King Capture Probability Test Cases
This page catalogs all our active test cases for king capture probability, allowing developers to visually inspect and verify scenarios.
1. Kings at a distance
Section titled “1. Kings at a distance”Kings positioned on opposite ends of the board with no intervening or threatening pieces.
- Expected Probability:
0.00% (0/216) - Defended Color:
White - Combinatorial rationale: No king can cross the seven-rank gap in three micro-moves: 0 winning rolls.
- FEN:
4k3/8/8/8/8/8/8/4K3 b - -
2. At least one bishop
Section titled “2. At least one bishop”A single bishop directly attacks the king, making it vulnerable whenever that piece type appears.
- Expected Probability:
42.13% (91/216) - Defended Color:
Black - Combinatorial rationale: Bishop f7 captures e8 directly. At least one Bishop die: 216 - 5^3 = 91.
- FEN:
rnbqkbnr/pppppBpp/8/8/4P3/8/PPPP1PPP/RNB1K1NR w KQkq - 0 1
3. At least one of two pieces
Section titled “3. At least one of two pieces”Multiple attacking pieces are present, creating a threat if either piece type is rolled.
- Expected Probability:
70.37% (152/216) - Defended Color:
Black - Combinatorial rationale: Knight g5 or Queen f3 captures f7 directly. At least one of these two types: 216 - 4^3 = 152.
- FEN:
rnb1qbnr/pppppkpp/8/6N1/8/4PQ2/PPPP1PPP/RNB1K2R w KQ - 0 1
4. Two pieces (different)
Section titled “4. Two pieces (different)”Two different attacking pieces must both appear on the dice to facilitate a capture threat.
- Expected Probability:
13.89% (30/216) - Defended Color:
Black - Combinatorial rationale: Pawn b4-b5 clears Bishop a3-e7. At least one Pawn and one Bishop: 216 - 2 * 5^3 + 4^3 = 30.
- FEN:
rnbq1bnr/ppppkppp/8/4p3/1P6/B7/P1PPPPPP/R3KBNR w KQ - 0 1
5. Two identical pieces (doubles)
Section titled “5. Two identical pieces (doubles)”Vulnerability depends on rolling a specific pair of identical attacking pieces.
- Expected Probability:
7.41% (16/216) - Defended Color:
Black - Combinatorial rationale: Bishop c4-f7-e8 needs at least two Bishop dice: 3 * 5 + 1 = 16.
- FEN:
rnbqkbnr/pppppppp/8/8/2B1P3/8/PPPP1PPP/RNB1K1NR w KQ - 0 1
6. Three identical pieces (triplets)
Section titled “6. Three identical pieces (triplets)”The king is threatened only if three identical attacking pieces are rolled simultaneously.
- Expected Probability:
0.46% (1/216) - Defended Color:
Black - Combinatorial rationale: Knight c3-e4-d6-e8 needs three Knight dice: 1 ordered roll.
- FEN:
rnbqkbnr/pppppppp/8/8/8/2N5/PPPPPPPP/R1BQKBNR w KQ - 0 1
7. One of three pieces
Section titled “7. One of three pieces”Multiple attacking piece types are capable of threatening the king if any one of them appears.
- Expected Probability:
87.50% (189/216) - Defended Color:
Black - Combinatorial rationale: Knight d5, Bishop h4 or Queen a3 captures e7 directly. At least one of three types: 216 - 3^3 = 189.
- FEN:
rnbq1bnr/ppppkppp/4p3/3N4/3P3B/Q7/PPP1PPPP/R3KBNR w KQ - 0 1
8. One of four pieces
Section titled “8. One of four pieces”High likelihood of king capture threat as it depends on any one of four different attacker types appearing.
- Expected Probability:
96.30% (208/216) - Defended Color:
Black - Combinatorial rationale: Knight d5, Bishop g5, Rook e3 or Queen a3 captures e7 directly. At least one of four types: 216 - 2^3 = 208.
- FEN:
rnbq1bnr/ppppkppp/8/3N2B1/P2P4/Q3R3/1PP1PPPP/4KBNR w K - 0 1
9. One of five pieces
Section titled “9. One of five pieces”Almost certain capture threat as nearly any piece type appearing on the dice enables the attack.
- Expected Probability:
99.54% (215/216) - Defended Color:
Black - Combinatorial rationale: Pawn d4, Knight f3, Bishop h2, Rook e8 or Queen a5 captures e5 directly. Only three King dice fail: 216 - 1 = 215.
- FEN:
4R3/8/8/Q3k3/3P4/5N2/7B/6K1 w - - 0 1
10. Three different pieces
Section titled “10. Three different pieces”Threat requires the specific combination of three different attacking piece types.
- Expected Probability:
2.78% (6/216) - Defended Color:
Black - Combinatorial rationale: Pawn c4-c5 and a Knight move from d5 clear Bishop b3-f7. One Pawn, Knight and Bishop: 3! = 6 ordered rolls.
- FEN:
rnbq1bnr/pppppkpp/8/3N4/2P5/1B1P2P1/PP2PP1P/R1B1K2R w KQ - 0 1
11. Two identical pieces + one different piece
Section titled “11. Two identical pieces + one different piece”Threat relies on a specific combination consisting of a pair of identical pieces and one different piece.
- Expected Probability:
1.39% (3/216) - Defended Color:
Black - Combinatorial rationale: Pawn e2-e3 clears Bishop f1-c4-f7. One Pawn and two Bishop dice: 3 ordered rolls.
- FEN:
rnbq1bnr/pppppkpp/8/8/8/2P5/PP1PPPPP/R1B1KB1R w KQ - 0 1
12. Queen and Bishop threatening the King
Section titled “12. Queen and Bishop threatening the King”Combined attacking influence from both the queen and bishop.
- Expected Probability:
14.81% (32/216) - Defended Color:
Black - Combinatorial rationale: Bishop b5-d7-e8 or Queen f3-f7-e8 needs a matching pair. These events are disjoint in three dice: 16 + 16 = 32.
- FEN:
rnbqkbnr/pppppppp/8/1B6/4P3/5Q2/PPPP1PPP/RNB1K1NR w KQkq - 0 1
13. A bishop and the three queens
Section titled “13. A bishop and the three queens”Direct attacking pressure combined with support from multiple queen threats.
- Expected Probability:
42.59% (92/216) - Defended Color:
Black - Combinatorial rationale: Bishop f7-e8 needs any Bishop die (91 rolls); Queen d1-g4-d7-e8 adds the disjoint triple-Queen roll: 91 + 1 = 92.
- FEN:
rnbqkbnr/pppppBpp/8/8/4P3/8/PPPP1PPP/RNBQK1NR w KQkq - 0 1
14. Two pieces or queens
Section titled “14. Two pieces or queens”Capture threat necessitates specific different piece types to be rolled.
- Expected Probability:
14.35% (31/216) - Defended Color:
Black - Combinatorial rationale: Pawn b4-b5 clears Bishop a3-e7 (30 rolls); Knight b1-c3-d5-e7 adds the disjoint triple-Knight roll: 30 + 1 = 31. The historical title mentions queens, but the extra winning roll is Knights.
- FEN:
rnbq1bnr/ppppkppp/8/4p3/1P6/B7/P1PPPPPP/RN1QKBNR w KQ - 0 1
