Gaming math lab · Rewards · Original calculator
Drop chance calculator and attempt planner
On this page
For a constant independent drop chance p, the probability of at least one drop in n attempts is 1 − (1 − p)^n. No finite number of attempts guarantees a drop when p is below 100%.
Generic mathematical model, not a named game’s simulator. All starting values are invented examples. Supply verified values for your game and check the assumptions below.
Your scenario
Formula and units
P(at least one) = 1 − (1 − p)^n. Attempts for target q = ceil[ln(1 − q) / ln(1 − p)] for 0 < p,q < 1. Expected drops = n × p.
Worked example
A 5% independent chance over twenty attempts gives 1 − 0.95^20, approximately 64.15% for at least one drop. The expected number of drops is one, which is not the same as a guaranteed drop. Reaching at least 90% probability requires 45 attempts in this model.
How to use this comparison
Enter the chance for one eligible roll, not necessarily one boss kill. If a run contains multiple independent identical rolls, count eligible rolls. Do not multiply unrelated drop rates together unless you have established how the events interact.
Read the result correctly
A long losing streak does not raise the next independent roll’s chance. The table compares different totals of attempts; it does not forecast when your item will appear. A 100% target at a sub-100% drop rate correctly reports no finite count.
Model boundaries
There is no pity counter, duplicate protection, changing drop table, shared group roll or guarantee. Use a documented chance or an explicit scenario, not a rate guessed from a few runs. The tool cannot discover a real drop rate from your item history.
Method: original arithmetic implementation and editorial examples reviewed October 16, 2026. Outputs follow the displayed formula and your inputs. We have not tested these mechanics inside a particular game.