KBNK: The Bishop and Knight Checkmate

Overview

1. Example Games with Automatically-Generated Instructions
2. The Bishop and Knight Checkmate: Textbook Instructions
3. The Hierarchical Model of Ordered Set of Rules
4. Descriptions of Attributes


1. Example Games with Automatically-Generated Instructions

Example games containing automatically generated commentary are presented here.


2. The Bishop and Knight Checkmate: Textbook Instructions

Textbook instructions for teaching the KBNK endgame: KBNK textbook instructions (PDF, 1.12 MB).


3. The Hierarchical Model of Ordered Set of Rules

  1. IF true
    THEN checkmate = true

  2. IF min_area = true
    THEN knight_prepare = true

  3. IF min_area = false
    THEN min_area = true

  4. IF king_area > 70 AND ndist <= 3
    THEN king_area should decrease AND king_area minimise

  5. IF cpdist > 1
    THEN cpdist should decrease AND king_area should not increase AND mkdist should not increase AND mkdist minimise

  6. IF edist < 1
    THEN edist should not increase AND knight_on_edge = false AND wrong_corner_way should decrease AND wrong_corner_way minimise AND white_king_more_central = true

  7. IF kdist < 3 AND ndist < 6 AND rcdist > 0
    THEN edist should not increase AND rcdist should decrease

  8. IF kdist < 3 AND edist > 0
    THEN edist should decrease AND piece_safety = true AND wrong_corner_way should not increase

  9. IF cpdist > 0 AND mkdist > 2
    THEN edist should not increase AND mkdist should decrease AND mkdist minimise

  10. IF ndist > 2
    THEN ndist should decrease

  11. IF true
    THEN kdist should not increase AND mkdist minimise


4. Descriptions of Attributes

attribute description
checkmate deliver checkmate within 5 plies
min_area white king and bishop are on adjacent squares, and constrain black king to only two squares beside the right-coloured corner
knight_prepare white knight is able to attack the square adjacent to the right-coloured corner square in just one move
king_area 8 * the farther diagonal black king can reach from the right-coloured corner + number of squares black king can reach on the farther diagonal
wrong_corner_way 8 * the farther diagonal black king can reach from the right-coloured corner + number of squares black king can reach on the farther diagonal, but only in the direction towards the nearest wrong-coloured corner
kdist distance between the kings
mkdist Manhattan distance between the kings
edist distance between black king and the edge of the board (max=3)
ndist distance between black king and white knight
rcdist distance between black king and right-coloured corner
cpdist distance between white king and the closest square to black king on a straight line between black king and the very center of the board
piece_safety white pieces are not closer to black king then to white king
white_king_more_central white king is no closer to the right-coloured corner than black king, when rcdist < 5, otherwise always true