Coupon Collector Completion Calculator
Estimate collection time and completion probability when random draws can repeat equally likely types.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sum geometric waiting times for expected completion, then propagate the count of distinct types for the entered draw count.
E[T]=nΣ(1/k); Var(T)=n²Σ(1/k²)−nΣ(1/k); Pnext(k)=P(k)k/n+P(k−1)(n−k+1)/n
Worked example
With two equally likely types, expected completion is 3 draws and variance is 2. After two draws, completion probability is 50% and expected distinct count is 1.5.
Assumptions and input details
Use 1–200 types and 0–10000 draws. Every type is equally likely, draws are independent with replacement, and collection starts empty. The model does not cover unequal rarity, exchanges, guarantees or a pre-existing partial collection. Probability is propagated in floating point and extreme tails may round or underflow to zero. An expectation is not a promised completion time.
References: MIT: coupon collector expectation and variance
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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