Gacha Pull Probability Simulator Pity

A single gacha draw is a Bernoulli trial, so with no safeguard the number of pulls until a first success follows a geometric distribution with mean 1 divided by p. At the common advertised rate of 0.6 percent that mean is about 167 pulls, and roughly one player in a thousand would still have nothing after 1,145. Publishers therefore layer two corrections on top of the flat rate. Soft pity raises the per-pull probability once a counter passes a threshold, commonly around 75 percent of the cap, and hard pity forces a guaranteed award at the cap itself, frequently 80 or 90 for the highest rarity tier. Cumulative probability is one minus the running product of per-pull failure probabilities, evaluated at the escalating rates rather than a single constant. That escalation moves the distribution sharply: with a 0.6 percent base, soft pity near pull 74 and a hard cap of 90, the median outcome lands around pull 75 to 80 and the effective rate averaged over a full cycle is closer to 1.6 percent than to the advertised 0.6. Two caveats dominate any budget built from these numbers. Many banners impose a 50/50 rule under which the first guarantee may award a non-featured item, roughly halving efficiency and pushing the worst case to twice the cap. And the pity counter, not the headline rate, is the state variable that matters, so odds quoted from a fresh counter do not describe a partially advanced one.

The mechanic takes its name from gachapon, the coin-operated capsule toy machines that arrived in Japan in 1965 and which Bandai turned into a mass market with its Gashapon line from 1977. The appeal was always the sealed random prize rather than the toy itself. The digital form is usually dated to Dragon Collection, a Konami title launched on the GREE social platform in 2010, which sold randomized card packs and became the template copied across Japanese mobile gaming within a couple of years. Regulation shaped the pity system more than design fashion did. In May 2012 Japan's Consumer Affairs Agency ruled that kompu gacha, which required players to complete a set of randomly awarded items to unlock a prize, violated the Act against Unjustifiable Premiums and Misleading Representations, and publishers withdrew the mechanic within weeks. Industry bodies then moved toward voluntary probability disclosure. China went further, with rules taking effect in May 2017 that required online game operators to publish draw rates for randomized items. Guaranteed ceilings spread as a competitive and reputational response, giving players a bounded worst case in place of an unbounded one. Genshin Impact, released worldwide in 2020, made the 90-pull cap, the soft pity ramp and the 50/50 featured rule familiar far outside Japan, and player communities reverse-engineered the soft pity curve from large samples of logged pulls rather than from published figures.