Roll Probability per Ten Pull
Calculate gacha, loot box, and dice roll odds for 10-pull batches
How to Use This Tool
Follow these steps to calculate roll probabilities for your gacha or loot box system:
- Enter the base drop rate percentage for your target item per single roll.
- Select the pity system type that matches your game's mechanics from the dropdown.
- If using a soft pity system, fill in the start roll, rate increase per roll, and maximum rate cap.
- If using a hard pity system, enter the roll number where a target item is guaranteed.
- Adjust the number of rolls if needed (defaults to 10 for ten-pull calculations).
- Click the Calculate button to see your detailed probability breakdown.
- Use the Reset button to clear all inputs and start over, or Copy Results to save your breakdown.
Formula and Logic
The core calculation uses binomial probability for independent rolls, with adjustments for pity systems:
- Base probability per roll (p) is converted from a percentage to a decimal (e.g. 1.5% = 0.015).
- For no pity: Probability of k successes in n rolls is C(n,k) * p^k * (1-p)^(n-k), where C(n,k) is the binomial coefficient.
- Soft pity: Each roll after the start threshold uses an increasing drop rate up to the maximum cap, so the probability of 0 successes is the product of (1 - p_i) for each roll i.
- Hard pity: If a guarantee roll is reached within the total roll count, the probability of at least 1 success becomes 100% minus the probability of 0 successes before the guarantee roll.
- Expected value is the sum of drop rates across all rolls, adjusted for pity mechanics.
Practical Notes
These tips help apply the tool to real-world gaming scenarios:
- Gacha rates are often adjusted in game patches, so always use the most recent official drop rate values.
- Soft pity thresholds vary widely: for example, Genshin Impact 5-star pulls start soft pity at roll 74, with a ~6% rate increase per roll up to a 100% cap.
- Hard pity guarantees are usually absolute, but some games may have hidden mechanics that deviate slightly from stated rates.
- Tabletop games like Dungeons & Dragons use fixed probabilities with no pity, so select "No Pity" for those calculations.
- RNG variance means actual results may differ from calculated probabilities in small sample sizes.
Why This Tool Is Useful
This tool solves common pain points for gaming enthusiasts and professionals:
- Gamers can plan in-game currency spending to avoid overspending on gacha pulls.
- Game designers can balance drop rates and pity systems to meet player retention goals.
- Streamers can use probability breakdowns to explain pull odds to their audience in real time.
- Competitive players can calculate the expected resource cost to acquire specific items for meta builds.
Frequently Asked Questions
Does this tool account for duplicate protection?
No, this tool calculates base drop rates for target items without factoring in duplicate protection systems. If your game removes duplicates from the pool, adjust the base drop rate upward to reflect the reduced pool size.
Can I use this for tabletop dice rolls?
Yes, select "No Pity" and enter your dice success probability (e.g. 16.67% for rolling a 20 on a d20) to calculate odds for 10 consecutive rolls.
How accurate are the pity calculations?
Calculations assume pity mechanics activate exactly as described in game documentation. Always verify your game's specific pity rules, as some titles have hidden caveats or region-specific rate adjustments.
Additional Guidance
Maximize the value of this tool with these best practices:
- Cross-check drop rates with official game announcements or developer blogs to ensure accuracy.
- For multi-target banners, adjust the base rate to reflect the combined probability of all target items.
- Save result breakdowns to track how rate changes in patches affect your pull odds over time.
- Use the expected value calculation to compare the efficiency of single pulls vs. ten-pull bundles if your game offers discounts.