Gambler's Ruin Probability Calculator
Finitegambler ruinprobabilitybeforetargetunderindependentunitstakes,nohouse credit/variablebets,0<start<target≤1000;extremeoverflow rejected.
Description
Gambler’s ruin is the chance that a fixed-step bankroll reaches zero before a chosen target.
Gambler’s ruin is the chance that a fixed-step bankroll reaches zero before a chosen target.1
This calculator assumes independent one-unit wins or losses with an unchanged win probability and no time limit.
When to use Gambler's Ruin Probability Calculator
Use this tool to apply the stated gambler's ruin probability calculator operation with an explicit input and unit basis.
How to use Gambler's Ruin Probability Calculator and how it works
- Establish the text or game convention described above.
- Enter actualWinProbability, actualStartingUnits, actualTargetUnits 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 |
|---|---|---|---|
| actualWinProbability | Win Probability. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; 0–1 inclusive; further conditions in the algorithm |
| actualStartingUnits | Starting Units. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; integer from 1 to 1000000; further conditions in the algorithm |
| actualTargetUnits | Target Units. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; integer from 1 to 1000000; further conditions in the algorithm |
Require win probability p in [0,1], integer target N from 2 to 1000 and integer starting units a from 1 to N−1. At p=0 return 1, at p=1 return 0 and at p=0.5 return 1−a/N. Otherwise evaluate the ratio with logarithms and expm1; reject nonfinite arithmetic rather than promise a stable answer for every extreme p.
r=(1−p)/p; ruin = 1 − (r^a−1)/(r^N−1), away from the stated special cases 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": {
"actualWinProbability": 0.5,
"actualStartingUnits": 2,
"actualTargetUnits": 4
},
"output": {
"result": {
"value": 0.5
}
}
}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 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.
For a related operation, use Coin Flip Best-of-N Decider. A best-of-an-odd-number coin decision uses a majority to avoid a tie.
References
-
Gambler's Ruin Probability Calculator — tool.io
Similar or alternative tools
- 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.
- Coin Flip Best-of-N Decider
A best-of-an-odd-number coin decision uses a majority to avoid a tie.