Calculator
Plotly graph
The graph tracks cumulative success growth across attempts. The selected mode also adds a focused comparison line when useful.
Example data table
This example uses a 5% drop rate. It shows how repeated attempts shrink dry-streak risk and increase expected rewards.
| Attempts | At least one drop | No drop | Expected drops |
|---|---|---|---|
| 10 | 40.13% | 59.87% | 0.50 |
| 25 | 72.26% | 27.74% | 1.25 |
| 50 | 92.31% | 7.69% | 2.50 |
| 100 | 99.41% | 0.59% | 5.00 |
Formula used
1) No-drop probability
P(no drop in n attempts) = (1 - p)n
2) At least one drop
P(at least one) = 1 - (1 - p)n
3) Exactly K drops
P(X = K) = C(n, K) × pK × (1 - p)n-K
4) At least K drops
P(X ≥ K) = Σ C(n, i) × pi × (1 - p)n-i for all i from K to n.
5) Attempts needed for a target confidence
n = ceil( ln(1 - c) / ln(1 - p) ), where c is the desired chance of getting at least one drop.
These formulas assume independent attempts and a constant drop rate. Pity systems, streak bonuses, and changing loot pools need a custom model.
How to use this calculator
- Choose the probability mode that matches your question.
- Enter the drop rate for one attempt.
- Enter the number of attempts you plan to run.
- Set target drops when using exact or cumulative K modes.
- Set a confidence target when solving required attempts.
- Choose decimal precision and press the calculate button.
- Review the summary cards, graph, and interpretation notes.
- Export your results with the CSV or PDF buttons.
Frequently asked questions
1) What does drop chance mean?
Drop chance is the probability that one attempt rewards the target item. A 5% rate means each independent attempt has a 0.05 chance of success.
2) Why do long dry streaks still happen?
Random results can cluster. Even fair probabilities produce streaks, especially when rates are low. This calculator shows exactly how likely those dry runs really are.
3) Is expected drops the same as guaranteed drops?
No. Expected drops are a long-run average. You can expect 2.5 drops on average, yet still get zero or four in one specific session.
4) When should I use exactly K drops?
Use exactly K when you want one precise outcome, such as exactly two rare drops in 40 attempts. It does not include higher outcomes.
5) When should I use at least K drops?
Use at least K when reaching a threshold matters more than matching one exact value. It adds every qualifying outcome from K through the maximum attempts.
6) Can this calculator model pity systems?
Not directly. This version assumes a constant independent chance each attempt. For pity systems, you would need separate rates by stage or a custom simulation.
7) What confidence target should I choose?
Players often test 50%, 75%, 90%, or 95%. Higher confidence needs more attempts. Your best target depends on time, resources, and frustration tolerance.
8) Why does the graph rise quickly at first?
Each new attempt adds another chance to succeed. Early attempts change the total a lot, but later gains shrink because cumulative probability approaches its upper limit.