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The Advertised Rate Describes Almost None of What Happens

Published 9/14/2026 · 4 min read · Everyday calculators

Lena Hoffmann

Lena HoffmannScience & education writer at OneKitly

Mathematics · Physics

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In short

A pity system replaces a constant rate with a rising one. Take the common shape: 0.6 % on every pull up to the seventy-fourth, then an increase of six points per pull, then a guarantee at ninety. The effective chance of the next pull is 0.6 % at pull 1 and still 0.6 % at pull 74; it becomes 6.6 % at 75, 36.6 % at 80, 66.6 % at 85, 90.6 % at 89 and 100 % at 90. Running the whole ramp gives a cumulative probability of 100 % within ninety pulls, by construction, and an average of 62.9 pulls to a hit. Compare that with the same ninety pulls at the advertised rate alone: 41.8 %. So the published 0.6 % is true of each individual pull below the threshold and describes almost nothing about the experience, because the system was designed to make sure it does not. Knowing where you are on the ramp is the only figure that answers the question people actually have, which is how much further.

With a 0.6 % base rate, a soft pity at 74 and a hard pity at 90, the effective chance climbs from 0.6 % to 36.6 % by pull 80 and 90.6 % by pull 89. Without pity, ninety pulls would give 41.8 %.

Two thresholds doing different jobs

The hard pity is a promise: at ninety, the item is granted. It bounds the worst case and is the number a player can budget against. The soft pity is the one that shapes the experience, and it is rarely published: from the seventy-fifth pull the rate climbs steeply, so most hits land in the eighties rather than at the guarantee. That is why the average is 62.9 rather than something near ninety — the ramp resolves most attempts before the promise has to. A system with only a hard pity would feel very different: a long flat stretch and then a cliff.

The numbers here are a common configuration and not a claim about any particular game. Publishers set the base rate, the soft threshold, the increment and the guarantee independently, and a change to any one of them moves the whole curve — which is why the calculator asks for all four rather than assuming them. Put in the values your game publishes and the shape will be right even where the figures differ.

What the counter is worth knowing for

Because the rate is not constant, the sunk-cost reasoning that is wrong for an ordinary drop is partly right here: pulls already spent genuinely do improve the next one, once past the soft threshold. That makes the counter a real decision input rather than a superstition. It also makes the reverse true — below the threshold, nothing has been earned, and a run of eighty misses at a flat 0.6 % has bought exactly the position it says it has and no credit besides.

Effective rate of the next pull — base 0.6 %, soft pity 74, hard pity 90, +6 points a pull
PullEffective rate
1 to 740.6 %
756.6 %
8036.6 %
8566.6 %
8990.6 %
90100 % — the guarantee
Average pulls to a hit62.9
Ninety pulls at the base rate alone41.8 %

Worked with our own calculator

Gacha pity calculator

Given

Current pity count
0
Base rate (%)
0.6
Soft pity starts at
74
Hard pity (guarantee)
90
Rate increase per pull in soft pity (%)
6

Result

Pulls to soft pity
74
Pulls to guarantee (hard pity)
90
Expected pulls to next 5★
62.297

These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.

Run it on your own figures

Frequently asked questions

Does the counter reset after a hit?
In every common design, yes: the pull that lands resets the count and the ramp starts again from the base rate. Some systems keep a separate counter for a featured item and reset only that one, so a hit on the wrong item advances neither, both, or one of them depending on the game. That detail is published in the rates disclosure rather than in the interface, and it is the one worth reading before planning around a threshold.
Is the published rate a lie, then?
No, and that is the point worth being precise about. Every individual pull below the soft threshold really is 0.6 %, and the figure is verifiable. What it is not is a description of the process, because the process changes rate partway through — and a single number cannot describe a curve. The honest complaint is not that the rate is false but that it is the least informative true thing that could have been published.
How do I find my game's actual numbers?
The base rate and the hard pity are almost always published — several jurisdictions require a rates disclosure, and it is usually reachable from the shop screen. The soft threshold and the increment usually are not, and the figures in circulation come from players recording large numbers of pulls. Treat those as estimates: they are often close, they are not authoritative, and a patch can change them without announcement.

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