Gacha maths

What a featured unit actually costs, in every game we track

The advertised rate tells you almost nothing about what you will spend. Here is the same question — how many pulls to land the unit on the banner — answered identically for all 19 games we track, from 50 pulls to 167.

By the GachaData team Updated 6 min read

Every gacha game publishes a rate. Dragon Ball Z Dokkan Battle advertises 10% at an SSR on its featured banner; Honkai: Star Rail advertises 0.6% for a 5★. Read those two numbers side by side and Dokkan looks about seventeen times more generous.

It is not. On the question players actually care about — how many pulls until I have the unit on the banner — Dokkan needs about 140 and Star Rail about 94.

The advertised rate is the chance on one pull. What you spend is decided by pity: whether the game promises you anything for failing, and how quickly that promise arrives.

The same question, asked 19 ways

The table below asks one question of every game: starting from zero, with no carried-over pity, how many pulls until you have the banner’s featured unit? Not “a unit of the top rarity” — the specific one you are pulling for, which in many of these games means surviving a 50/50 as well.

Every figure comes from that game’s own published rates and pity rules, run through the same model that powers each game’s Pull Planner on this site.

GameTypicalMedianUnlucky (90%)Guaranteed by
Silver And Blood5036111never
Blue Protocol: Star Resonance65687180
Reverse: 19996570123140
Arknights6957142never
Azur Lane7658191200
Wuthering Waves8375145160
Hololive Dreams8769200200
Persona5: The Phantom X8874145160
Genshin Impact9180156180
Duet Night Abyss9481156180
Honkai: Star Rail9481156180
Zenless Zone Zero9481156180
Limbus Company10696200200
Blue Archive10899200200
Fate/Grand Order11687287330
DIGIMON UP127139200200
Umamusume: Pretty Derby13393306not carried
Dragon Ball Z Dokkan Battle14097322never
CookieRun: Crumble167116383never

“Typical” is the mean number of pulls. “Median” is the point where half of players are done. “Unlucky” is the 90th percentile — one player in ten spends at least this much. “Guaranteed by” is the pull at which the game owes you the specific unit, where it ever does. Several games run more than one pool; each row measures the one named on that game’s own Pull Planner, and where that choice changes the answer the game’s page says so.

Why the advertised rate misleads

Three things sit between the published rate and your wallet, and none of them appear on the banner.

1. Pity converts bad luck into a bounded cost

Reverse: 1999 has a 1.5% rate and a hard guarantee at 70 pulls. Dokkan has a 10% rate and no pity at all — every summon is independent, forever. That single difference reverses the ranking: Reverse: 1999 lands at 65 typical pulls and Dokkan at 140.

With no pity the distribution has no right-hand wall. Dokkan’s median is 97 pulls — better than Blue Archive’s 99 — but one player in ten needs 322 or more, and there is no number at which the game gives in. Reverse: 1999’s unluckiest tenth stops at 123.

The median is the wrong statistic to plan with. By median, Dokkan (97) very nearly ties Blue Archive (99). By 90th percentile it is worse by 122 pulls — 322 against 200. When a game has no ceiling the tail is where the money goes, and the tail is exactly what a median hides. The unlucky tail works through that gap for every game here.

2. The 50/50 doubles the price of losing

Wuthering Waves, Honkai: Star Rail, Zenless Zone Zero, Genshin Impact, Duet Night Abyss and Persona5: The Phantom X all run the same shape: a soft-pity ramp, a hard pity, and a coin flip on whether the guaranteed unit is the one you wanted. Lose the flip and you start the climb again, with the consolation that the next top-rarity is guaranteed to be featured.

That is why Star Rail’s hard pity is 90 but its guarantee in the table above is 180. Ninety is the guarantee for a 5★. One hundred and eighty is the guarantee for the 5★.

3. “Rate-up” is not the same promise as a 50/50

Arknights is the interesting case, and the one most often misread. It has soft pity from pull 51 and a hard pity at 99, which sounds strict — but there is no guarantee that the 6★ you get is the featured one. Roughly half of banner 6★ pulls are the rate-up unit; the rest are anything else in the pool. Worse, pity resets on any 6★, not just the one you wanted.

So the honest Arknights answer is not “35 pulls to a 6★” — a figure you will see quoted often. It is a chain of independent attempts, each roughly 35 pulls, each a coin flip. That is why its typical cost lands at 69 and why, despite having pity, its Guaranteed by cell reads never. Silver and Blood sits at the top of the table for the same reason and with the same asterisk: its 80-pull pity forces an S-tier drawn evenly from a 26-unit pool, so it reaches the rate-up unit only about 4% of the time.

The spark games are the honest ones

Blue Archive and Limbus Company look expensive in the typical column, and they are — but they are also games where you can decide in advance exactly what the unit costs. Two hundred pulls, no ambiguity, no coin flip. Fate/Grand Order does the same at 330, DIGIMON UP, Hololive Dreams and Azur Lane at 200.

There is a real argument that this is the better design even at a higher price, because it is the only structure a player can budget against. A game with a 90th percentile of 322 and no ceiling cannot be budgeted for; it can only be gambled on.

How to use these numbers

  • Compare across games using the typical column, not the advertised rate. The rate is a per-pull probability and the games attach entirely different guarantees to it.
  • Plan with the 90th percentile, not the median. If you can only afford the median outcome, you have a one-in-two chance of running out.
  • Check whether pity carries over. Every figure here starts from zero. If you have accumulated pity on the banner type your real cost is lower — each game’s Pull Planner takes your current count as an input.
  • Check whether you have already lost a 50/50. In the hoyo-style games that halves your remaining cost, because the next top-rarity is guaranteed to be featured.
  • Remember these are pulls, not money. A pull costs a different amount in every game — see what a pull costs.

Scope and freshness

Each game’s rate, soft-pity start, ramp, hard pity and spark are exact and re-checked every patch. The model is the same one behind each game’s Pull Planner, so a figure here and a figure there will always agree — if they ever disagree, the Pull Planner is right and this page has gone stale. The cross-game view lives on the meta page.

One exception, stated plainly. Honkai: Star Rail is the only game on this table whose rates we cannot verify independently, so we take the publisher’s stated 0.6% base and 1.6% combined rate at face value and fit the ramp to them. Every other row is verified. Treat the Star Rail figures as accurate-if-the-publisher-is-accurate rather than verified, and note that Zenless uses the same underlying pity shape with rates we can verify, which is a useful cross-check.

Two games are held out of this comparison entirely — Epic Seven and Star Savior — because their rate-up disclosure is not yet complete enough to ask the same question of them. A game sits out until its numbers answer the identical question the other rows answer; ranking it on a different question would read as a verdict on the game.

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