Probability & Statistics Calculator
Calculate binomial probabilities, expected values, and drop rates
Quick Reference
At least 1 drop in 100 tries: 99.41%
Expected successes: 5.00
Expected attempts for 1 success: 20
Probability Results
Gacha / Loot Box Simulator
Probability Disclaimer
Binomial calculations assume independent trials. Gacha systems with pity mechanisms have modified probabilities after soft pity thresholds. The simulation above models standard pity systems with increasing rates.
Understanding Gaming Probability
Binomial Probability
The chance of getting exactly k successes in n independent trials, each with probability p. This is the foundation for calculating drop rates, crit chances, and any repeated independent event.
Pity Systems
Many gacha games implement pity systems that increase the probability of a rare drop after a certain number of unsuccessful pulls. Soft pity gradually increases rates, while hard pity guarantees the item.
Expected Value
The average outcome you can expect over many trials, calculated as the probability of success multiplied by the reward value. Use this to compare the expected return of different gambling or reward systems.
Drop Rate Estimation
To estimate an unknown drop rate, use the formula: 1 - (1 - p)^n = probability of at least one drop in n attempts. This helps you decide how many attempts you need for a reasonable chance of success.
Common Gaming Scenarios
Loot Boxes & Card Packs
With a 1% legendary drop rate, opening 100 packs gives you a 63.4% chance of getting at least one legendary. You need 299 packs for a 95% chance.
Gacha 5-Star Characters
Genshin Impact's base rate of 0.6% means a 45.3% chance of a 5-star in 90 pulls (soft pity included). With the guarantee system, you're virtually certain to get your target character within 180 pulls.
RPG Crit Chance
With a 25% crit rate and attacking 10 times, you have a 94.4% chance of landing at least one crit and an expected value of 2.5 critical hits per combat round.