Description
Count entries strictly above tolerance and entries no greater than it.
A strategy's support identifies actions assigned positive mass under a stated threshold. Support flags, normalized probabilities and payoff indifference are separate properties, so one check does not establish a valid mixed-strategy equilibrium.
Count entries strictly above tolerance and entries no greater than it.
When to use this tool
Use Strategy Support Positive Count when you need a probability-mass or thresholded-support diagnostic.
How to use the tool and how it works
- Enter probabilities, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read supportCount, zeroWithinTolerance. Use the output convention below.
Require each probability in [0, 1] and nonnegative tolerance. Count entries strictly above tolerance and entries no greater than it.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probabilities | Individual [0, 1] masses; sum-to-one is not enforced. | Required. Array of finite number; maximum items 256. |
| tolerance | Nonnegative threshold; support uses strictly greater than. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| supportCount | Support Count | Required. Safe integer. |
| zeroWithinTolerance | Zero Within Tolerance | Required. Safe integer. |
{
"input": {
"probabilities": [
0.5,
0.5,
0
],
"tolerance": 0
},
"output": {
"supportCount": 2,
"zeroWithinTolerance": 1
}
}Limitations and assumptions
- The probabilities are not required to sum to one; tolerance can exceed one. This is thresholded support counting, not distribution validation.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Validate the complete distribution and compare payoffs of all relevant deviations. State any numerical tolerance and zero-mass convention before interpreting support as an equilibrium property.
References
Similar or alternative tools
- Mixed Strategy Support Residual
Sum inside and outside support and return one minus total mass.
- Mixed Deviation Support Mass
Sum flagged probability mass and total mass.