Loot Drop Probability Calculator
Calculate loot drop probability by attempts. Chance after N tries, attempts needed for target %, expected attempts, and no-drop probability. Works for any game.
Enter drop rate and attempts, then click Calculate.
How Does the Formula Work?
The calculator gives the chance of getting a drop at least once in a number of attempts, the chance of getting nothing, the average number of attempts per drop and the attempts needed for a chosen probability. It assumes every attempt has the same drop rate and does not depend on the others, which is the model of the geometric distribution.
P(no drop in n attempts) = (1 - p)^n
p = drop rate as a decimal, n = attempts
Expected attempts per drop = 1 / p
Attempts for X% = smallest n with 1 - (1 - p)^n ≥ X
Example: 1% drop, 100 attempts
P = 1 - 0.99^100 = 63.4% (not 100%)
The Gambler's Fallacy
A drop that has missed 99 times is not due on the 100th: with independent attempts, the 100th still has the same 1%. That is why the geometric distribution is called memoryless: the chance of what comes next does not depend on how long you have waited. Adding the chances (100 × 1% = 100%) is the mistake; multiplying the misses is the method. 0.99^100 leaves 36.6% with nothing, so 63.4% have the item.
Reading the Results
The main figure is the chance of at least one drop, and the no-drop chance is its complement. Expected attempts is an average, 1 / p: at 0.3% that is 333.33 attempts, and single runs scatter widely around it. Tries for 50% and tries for target are whole attempt counts: the first count at which the chance reaches that percentage. The panel never prints 0% or 100% for a chance that is neither; it writes < 0.01% or > 99.99% instead.
Worked Examples
At a 3% drop rate, 50 attempts give 78.2%, and attempt 76 is the first to pass 90% (90.1%). In the Pokémon games of generations II to V a wild Pokémon is shiny with odds of 1 in 8,192; from generation VI the base odds are 1 in 4,096. At 1 in 8,192 the 50% mark arrives after 5,678 encounters.
Choosing a Target
A 90% target means accepting a 10% chance of still missing the item. At a 1% drop rate that takes 230 attempts, and 99% takes 459. For an item you only want eventually, 50% at 69 attempts is a reasonable first checkpoint.
Variance and Streaks
About one player in three who makes exactly 1 / p attempts still has nothing, because (1 - p) raised to 1 / p stays close to 36.8% for small drop rates. At 1% and 500 attempts the chance of still having nothing is 0.66%, so roughly one player in 150 is that unlucky.
Drop Rate Formats
A 1% drop rate is entered as 1, and so is one in 100. One in 1,000 is 0.1. For any one in X, divide 100 by X: one in 8,192 is 0.01220703125. The field accepts rates down to 0.0001, one in a million.
Tips & Recommendations
Works for any drop whose rate stays the same from one attempt to the next.
A 90% target means a 10% chance of still missing the item.
Your own attempt count is always a row, along with the counts for 50% and your target.
Divide 100 by X: one in 8,192 is 0.01220703125.
Frequently Asked Questions
What is the loot drop probability formula?
P(at least 1 drop) = 1 - (1 - p)^n, where p is the drop rate as a decimal and n the number of attempts. At a 1% drop rate, 100 attempts give 1 - 0.99^100 = 63.4%, not 100%.
Why isn't 100 kills × 1% a 100% chance?
Chances of independent attempts do not add up. Each kill misses 99% of the time, and 100 misses in a row happen 0.99^100 = 36.6% of the time, so the chance of at least one drop is 63.4%.
How many tries do I need for a 90% chance?
Enter the drop rate and 90 as the target. At a 1% drop rate the answer is 230 attempts; at 5% it is 45.
What is the expected number of attempts?
1 divided by the drop rate as a decimal: 100 attempts at 1%, 333.33 at 0.3%. It is an average; many players need more and many need fewer.
Does this work for any game?
It works whenever every attempt has the same drop rate and does not depend on earlier attempts. Systems with pity or bad-luck protection, where the chance rises after misses, follow other rules.
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