A small example makes the effect visible. Suppose the first attempt has a 10% chance, and each failure adds 10 percentage points. The chances by attempt number are 10%, 20%, 30%, up to 100% on the tenth attempt, so success is certain by then.
To find the long-run success rate, first find the average number of attempts between successes. The probability that an attempt number k is reached is the product of the earlier failure chances:
- Attempt 1 is always reached: 1.
- Attempt 2: 0.9.
- Attempt 3: 0.9 x 0.8 = 0.72.
- Attempt 4: 0.72 x 0.7 = 0.504.
- Attempt 5: 0.504 x 0.6 = 0.3024.
- Attempt 6: 0.3024 x 0.5 = 0.1512.
- Attempt 7: 0.1512 x 0.4 = 0.06048.
- Attempt 8: 0.06048 x 0.3 = 0.018144.
- Attempt 9: 0.018144 x 0.2 = 0.0036288.
- Attempt 10: 0.0036288 x 0.1 = 0.00036288.
Adding these gives about 3.66 attempts per success on average. The long-run success rate is the inverse, 1 / 3.66, about 27.3%.
So a system that starts at 10% and adds 10 points per failure behaves, over the long run, like a flat 27.3% chance. A designer who wants a flat 27.3% effect can choose these numbers, and a player would be told, or would measure, an effective 27% chance. In practice, designers work backward: pick the nominal rate they want to present, then compute the starting value and increment that produce it. The calculation has no simple closed form, so it is typically solved numerically.
What Changes and What Stays the Same
The long-run average success rate matches the target, so over thousands of attempts the total is the same as a flat chance. What changes is the shape of the sequence.
- Long dry streaks become far less likely. In the example, a failure streak cannot exceed nine attempts. A flat 27.3% chance can run well past that; the probability of ten straight failures is 0.727^10, about 4%.
- Back-to-back successes become less likely. After a success the chance resets to its low starting value, here 10%, so immediate repeats occur less often than in a flat system.
- Results cluster around the average. Sequences feel more evenly spaced, which many players perceive as fairer.
This is also why the system produces different short-run results than the flat equivalent. Players with experience of it often learn that after a long gap, the next attempt is very likely to succeed, and that matters for planning.
Events are no longer independent events. The chance depends on recent history, which means the usual intuition that “the previous failure doesn’t matter” is false in this system. It is also different from the gamblers fallacy, where the belief in a due result is mistaken because the underlying system has no memory.
Shuffle Bags as Another Form of Streak Control
A different technique reaches a similar goal without changing a probability. A shuffle bag holds a fixed set of outcomes in the exact proportion desired, for instance one success and three failures to represent a 25% chance. Outcomes are drawn without replacement in random order, and when the bag is empty it is refilled.
With one success and three failures in each bag of four, you are guaranteed at least one success in each full bag, and the longest possible failure streak is six: three failures at the end of one bag followed by three at the start of the next. The long-run rate is exactly 25%. The drawback is that the system is partly predictable, since a player who tracks the bag knows what is left.
Where Games Use These Systems
Streak protection is typically applied to effects that trigger repeatedly in combat, such as critical hits, evasion, stuns and passive item procs, where a long run of either extreme can distort a fight. Reward systems apply a similar idea in the form of a pity counter, which usually goes further by guaranteeing a result. Level generators use bags to place resources evenly.
Not every game documents its approach, and some use a mix of methods. If a game says only “25% chance”, the true behavior may be a flat roll, a rising counter or a bag. Community testing can reveal which, but be cautious about conclusions from small samples, since a modest number of observed events cannot reliably separate a flat chance from a smoothed one.
Tradeoffs
Smoothing makes experience steadier, but it carries costs. It reduces the highs as well as the lows, so extreme lucky streaks are rarer too. It can make results partly predictable, which skilled players can exploit by timing actions. It also complicates calculation: the simple formulas for average damage hold on average, but a short-term estimate needs the sequence rules. For a crit-based build, the average damage output from critical hits is the same, while the experience of a single fight differs.
Designers weigh these costs against the benefit of fewer frustrating outliers, and different games land in different places. The underlying probability remains, the long run matches the stated rate, and the difference is mostly in how bad and good luck are spread over time.