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.
Reviewed by Daniel Agrici, Founder & Lead Developer
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.
Worked Examples
Example 1: Standard Banner with Soft Pity
Problem:A game has 0.6% base rate, 90-pull hard pity, soft pity at pull 74. You are at 65 pity and have 25 pulls. What is your chance of getting the item?
Solution:Pulls 66-73 (8 pulls at 0.6%): Fail prob = (0.994)^8 = 0.953. Pulls 74-90 (soft pity, rates escalate from 0.6% to ~50%): At pull 74, rate jumps to ~6%. By pull 80, rate is ~22%. By pull 85, rate is ~38%. Cumulative success by pull 90 (25 pulls from current): > 99.5%. Expected to hit around pull 78-80 (13-15 pulls from current).
Result:Success probability: 99.5% with 25 pulls | Expected: ~14 pulls | Cost: $37.50
Example 2: Early Pity Planning
Problem:Starting from 0 pity with 0.6% rate and 90 pity. How many pulls for 90% confidence? Budget at $1.50 per pull.
Solution:At 0.6% base rate, probability of early hit in first 73 pulls: 1-(0.994)^73 = 35.5%. Soft pity from 74-90 adds significant probability. By pull 80: ~75% cumulative. By pull 85: ~92% cumulative. For 90% confidence, need approximately 83-84 pulls. Cost: 84 x $1.50 = $126.00.
Result:90% confidence: ~84 pulls ($126) | Guarantee: 90 pulls ($135)
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy