What a pity timer is
In many gacha and collectible games, a player spends a currency for a random pull from a pool of rewards. The best rewards have low chances, so without any protection a player could in principle go a very long time without one. A pity timer is a rule that limits this: a hidden or visible counter tracks the pulls since the last top-tier reward and the game guarantees one once the counter reaches a set number.
Details vary widely. Rules may differ by game, by event and by version, and they are not always documented. The examples below use made-up numbers to show the shape of the maths, not any particular game’s real rates.
Waiting time without a pity rule
Take a top-tier reward with a 2% chance per pull and independent pulls.
- The chance of no success in the first 50 pulls is 0.98⁵⁰, which is about 0.364, or 36%.
- The average wait is 1 ÷ 0.02 = 50 pulls.
- The most likely single result is success on the very first pull (2%), and the chance falls slightly with each later pull.
The distribution has a long tail. Some players succeed early, and a meaningful minority wait well beyond the average. The same arithmetic is explored with a 1% example in the article on the gambler’s fallacy in loot systems.
Waiting time with a hard pity at 50
Now add a rule: if the first 49 pulls fail, the 50th is guaranteed to succeed.
- Chance of reaching the guaranteed pull: 0.98⁴⁹, about 0.372, or 37%.
- The average number of pulls drops to (1 − 0.98⁵⁰) ÷ 0.02. With 0.98⁵⁰ about 0.364, that is about 0.636 ÷ 0.02, or roughly 32 pulls.
- The longest possible wait is exactly 50 pulls.
So a hard cap at 50 lowers the average wait from 50 to about 32 in this illustration, and removes the tail. It also reshapes the distribution: instead of a smooth decline, there is a large spike at pull 50, where about 37% of players end up. Roughly speaking, the guarantee is the outcome for more than one player in three, even though the base chance is only 2%.
The median, which is the number of pulls by which half the players have succeeded, stays near 35. A pity cap mainly affects the unlucky half of the distribution; the lucky half is unaffected because they never reach the cap.
Soft pity
Some systems do not wait for a hard cap. Instead the chance per pull rises once the counter passes a threshold, so success becomes increasingly likely. In shape, this is the rising-chance approach described in the article on streak breakers.
Compared with a hard cap, a soft pity usually spreads successes over a range of pulls near the threshold instead of piling them up at one number. Where the success pulls cluster depends on the base rate, the threshold and the size of each increase, none of which this article can assume for a real game. The key point is that the waiting-time curve has a different shape from a plain independent roll, with a noticeable bulge and a thinner tail.
What pity rules do and do not do
They reduce the worst cases. A player cannot go indefinitely without the top reward, which can make a system feel fairer and the spend more predictable.
They do not guarantee value. A pity rule typically guarantees a reward of a certain tier, not a particular item. Some games add a second layer where the guaranteed reward may not be the one a player wants, so that the real cost of a specific target can be higher than the headline pity number.
They do not usually lower the average chance to nothing. The designer has to account for the effect on the overall rate. One way is to set the base rate lower than it would otherwise be, so that the effective average, including pity, matches the figure the designers want. A game that advertises a base rate and a guarantee is giving two numbers that interact.
Counters may or may not carry over. Some games keep the counter across different pools or events and some reset it. The rules for this matter, because a counter that resets can wipe out progress that a player had been counting on.
Pity and decision-making
A visible counter can change behaviour. Seeing a number climb towards a guarantee can create the feeling that stopping now would waste what has been spent, which is the pattern of a sunk cost. Past pulls do not make future ones cheaper or more likely if the counter resets, and when it does not reset, the right question is the cost of the remaining pulls compared with what the reward is worth to you.
Because pulls typically cost real or in-game currency, it helps to decide on spending limits before starting and to treat any pull as spending with an uncertain result, in line with basic responsible play. A guarantee reduces the chance of an extreme wait. It does not make spending safe, and it does not make the reward a good value by default. If spending on games starts to feel hard to control, setting firm limits or speaking to a local support service is sensible.
Reading a pity system
Questions worth asking about any guarantee:
- What exactly is guaranteed: a tier, or a specific item?
- Is the guarantee hard (a fixed cap) or soft (a rising chance)?
- Does the counter reset when you get the reward, switch pools or an event ends?
- What is the base rate, and is the published rate the base rate or the effective average?
If the game’s published odds answer these, the numbers can be compared, and the expected value of the spend can be estimated, though only as an average that no individual player is guaranteed to match. If they do not, any estimate of expected spend is a guess, and the actual cost could be quite different.