Expected rolls
Divide 1 by the chance as a decimal. A 1% chance is 0.01, so the expected number of rolls is 1 / 0.01 = 100.
Plan your rerolls
Enter a drop chance and see your expected rolls, your chance within the rolls you have, and the targets for 50%, 90%, and 99% confidence.
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The math, without the jargon
Divide 1 by the chance as a decimal. A 1% chance is 0.01, so the expected number of rolls is 1 / 0.01 = 100.
Subtract the chance of missing every time from 1: 1 - (1 - p)n. Here, p is the drop chance as a decimal and n is the number of rolls.
Use ceil(ln(1 - c) / ln(1 - p)), where c is your target confidence. For example, c = 0.9 means a 90% target.
Important: This calculator assumes each roll is independent and has the same fixed chance. Pity systems, guarantees, or changing odds can make the real number of rolls lower or different.
Common questions
Expected rolls is the long-run average number of independent attempts needed for one hit. It is 1 divided by the drop chance as a decimal, not a guarantee.
No. With a 1% chance per roll, 100 independent rolls give about a 63.4% chance of at least one hit. You can still miss.
Yes. Pity systems can make real odds better than the independent-roll result shown here. This calculator assumes every roll has the same fixed chance and rolls do not affect each other.
Yes. Use it for gacha-style games when you know the per-roll chance and can assume independent rolls. The Clover RPG page has game-specific race and magic odds.
Game-specific odds