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task_games__backgammon__pip_count_value

Contract

  1. Domain: games
  2. Scene id: backgammon
  3. Public task id: task_games__backgammon__pip_count_value
  4. Supported query_id values: single
  5. Answer schema: integer_value
  6. Annotation schema: bbox_set
  7. Program schema: sum(map(active_player_occupied_points, checker_count * distance_to_bear_off)); scene=backgammon; scope=pip_count_value

Program Contract

Program: sum(map(active_player_occupied_points, checker_count * distance_to_bear_off)); scene=backgammon; scope=pip_count_value

Candidate set: the visible game board, pieces, tokens, cards, tiles, marked state, legal-move cues, result panels, and labeled options inside the pip_count_value objective scope. Operands: visible scene state and prompt-bound operands named by map, active_player_occupied_points, checker_count, distance_to_bear_off, backgammon, pip_count_value. Operation: evaluate sum over the candidate set using the visible game state, rules, legal moves, comparisons, counts, simulations, or option-selection constraints encoded in the program expression; generation enforces a unique final answer. Output binding: answer uses the integer schema; generation binds a unique final answer. Annotation witnesses: annotation uses the bbox_set schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: aggregation, topology, formula_evaluation

Generation Notes

  1. Query ids are internal replay/sampling keys and do not define public task units.
  2. The generated board is a sparse exact-answer race position with answer support 1..8.
  3. Pip distance follows standard Backgammon bearing-off distance: black checkers on point p contribute p each, while white checkers on point p contribute 25 - p each.
  4. Pip-count renders omit dice and add D labels beside active-player stacks to show the distance-to-bear-off value used in the sum.
  5. Annotation is projected from active-player occupied point bboxes that contribute to the pip-count sum, not individual checker bboxes.