What expected cost means
Expected cost is a planning number, not a promise. If the success rate is 3%, the long-run average number of attempts for one success is about 33.33 attempts. If each attempt costs 2, the expected cost is about 66.67 in that same currency or point value.
That does not mean you will definitely get the target by spending that amount. Some people hit early, and some miss far longer than the average. For collectors and gacha players, expected cost is best used as a reality check before buying.
The second part of this calculator estimates the attempts and cost needed to reach a chosen probability such as 50%, 80%, 90%, or 95%. This is often more practical than the raw expected value because it connects directly to a confidence level you can understand.
Expected attempts and target probability
expected attempts = 1 / r; target attempts = ln(1 - target probability) / ln(1 - r) The expected attempts formula gives the long-run average for one success under independent attempts. The target probability formula calculates how many attempts are needed to reach a chosen chance of at least one success.
Both outputs assume a fixed success rate and no pity, guarantee, inventory depletion, trading, resale, or refunds. Use them as estimates, not financial advice.
Example use cases
3% rate and cost of 2
The expected attempts for one success is 33.33, and the expected cost is 66.67. To reach an 80% chance, you need 53 attempts, costing about 106.00.
1% chase item
A 1% item has an expected 100 attempts for one success. Reaching a 90% chance takes 230 attempts, which can be much more expensive than it first appears.
Blind box comparison
If one desired figure out of 12 costs 12 per box, the expected attempts are 12 boxes and the expected cost is 144. That can be compared with a direct purchase price.
Responsible use
Probability can help you understand risk, but it cannot guarantee a win. If you are buying pulls, boxes, packs, or prize tickets, set a budget first and avoid spending more than you can afford. A calculator is a planning aid, not a reason to chase losses or ignore your limit.
FAQ
Does expected cost guarantee a success?
No. Expected cost is an average over many repeated situations. A single person can spend less or more and still get normal random results.
What target probability should I use?
50% is a coin-flip level, 80% is more comfortable, and 90% or 95% can become expensive quickly. Pick a target that fits your budget.
Can I use gems, tickets, or points instead of money?
Yes. Enter the cost per attempt in whatever unit you want. The output uses the same unit.
Does this include pity systems?
No. Pity and guarantees change the probability curve. This calculator uses a fixed independent success rate.
Related tools
Gacha Calculator
Calculate your chance of getting at least one target item from gacha pulls based on drop rate and number of pulls.
Blind Box Calculator
Calculate the chance of getting your desired figure or secret item from blind boxes based on item count and boxes purchased.
At Least One Success
Calculate the chance of getting at least one success after multiple attempts, or find how many attempts you need.
Helpful guides
How Gacha Probability Works
Learn how gacha probability works, why repeated pulls do not add up directly, and how to read at least-one-success odds.
Blind Box Odds Explained
Understand blind box odds, equal variant assumptions, secret item limits, duplicate risk, and how to compare boxes with resale prices.