Gacha Pull Probability Simulator Pity Calculator
Use our free Gacha pull probability simulator pity tool to get instant, accurate results. Powered by proven algorithms with clear explanations.
Formula
P(success in N) = 1 - Product(1 - rate_i) for i = 1 to N
The cumulative success probability equals 1 minus the product of failure probabilities at each pull. The effective rate at each pull position accounts for soft pity (linearly increasing rates after a threshold) and hard pity (guaranteed at the cap). This geometric-like distribution with rate escalation models real gacha systems accurately.
Frequently Asked Questions
What is the pity system in gacha games?
The pity system is a mechanic that guarantees a rare item after a certain number of unsuccessful pulls. It exists to prevent extremely unlucky streaks and give players a deterministic upper bound on spending. Most games implement two forms: soft pity (gradually increasing rates after a threshold, typically 75% of the hard pity) and hard pity (guaranteed item at a fixed pull count). For example, in a game with 90-pull hard pity and 0.6% base rate, soft pity might start at pull 74 where rates increase from 0.6% to roughly 6-33% per pull until the guarantee at pull 90.
How does soft pity affect the expected number of pulls?
Soft pity dramatically reduces the expected number of pulls compared to pure random chance. Without any pity system at a 0.6% rate, the expected pulls for one copy would be about 167. With soft pity starting at pull 74, the expected drops to roughly 62-65 pulls because the escalating rates mean most players get the item between pulls 75-85. Only about 1-2% of players actually reach hard pity. This makes the effective rate much higher than the advertised base rate, which is why experienced players track their soft pity threshold carefully.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Can I use Gacha Pull Probability Simulator Pity Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.