d20 Meet-or-Beat DC Probability
Compute exact d20 meet-or-beat chance with explicit modifier and max/min-of-two mode; natural 1/20 have no automatic failure/success in this generic check contract.
Description
A d20 threshold check counts successful natural faces after a modifier.
A d20 threshold check counts successful natural faces after a modifier. Advantage and disadvantage select a maximum or minimum of two independent rolls.1
Enter integer DC/modifier bounded by absolute 1000000 and normal/advantage/disadvantage mode. Clip the successful face count to 0–20 and return mode probability.
When to use d20 Meet-or-Beat DC Probability
Use d20 Meet-or-Beat DC Probability when you need to evaluate the supplied records under the calculation and evidence rules below. Natural 1/20 automatic failure/success rules are not applied.
Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
How to use d20 Meet-or-Beat DC Probability and understand its results
- Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
- Enter targetDifficulty, flatRollModifier, rollMode using the field table and calculation rules, then run the tool.
- Read successfulNaturalFaces, exactSuccessProbability. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| targetDifficulty | Target difficulty | number | Required |
| flatRollModifier | Flat roll modifier | number | Required |
| rollMode | Roll mode | string | Required |
Enter integer DC/modifier bounded by absolute 1000000 and normal/advantage/disadvantage mode. Clip the successful face count to 0–20 and return mode probability.
normal=p; advantage=1−(1−p)²; disadvantage=p² Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| successfulNaturalFaces | Successful natural faces | number |
| exactSuccessProbability | Exact success probability | number |
{
"input": {
"targetDifficulty": 15,
"flatRollModifier": 2,
"rollMode": "advantage"
},
"output": {
"successfulNaturalFaces": 8,
"exactSuccessProbability": 0.64
}
}Limitations and assumptions
Natural 1/20 automatic failure/success rules are not applied.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Extremely large text inputs are rejected. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use D&D Ability Modifier floor((score−10)/2): Dungeons & Dragons ability modifiers use downward rounding. Negative odd differences therefore round away from zero. For a complementary task, use Nd6 Dice Sum Mean & Variance: Loaded-die weights define a probability model only after normalization. Independent dice add expectations and variances.
References
-
d20 Meet-or-Beat DC Probability — tool.io
Similar or alternative tools
- D&D Ability Modifier floor((score−10)/2)
Dungeons & Dragons ability modifiers use downward rounding. Negative odd differences therefore round away from zero.
- Nd6 Dice Sum Mean & Variance
Loaded-die weights define a probability model only after normalization. Independent dice add expectations and variances.