Soft pity, and why the banner's rate is not the rate you experience
A 0.6% banner does not give you a 0.6% chance on pull 75. Here is what the ramp actually does to your odds, and why the number in the corner of the banner is technically true and practically useless.
Open the details screen on a Honkai: Star Rail banner and it will tell you the 5★ rate is 0.6%. Somewhere further down it may also mention a "comprehensive probability" of around 1.6%. Both numbers are accurate. Neither describes what happens when you actually pull.
The reason is that in most modern gacha games the rate is not constant. It sits flat for most of the cycle and then climbs steeply near the end. Almost every 5★ you have ever pulled arrived inside that climb.
What the ramp looks like
The shape is the same across the hoyo-style games and it has three parts:
- A base rate, which applies from pull 1 up to the soft-pity start. This is the number on the banner.
- A ramp, which begins at the soft-pity threshold and adds a fixed increment to your chance on every subsequent pull.
- A hard pity, the pull at which the chance reaches 100%.
| Game | Base rate | Ramp starts | Hard pity |
|---|---|---|---|
| Honkai: Star Rail | 0.6% | 74 | 90 |
| Zenless Zone Zero | 0.6% | 74 | 90 |
| Wuthering Waves | 0.8% | 70 | 80 |
| Arknights | 2% | 51 | 99 |
| Reverse: 1999 | 1.5% | 60 (ramp unpublished) | 70 |
Reverse: 1999 states a soft pity at 60 but does not publish the increment, so our planner models the guarantee at 70 and ignores the ramp. That makes its figures slightly pessimistic rather than optimistic, which is the right direction for a number you are budgeting against.
Read the Star Rail row carefully. The advertised 0.6% governs pulls 1 through 73 — that is 73 of the at-most 90 pulls in a cycle, or 81% of the pulls but only a small minority of the 5★s. From pull 74 the rate climbs hard, and the overwhelming majority of 5★ drops land in that final stretch.
If you have ever felt that 5★s "only come at pity", that is not superstition. It is the design working as intended.
The comprehensive rate is an average, and averages hide shape
The second number some games publish — the "comprehensive" or "combined" probability — is the base rate and the ramp averaged over a full cycle. It is the honest summary statistic, and it is the one to use when comparing games. Wuthering Waves states 1.8% against a 0.8% base. Zenless Zone Zero states 1.6% on its standard channel and 1.067% on the limited one — and, unusually, publishes what that costs in money: a limited S-Rank agent lands somewhere in a $1.98 to $475.20 band depending on how the pulls fall. Star Rail states 1.6%, though see the provenance note below.
That $475.20 figure is worth sitting with. It is not a critic's estimate; it is the publisher's own disclosure of the top of the range, printed in the game.
But it is still an average over a distribution that is nothing like flat. A 1.6% average built from "0.6% for 73 pulls then a cliff" behaves completely differently from a genuine flat 1.6%. With a flat rate, pull 1 and pull 89 are the same bet. With a ramp, they are not remotely the same bet, and no single percentage can tell you which one you are making.
What this changes about how you pull
Pity is an asset. Treat it like one.
In every game on the table above, accumulated pity carries forward on the banner type. Sitting at 70 pulls into a Star Rail cycle is not "70 wasted pulls" — it is a position most of the way up the ramp, and it has real value. Spending it on a banner you are lukewarm about, and then facing the next banner from zero, is the single most common way players overspend.
Ten-pulls are not better odds
A ten-pull is ten single pulls resolved at once. Where a game guarantees something inside a multi, it is almost always a lower rarity, not the top one. There is no mathematical advantage to pulling in tens; the convenience is the whole benefit.
"I'm due" is false in one game on this list
The gambler's fallacy is a fallacy when every trial is independent. Under soft pity, trials are not independent — the game genuinely is tracking your counter and genuinely is raising your odds, so "I'm close" can be literally true.
The exception is Dragon Ball Z Dokkan Battle, which has no pity of any kind. There, every summon really is independent, the counter really is imaginary, and "I'm due" really is false. Its cost profile is compared with the rest in what a featured unit actually costs.
Arknights hides a second coin flip
Arknights ramps from pull 51 and hard-pities at 99, which looks like the strictest guarantee on the table. It is not, because the guarantee is for a 6★, not the featured one — roughly half of banner 6★s are the rate-up unit, and pity resets on whichever one you get. In practice you are running a sequence of ~35-pull attempts and flipping a coin at the end of each.
Provenance. Wuthering Waves, Zenless, Arknights and Reverse: 1999 rates on this page are read from each game's own shipped tables. Honkai: Star Rail is the exception: its data is device-gated, so its 0.6% base and 1.6% combined rate are the publisher's stated figures taken at face value, with the ramp fitted to them. Zenless runs the same pity shape with rates we can read, and the two agree.
One thing the ramp does not do
Soft pity does not make a banner cheaper on average in any deep sense — the publisher chose the base rate knowing the ramp exists, and the two are tuned together. What it does is reshape the risk: it trades a long, unbounded tail for a slightly worse median. That is a genuinely better deal for a player, because the tail is what causes people to spend money they did not intend to spend.
Which is also why a game with a high headline rate and no pity at all deserves more suspicion than a game with a low headline rate and a hard ceiling.