PullMeter.
← All guides

FIELD NOTES

Soft and Hard Pity Math Explained

Understand changing per-attempt probabilities without relying on game-specific assumptions.

Hard pity is a cap, not a constant rate

Hard pity means a qualifying success must occur by a specified attempt since the last reset. With a hard cap H, missing all H attempts is impossible. That does not make each attempt a 1/H chance.

Soft pity changes the hazard

The chance on attempt i, conditional on every earlier miss, is pᵢ. Multiply the conditional miss chances to find survival: S(n) = ∏(1 − pᵢ). The first-success cumulative chance is 1 − S(n). This works even when rates differ between attempts.

Our custom ramp is explicit

The calculator uses a linear increase entered by you. On the soft-start attempt S, the rate becomes base + increment; on S + 1 it is base + 2 × increment, capped at 100%. The hard cap overrides that ramp. These are modeling inputs, not claims about any product.

Current pity and expected attempts

If c consecutive misses have already occurred, calculation starts at attempt c + 1. Expected additional attempts are the sum of survival probabilities before each future attempt, up to the guarantee. We stop at the first qualifying success, so split outcomes and multiple-copy rules need more detailed models.

Put the idea to work

Pull odds · Raffle odds · Custom pity · Tries for a target chance