Summon and trait rates are community estimates. Sources disagree on the Secret rate (0.01% vs 0.1%) and only the Immortal trait has a widely reported figure (0.1% with a ~1,300-reroll pity). Use these odds as planning guidance, not published rates.
baseRate · luckMultiplier — flat region until softStart
soft-pity ramp = baseRate · luckMultiplier · (1 + 0.05·(pull − softStart))
hard pity — guaranteed success once currentPity ≥ hardPity
P(success in N pulls) = 1 − Π (1 − p(k)) for k = currentPity..currentPity+N−1
soft-pity ramp = baseRate · luckMultiplier · (1 + 0.05·(pull − softStart))
hard pity — guaranteed success once currentPity ≥ hardPity
P(success in N pulls) = 1 − Π (1 − p(k)) for k = currentPity..currentPity+N−1
Base Rate—
Soft Pity Start—
Hard Pity—
Expected Pulls—
Pity Remaining—
P(success in N)—