What is a pity system?

A pity system is a game mechanic that guarantees the featured item if you have not received it within a certain number of pulls. For example, Genshin Impact guarantees a 5-star at pull 90 and a featured 5-star at pull 180 (with 50/50). This calculator models a simple hard pity where the item is guaranteed at the cap.

What formula does this use?

The calculator models each pull cycle (from pull 1 up to the pity cap) and computes the probability of NOT getting the item across each pull, applying the base rate for pulls below the cap and a guarantee at the cap. Cumulative probability is 1 minus the probability of getting nothing across all N pulls.

Does this account for soft pity?

No. Soft pity (an increased rate that ramps up before the hard cap) is game-specific and not modeled here. The actual odds in games with soft pity may be somewhat higher than shown for pull counts near the pity cap.

What if I set pity cap to 0?

Setting pity cap to 0 disables the pity system and uses a simple binomial model: P = 1 − (1 − rate)^n. This matches games or banners with no pity guarantee.

How do I enter the rate for Genshin Impact?

Genshin Impact has a base 5-star rate of 0.6% and a pity cap of 90 (for standard 5-stars). For a 50/50 featured banner, the effective featured rate is about 0.3% (0.6% base times 50% featured chance), with an effective pity around 90 pulls to get any 5-star and 180 to guarantee the featured one.

Why does probability not reach 100% without pity?

Mathematically, a non-zero failure chance each pull means there is always a tiny possibility of never getting the item. With no pity, even at 1,000 pulls the probability is very high but never exactly 100%.

Gacha Pull Calculator

Name: Gacha Pull Calculator
Availability: InStock
Author: Nham Vu

Enter your pull rate, pity cap, and number of pulls to see the exact probability of getting the featured item.

Quick Presets

Pull Parameters

Base Pull Rate (%)

Per-pull chance of getting the featured item

Hard Pity Cap (pulls)

Pull number that guarantees the item. Set 0 for no pity.

Number of Pulls

How many pulls you plan to make (max 50,000)

Configure your pull parameters and click Calculate.

Cumulative Probability Curve

Chart will appear after calculation.

Summary

Enter your pull rate, pity cap, and number of pulls to see the exact probability of getting the featured item.

How it works

Enter the base per-pull rate for the featured item (e.g., 0.6% for Genshin Impact).
Enter the pity cap — the pull count at which the game guarantees the item (e.g., 90 for Genshin).
Enter how many pulls you plan to make.
The calculator computes cumulative probability accounting for the pity guarantee.
Key milestones (pulls needed for 50%, 75%, 90% chance) are shown alongside an interactive chart.

Use cases

Plan how many primogems or in-game currency to save before pulling on a banner.
Calculate the probability of getting a 5-star character in Genshin Impact, Honkai: Star Rail, or similar games.
Decide whether to spend saved pulls now or wait for a more desirable banner.
Understand how hard pity changes the effective odds versus the raw base rate.
Compare pull efficiency across different gacha games with different pity caps.
Estimate how many pulls are needed for a 90% or 99% success probability.
Settle debates about whether saving for pity or pulling immediately is the better strategy.
Calculate multi-account or co-op farming goals for gacha items.

Frequently Asked Questions

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Last updated: 2026-05-29 · Reviewed by Nham Vu