Character Reroll Probability Calculator

How to Use This Tool

Select your reroll scenario from the dropdown: Fixed Stat Threshold (tabletop RPGs like D&D), Gacha Pull (gacha games like Genshin Impact), or Tabletop Trait (campaign trait rerolls).

Fill in the required fields for your selected scenario: for fixed stats, enter dice count, sides, number to drop, and target value. For gacha, enter pull rates, optional pity values, and desired item count. For traits, enter trait probability and max rerolls.

Click Calculate Probability to see a detailed breakdown of your odds, including expected values and probabilities for common reroll counts. Use the Reset button to clear all inputs, or Copy Results to save your breakdown.

Formula and Logic

Each reroll type uses standard probability models tailored to gaming scenarios:

• Fixed Stat Threshold: Brute-force enumeration of all possible dice combinations for pools up to 8 dice. We sort each roll, drop the specified number of lowest dice, sum the remaining, and calculate the percentage of rolls meeting or exceeding your target value.
• Gacha Pull: Uses binomial probability for independent pulls: probability of at least 1 success in N pulls is 1 - (1 - p)^N, where p is the pull rate as a decimal. Pity systems adjust the rate after a set number of pulls to improve odds. Expected pulls for 1 item is 1/p (geometric distribution).
• Tabletop Trait: Geometric distribution model: probability of success in N rerolls is 1 - (1 - p)^N, where p is the trait probability per reroll. Expected rerolls to get the trait is 1/p.

Practical Notes

Gaming probability is often context-dependent. Keep these real-world factors in mind:

• Live-service gacha games frequently adjust pull rates via patches—always verify rates in the latest patch notes before planning rerolls.
• Tabletop dice rolls are truly random, but "dice luck" streaks are common; use this tool to set realistic expectations for one-shot sessions or long campaigns.
• Fixed stat calculations assume fair, unweighted dice; physical dice may have slight biases that shift odds marginally.
• Pity systems vary widely between games: some cap bonus rates, others reset pity on a successful pull. Check your game’s specific rules for accurate results.

Why This Tool Is Useful

Gamers, designers, and streamers use this tool to:

• Plan efficient reroll sessions for gacha games, avoiding wasted time on low-probability pulls.
• Balance tabletop RPG encounters by verifying stat roll odds for players and NPCs.
• Optimize streaming content by predicting reroll outcomes for audience engagement.
• Test game design balance by simulating trait or stat roll probabilities for custom tabletop or video game systems.

Frequently Asked Questions

Does this tool account for weighted dice or modded game files?

No, all calculations assume fair, unmodified game systems. Weighted dice or modded files will shift probabilities outside the tool’s estimates.

Why is there a dice count limit of 8 for fixed stat calculations?

Brute-force enumeration of dice combinations becomes computationally intensive for pools larger than 8 dice. For larger pools, we recommend using a normal approximation or adjusting your dice pool size.

How accurate are gacha pity calculations?

Pity calculations are approximate, as each game implements pity systems differently. Always cross-reference with your game’s official pity rules for exact odds.

Additional Guidance

For competitive gacha players, track your pull history to verify if your game’s rates match published values—some regions have different rate regulations. Tabletop GMs can use this tool to adjust trait reroll limits for campaigns, ensuring players have fair but challenging odds. When designing custom games, use the fixed stat calculator to balance character creation rules, avoiding overpowered or underpowered stat roll methods.