Independent attempt calculators
The gacha, random booster, blind box, and at least one success calculators use the formula P = 1 - (1 - r)^n when each attempt is treated as independent. In this formula, r is the success rate for one attempt and n is the number of attempts.
For blind boxes and random boosters with equal variants, the calculator first estimates r as desired variants divided by total variants. If odds are weighted or a secret item has a separate rate, users should enter the known rate in the general at least one success calculator instead.
Without-replacement prize pools
The prize draw calculator uses a without-replacement model. It calculates the probability of missing every target prize as C(total - target, draws) divided by C(total, draws), then subtracts that miss probability from 1.
The calculator handles the edge case where the number of draws is larger than the number of non-target prizes remaining. In that case, missing all target prizes is impossible.
Expected cost calculations
Expected attempts are calculated as 1 divided by the success rate. Expected cost multiplies that value by cost per attempt. Target probability attempts use logarithms to solve the at-least-one formula for n.
Expected cost is not a spending recommendation or guarantee. It is a planning estimate under fixed-rate assumptions.
Editorial standards
PrizeOdds Calculator avoids official affiliation claims and does not use copyrighted character images, game logos, or toy brand artwork. The goal is to provide generic educational tools for probability-based collectibles.
Pages are written to explain assumptions in plain language. If a formula, example, or wording issue needs correction, visitors can use the contact page to suggest an update.
Responsible use reminder
Probability can help you understand risk, but it cannot guarantee a result. Set a budget before buying pulls, boxes, packs, or prize tickets, and stop when that limit is reached.
FAQ
Are the calculators simulations?
No. They use direct probability formulas, not random simulations.
Do you store calculator inputs?
No account is required, and calculations run locally in the browser.
Can these formulas model every game or toy system?
No. Pity systems, guarantees, weighted odds, and fixed case distributions may need more specific models.
How should I report a correction?
Use the contact page with the page URL, the value entered, the expected result, and a short explanation.