Birthday Paradox Checker
Exact365equallylikelyindependentbirthdaycollisionprobability,not cryptographicbirthdayboundapproximation;group≤365.
Description
The birthday paradox describes shared birthdays in a group under a simplified random model.
The birthday paradox describes shared birthdays in a group under a simplified random model.1
This calculator assumes 365 equally likely independent birthdays and gives the probability of at least one shared date.
When to use Birthday Paradox Checker
Use this tool to apply the stated birthday paradox checker operation with an explicit input and unit basis.
How to use Birthday Paradox Checker and how it works
- Establish the text or game convention described above.
- Enter actualGroupSize and run the tool.
- Read result.value using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualGroupSize | Group Size. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; integer from 0 to 1000000; further conditions in the algorithm |
Require integer group size 0–365. Multiply the probability that each successive birthday avoids previous dates, then subtract from one; groups of zero or one return zero. Leap days and seasonal birth frequencies are outside the model.
P(shared birthday) = 1 − product from i=0 to n−1 of (1−i/365) Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.value | Probability in [0,1] under the declared model. | number |
{
"input": {
"actualGroupSize": 2
},
"output": {
"result": {
"value": 0.002739726027397249
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A returned boolean, signed difference or tied result follows the stated convention; an input error instead means the required input contract was not satisfied. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Gambler's Ruin Probability Calculator. Gambler’s ruin is the chance that a fixed-step bankroll reaches zero before a chosen target.
For a related operation, use Flip a Coin Streak Probability Calculator. The probability of one specified all-heads block differs from the chance of finding a run somewhere in many tosses.
References
-
Birthday Paradox Checker — tool.io
Similar or alternative tools
- Gambler's Ruin Probability Calculator
Gambler’s ruin is the chance that a fixed-step bankroll reaches zero before a chosen target.
- Flip a Coin Streak Probability Calculator
The probability of one specified all-heads block differs from the chance of finding a run somewhere in many tosses.