2d6 Sum Probability Table
Enumerate ordered outcomes for two independent fair d6 to resolve exact caller requested sum, not random sampling or mean/variance.
Description
Two fair six-sided dice have 36 equally likely ordered outcomes.
Two fair six-sided dice have 36 equally likely ordered outcomes. Different sums have different counts.1
Enter an integer target sum 2–12. Enumerate both dice 1–6 and return favorable outcomes and exact-model probability.
When to use 2d6 Sum Probability Table
Use 2d6 Sum Probability Table when you need to evaluate the supplied records under the calculation and evidence rules below. Dice are assumed fair and independent.
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 2d6 Sum Probability Table 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 requestedSum using the field table and calculation rules, then run the tool.
- Read favorableOrderedRollCount, totalOrderedRollCount, exactRequestedSumProbability. 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 |
|---|---|---|---|
| requestedSum | Requested sum | number | Required |
Enter an integer target sum 2–12. Enumerate both dice 1–6 and return favorable outcomes and exact-model probability.
probability=favorablePairs/36 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| favorableOrderedRollCount | Favorable ordered roll count | number |
| totalOrderedRollCount | Total ordered roll count | number |
| exactRequestedSumProbability | Exact requested sum probability | number |
{
"input": {
"requestedSum": 7
},
"output": {
"favorableOrderedRollCount": 6,
"totalOrderedRollCount": 36,
"exactRequestedSumProbability": 0.16666666666666666
}
}Limitations and assumptions
Dice are assumed fair and independent.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Nd6 Dice Sum Mean & Variance: Loaded-die weights define a probability model only after normalization. Independent dice add expectations and variances. For a complementary task, use Risk 3v2 Attack Odds Lookup: Risk compares sorted attacking and defending dice, with ties favoring the defender. Exhaustive enumeration gives an exact fair-dice casualty model.
References
-
2d6 Sum Probability Table — tool.io
Similar or alternative tools
- Nd6 Dice Sum Mean & Variance
Loaded-die weights define a probability model only after normalization. Independent dice add expectations and variances.
- Risk 3v2 Attack Odds Lookup
Risk compares sorted attacking and defending dice, with ties favoring the defender. Exhaustive enumeration gives an exact fair-dice casualty model.