THE NUMBERS, EXPLAINED
How to use this calculator.
Stop after first success or the cap. Each attempt has equal independent failure probability and equal compute cost; backoff time is excluded.
Start with your inputs
Enter independent attempt failure probability (fraction), maximum attempts including first (count), compute cost per attempt (currency). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Independent attempt failure probability (fraction) | 0.5 |
| Maximum attempts including first (count) | 3 |
| Compute cost per attempt (currency) | 2 |
A worked example
With the example inputs above, expected attempts (count) is 1.75. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Expected attempts (count) | 1.75 |
| Success by attempt cap (%) | 87.5 |
| Expected compute cost (currency) | 3.5 |
How this is calculated
Expected attempts (count)
Sum the probability that each permitted attempt is reached.
Success by attempt cap (%)
Subtract the probability all allowed attempts fail from one.
Expected compute cost (currency)
Multiply expected attempts by per-attempt cost.
Symbols and units
- a
- Independent attempt failure probability (fraction)
- b
- Maximum attempts including first (count)
- c
- Compute cost per attempt (currency)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Stop after first success or the cap. Each attempt has equal independent failure probability and equal compute cost; backoff time is excluded.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Expected attempts (count); Success by attempt cap (%); Expected compute cost (currency). The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Stop after first success or the cap. Each attempt has equal independent failure probability and equal compute cost; backoff time is excluded.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
OpenStax Algebra and Trigonometry — Series and Their Notations ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →