Gacha Pity & Pull Cost Calculator

How this is calculated

THIS TOOL IS ABOUT PITY, AND THAT IS WHAT SEPARATES IT FROM THE DROP CHANCE CALCULATOR. If your game has NO pity system, this is the wrong tool - use the drop chance calculator, which handles pure independent chance. The split is deliberate: uncapped odds are one question and a guaranteed cap is a different one, and a tool that tries to do both answers neither well. PITY IS WHY THE PUBLISHED RATE IS ALMOST MEANINGLESS ON ITS OWN. At a 0.6 percent rate the raw arithmetic says you should average about 167 pulls per copy. A hard pity of 90 means you can never exceed 90. So the cap is not a safety net for the unlucky - it is roughly half the number the base rate implies, and it arrives first for almost everybody. Reading the published rate and stopping there badly overstates what a copy costs. ⚠️ THE 50/50 DOUBLES THE WORST CASE, AND IT IS THE PART THAT CATCHES PEOPLE OUT. In many games reaching pity guarantees an item of the top RARITY but not the FEATURED one - it is a coin flip between the featured item and something from the standard pool. Lose that flip and most games then force the next guaranteed pull to be the featured item. So the true ceiling for the thing you are actually chasing is two full pity runs, not one. It is reported separately here because it is the figure that decides whether a banner is affordable, and it is the one people discover at the worst possible moment. SOFT PITY IS NOT MODELLED, WHICH MAKES THE ODDS HERE A FLOOR. Many games sharply raise the rate over the last stretch before the cap, so real players usually win somewhat short of the hard cap rather than at it. Those curves are rarely published as formulas, and this calculator will not invent one - a confident-sounding made-up curve would be worse than an honest bound. Treat the 'before pity' figure as 'at least this likely'. Where a game does publish its soft pity behaviour, trust that over this. EVERY PULL IS STILL INDEPENDENT UNDERNEATH. The pity counter is real and the game is genuinely counting, but the per-pull rate does not rise as you approach the cap unless the game says it does. A run of forty failures does not make the forty-first more likely on its own. The counter you can FEEL building is only real to the extent your game publishes it - everything else is the gambler's fallacy, which gacha interfaces make very easy to hold. CHECK WHICH RATE YOU ARE READING. Games usually publish a rate for the RARITY TIER and then a share of that for the featured item, so a '0.6 percent' headline can mean 0.3 percent for the character you are chasing. 'Rate-up' almost always means a larger share of an already-small chance, not a separate roll. COST PER PULL IS THE HONEST UNIT, and converting to it once is the most useful thing in this tool. Gacha currencies exist to keep the money abstract - bundles that never divide evenly into pulls, several currencies at once, bonus amounts on the first purchase. Divide what you actually paid by the pulls it actually bought. Every figure below then becomes a price, and a price is something you can compare against everything else you might do with the money. THE ODDS DO NOT KNOW HOW MUCH YOU WANT IT. Nothing here responds to how close you feel or how much you have already spent, and there is no such thing as being due. The only number fully in your control is the budget you set BEFORE you open the banner.

Common questions

How is this different from the drop chance calculator?

They answer different questions and now run different maths. The drop chance calculator handles PURE INDEPENDENT CHANCE - every attempt identical, no memory, no ceiling - which is how loot tables work in most games. This tool is about a PITY CAP: a guaranteed result after a fixed number of pulls, which is not independent at all, because the game is counting. If your game has no pity, the drop chance calculator is the right tool and this one will mislead you. If it does have pity, the cap dominates the answer and the raw probability becomes close to irrelevant.

Why is the worst case double the pity number?

Because in many games hitting pity guarantees the RARITY rather than the specific featured item - it is a coin flip between the featured item and something from the standard pool. Lose that flip and most games then force the next guaranteed pull to be the featured one. So the genuine ceiling for the thing you are chasing is two full pity runs, not one. People budget for one, lose the 50/50, and find out the real number at the worst possible moment. Untick the box if your game guarantees the featured item outright at pity.

Why does the published rate matter so little?

Because the cap usually arrives long before the average would. At a 0.6 percent rate the raw arithmetic implies about 167 pulls per copy, but a hard pity of 90 makes 90 the absolute maximum - roughly half. For most players the cap IS the outcome rather than a rescue from bad luck, so quoting the published rate as though it describes your experience overstates the cost badly. The rate still matters for the chance of an early win, which is exactly what the 'before pity' figure shows.

Is the 'before pity' chance accurate?

It is a floor rather than a best guess, deliberately. Many games use SOFT PITY, sharply raising the rate over the last stretch before the cap, so real players usually win somewhat before the hard cap rather than at it. Soft pity curves are rarely published as formulas, and this calculator will not invent one, because a confident-sounding made-up curve is worse than an honest bound. Treat the figure as 'at least this likely'. If your game publishes its soft pity behaviour, trust that instead.

What should I enter for cost per pull?

Real money, worked out once from the bundle you actually buy. Gacha currencies are designed to keep the money abstract: bundles that do not divide evenly into pulls, several currencies at once, bonus amounts on a first purchase. Divide what you actually paid by the pulls it actually bought. It is the single most clarifying step here, because it turns every other output from a token count into a price - and a price is something you can compare against everything else you might do with the money.

Does my pity counter carry between banners?

In most games yes, and it is worth checking yours because it changes the answer completely. A counter carried from a previous banner can mean you are far closer to a guarantee than a brand-new banner suggests, which is exactly when entering your real 'pulls so far' pays off. Many games also track the 50/50 state separately, so losing a coin flip on one banner can mean the next featured pull is already guaranteed. Both are published rules rather than secrets.

Does a long run of failures make the next pull more likely?

Only to the extent your game says so. The pity COUNTER is real and the game genuinely tracks it, but the per-pull rate does not rise as you approach the cap unless the game publishes soft pity. Underneath, each pull is still independent: the rate on your fortieth failed pull is the same as on your first. That is worth naming because gacha interfaces - counters, animations, near-misses - are built in a way that makes the opposite feeling very easy to hold, and that feeling is the expensive one.

Does any of this improve my odds?

No. Nothing in this arithmetic responds to how much you want the outcome, and there is no such thing as being due. What the numbers can do is let you decide in advance rather than mid-banner: work out the worst-case cost for the featured item, decide away from the banner screen whether that is money you are willing to spend, and treat it as spent the moment you commit it. The only figure genuinely in your control is the one you set before you start.

Take it further with AI

Copy this into ChatGPT or Claude with your own numbers filled in. It hands over the figures this calculator worked out, so the answer is built on real arithmetic instead of a guess.

I used the Gacha Pity & Pull Cost Calculator at https://www.bfcbrilliance.com/tools/gacha-pull-calculator.

What I entered:
- Published rate per pull (%): ___
- Hard pity - guaranteed at this pull (pulls): ___
- Pulls already on this banner (pulls): ___
- What one pull costs you ($): ___
- Featured item is a 50/50 at pity: ___

What it calculated:
- Pulls until a copy is guaranteed: ___
- Cost to guarantee from here: ___
- Chance it drops before you reach pity: ___
- Worst case for the FEATURED item, from zero: ___
- Worst case cost for the featured item: ___

Use those figures as given — they are already worked out, so please don't recalculate or estimate your own. Help me turn them into a plan: what to buy or do, in what order, roughly what it should cost, and the mistakes people most often make with this job.

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