Backgammon Pip Count Race Check

Reconcile race-only 15-checker inventories using each side relative home distance, borne-off zero pips; no bar/contact/hit analysis or win probability from pip difference.

Description

Backgammon pip count weights each on-board checker by its distance to bearing off.

Backgammon pip count weights each on-board checker by its distance to bearing off. Counts are given from each player’s own home direction.^[1]

Enter two 24-entry nonnegative integer lists and nonnegative borne-off counts, totaling exactly 15 per player. Return both pip counts and signed difference.

When to use Backgammon Pip Count Race Check

Use Backgammon Pip Count Race Check when you need to evaluate the supplied records under the calculation and evidence rules below. Checkers on the bar, contact, legal moves and winning probability are not modeled.

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 Backgammon Pip Count Race Check 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 whiteCheckerCountsAtDistanceOneToTwentyFour, blackCheckerCountsAtDistanceOneToTwentyFour, whiteBorneOffCount, blackBorneOffCount using the field table and calculation rules, then run the tool.
Read whiteRacePipCount, blackRacePipCount, signedWhiteMinusBlackPips. 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
whiteCheckerCountsAtDistanceOneToTwentyFour	White checker counts at distance one to twenty four	list of number	Required
blackCheckerCountsAtDistanceOneToTwentyFour	Black checker counts at distance one to twenty four	list of number	Required
whiteBorneOffCount	White borne off count	number	Required
blackBorneOffCount	Black borne off count	number	Required

Enter two 24-entry nonnegative integer lists and nonnegative borne-off counts, totaling exactly 15 per player. Return both pip counts and signed difference.

pips=sum(pointNumber×checkers); difference=white−black

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
whiteRacePipCount	White race pip count	number
blackRacePipCount	Black race pip count	number
signedWhiteMinusBlackPips	Signed white minus black pips	number

json

{
  "input": {
    "whiteCheckerCountsAtDistanceOneToTwentyFour": [
      0,
      0,
      0,
      0,
      1,
      1,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0
    ],
    "blackCheckerCountsAtDistanceOneToTwentyFour": [
      1,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0
    ],
    "whiteBorneOffCount": 13,
    "blackBorneOffCount": 14
  },
  "output": {
    "whiteRacePipCount": 11,
    "blackRacePipCount": 1,
    "signedWhiteMinusBlackPips": 10
  }
}

Limitations and assumptions

Checkers on the bar, contact, legal moves and winning probability are not modeled.

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 Inventory Encumbrance Over-Limit Check: Inventory weight pools item counts and per-unit weights with equipped load. A signed margin exposes overload. For a complementary task, use Double-Six Dominoes Total Pips: A double-six domino inventory treats a tile as an unordered pair. A complete set contains all 28 possible pairs.

References

Backgammon Pip Count Race Check — tool.io

Similar or alternative tools

Inventory Encumbrance Over-Limit Check
Inventory weight pools item counts and per-unit weights with equipped load. A signed margin exposes overload.
Double-Six Dominoes Total Pips
A double-six domino inventory treats a tile as an unordered pair. A complete set contains all 28 possible pairs.