Catan Dot Probability Pips
Audit actual adjacent Catan number tokens and robber exclusions; one unit per listed hex, summed resource expectation may exceed one and is not probability of any production. Cities/shortages omitted.
Description
Catan production expectation weights each adjacent number by its two-dice frequency.
Catan production expectation weights each adjacent number by its two-dice frequency. Multiple hexes can award more than one resource per roll.1
Enter aligned nonempty number tokens 2–12 excluding 7 and binary robber flags. Return effective pip weights and expected resources per roll.
When to use Catan Dot Probability Pips
Use Catan Dot Probability Pips when you need to evaluate the supplied records under the calculation and evidence rules below. This is an expected quantity, which may exceed one, rather than probability of any production; cities and resource types are excluded.
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 Catan Dot Probability Pips 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 adjacentProductionNumbers, robberBlockedFlags using the field table and calculation rules, then run the tool.
- Read perHexPrintedProbabilityPips, expectedUnblockedResourceUnitsPerRoll. 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 |
|---|---|---|---|
| adjacentProductionNumbers | Adjacent production numbers | list of number | Required |
| robberBlockedFlags | Robber blocked flags | list of number | Required |
Enter aligned nonempty number tokens 2–12 excluding 7 and binary robber flags. Return effective pip weights and expected resources per roll.
expectedResources=sum(unblocked (6−abs(7−number)))/36 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| perHexPrintedProbabilityPips | Per hex printed probability pips | list of number |
| expectedUnblockedResourceUnitsPerRoll | Expected unblocked resource units per roll | number |
{
"input": {
"adjacentProductionNumbers": [
6,
8
],
"robberBlockedFlags": [
0,
1
]
},
"output": {
"perHexPrintedProbabilityPips": [
5,
5
],
"expectedUnblockedResourceUnitsPerRoll": 0.1388888888888889
}
}Limitations and assumptions
This is an expected quantity, which may exceed one, rather than probability of any production; cities and resource types are excluded.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 10,000 entries; string lists to 128 strings of at most 128 characters each. The rules above may impose smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use 2d6 Sum Probability Table: Two fair six-sided dice have 36 equally likely ordered outcomes. Different sums have different counts. 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
-
Catan Dot Probability Pips — tool.io
Similar or alternative tools
- 2d6 Sum Probability Table
Two fair six-sided dice have 36 equally likely ordered outcomes. Different sums have different counts.
- Nd6 Dice Sum Mean & Variance
Loaded-die weights define a probability model only after normalization. Independent dice add expectations and variances.