Drop Chance Calculator

The probability of getting at least one drop is calculated using the formula: 1 - (1 - drop_rate)^attempts. For example, with a 1% drop rate and 100 attempts, you have approximately 63.4% chance of getting at least one drop. Use our calculator above to compute this automatically, or try our percentage calculator for related probability calculations.

Cumulative probability refers to the increasing likelihood of success as you make more attempts. Unlike individual attempt probability which stays constant, cumulative probability grows with each try. For instance, a 1% drop rate doesn't mean you're guaranteed a drop in 100 attempts, but your cumulative probability increases from 1% (one attempt) to 63.4% (100 attempts). This is because each independent attempt adds to your overall chances of success.

Pity systems, also called "bad luck protection," guarantee a rare drop after a certain number of failed attempts. For example, if a game has a 0.6% drop rate with a 90-pull pity, you're guaranteed the item on your 90th attempt if you haven't received it yet. This prevents extremely unlucky streaks and makes the game feel more fair. Use our Pity System Calculator above to calculate your actual odds when pity mechanics are involved.

The number of attempts needed depends on the drop rate. For a 1% drop rate, you need approximately 230 attempts to reach 90% probability. The formula is: attempts = ln(1 - desired_probability) / ln(1 - drop_rate). Use our "Attempts Needed Calculator" section above to find the exact number for any drop rate and target probability. For logarithmic calculations, check out our log calculator.

The Gambler's Fallacy is the mistaken belief that previous failures increase your chances of success on the next attempt. In reality, each attempt in a random drop system is independent. If you fail 99 times with a 1% drop rate, your 100th attempt still has exactly 1% chance, not higher. The game doesn't "remember" your failures (unless it has a pity system). Understanding this prevents frustration and unrealistic expectations.

Expected drops is the statistical average number of successful drops you would get over many trials. It's calculated by multiplying the drop rate by the number of attempts. For example, with a 1% drop rate and 100 attempts, you expect 1 drop on average. However, this is just the mean value - in reality, you might get 0, 1, 2, or more drops. The actual result varies due to randomness, but over thousands of players, the average will converge to the expected value.

RNG in games uses algorithms to generate pseudo-random numbers that determine drop outcomes. When you attempt to get a drop, the game generates a random number (usually between 0 and 1 or 0 and 100). If this number falls within the drop rate range, you get the item. For example, with a 1% drop rate, the game might generate a number between 1-100, and if it's exactly 1, you get the drop. True RNG means each attempt is completely independent and unpredictable.

Drop rates vary by rarity tier: Common items (10-25%), Uncommon (5-10%), Rare (1-5%), Epic (0.1-1%), Legendary (0.01-0.1%), and Mythic/SSR (less than 0.01%). These percentages are industry standards used in MMOs, looter shooters, and gacha games. Higher rarity items require significantly more attempts to obtain. For example, a 0.6% Legendary rate (typical in gacha games) means you need about 115 attempts to reach 50% probability of success.

A 1% drop rate doesn't guarantee a drop in 100 attempts. With 100 attempts at 1% drop rate, you only have a 63.4% chance of success, meaning roughly 37% of players will get nothing. This is normal probability - not bad luck or broken mechanics. To reach 90% confidence with a 1% drop rate, you actually need 230 attempts. Many players misunderstand drop rates as guarantees, leading to frustration when the statistics don't work in their favor.

For multiple independent drops from the same source (like getting either Item A or Item B), add the individual drop rates together first, then use our calculator. For sequential drops (getting Item A AND Item B from different sources), multiply the individual probabilities. For example, if you need two items each with 10% drop rate from different bosses, your chance of getting both is 10% × 10% = 1%. For complex probability scenarios, our percentage calculator can help with the underlying math.