What is soft pity and hard pity?

Below the soft-pity threshold each pull has the small base rate. From soft pity onward the per-pull rate climbs steeply each pull, and at hard pity the next pull is guaranteed. This calculator ramps the rate linearly from base to 100 percent across that window, the standard model for these banners.

How is the cumulative probability computed?

It multiplies together the per-pull miss chances for each upcoming pull from your current pity, then subtracts from one. Because the per-pull rate rises near hard pity, the cumulative chance accelerates as you approach the cap.

Why is the average closer to soft pity than base rate?

Although the headline base rate is tiny, most players never reach hard pity because the soft-pity ramp resolves the pull first. The effective average across a banner usually lands a little after soft pity, well below the hard cap.

What if I am already past soft pity?

Then each remaining pull uses the elevated ramped rate, so your odds per pull are much higher than the base rate. Enter your true pity count and the tool starts the ramp from the correct point.

Is reaching hard pity guaranteed?

Yes. At the hard-pity pull the rate is 100 percent, so a 5-star or legendary is certain on that pull at the latest. The number of pulls to guarantee is simply the hard-pity cap minus your current pity count.

RuneScape 3 Gacha Pity & Pull Calculator

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Gacha banners rarely use a flat rate — they use soft pity that ramps the chance near a hard guarantee, which makes naive probability estimates wrong. This calculator models the real ramping rate so you know your true odds within a set number of pulls and exactly how many pulls guarantee the drop.

How it works

Below soft pity each pull uses the base rate. From soft pity to hard pity the per-pull rate rises linearly to 100 percent. The cumulative chance multiplies the miss probabilities of each upcoming pull:

rate(n) = base                              if n < softPity
rate(n) = base + (1 − base) × (n − soft) / (hard − soft)   if n ≥ softPity
P(at least one) = 1 − Π over the next pulls of (1 − rate(n))

At n = hardPity the rate is 1, so a pull is guaranteed there at the latest, and pulls-to-guarantee is simply hardPity − currentPity.

Example and tips

With a 0.6 percent base, soft pity at 74, and hard pity at 90, a player at pity 0 has only about a 65 percent chance within 80 pulls but a 100 percent guarantee by 90. If you are already at pity 74, the very next pulls carry a sharply elevated rate, so saving until just before soft pity wastes no guarantee — the ramp does the heavy lifting in the final stretch.