Endgame tablebase - chess endgame databases
Endgame tablebase
Definition
An endgame tablebase is a precomputed database that contains the exact result of every legal chess position with a limited number of pieces on the board (for example, all positions with up to 7 pieces, counting both sides). For each position, the tablebase encodes perfect play: whether the side to move is winning, drawing, or losing, and often how many moves are required to force the result against best defense.
What a tablebase contains
- WDL (Win/Draw/Loss): The fundamental verdict for the side to move under the 50‑move rule.
- DTM (Distance To Mate): The exact number of moves to checkmate with perfect play, typically ignoring the 50‑move rule (classic Nalimov format).
- DTZ or DTZ50 (Distance To Zeroing): The number of moves until the next pawn move or capture that resets the 50‑move counter while maintaining the winning plan (Syzygy format). Engines use DTZ to avoid “wins” that would be nullified by the 50‑move rule.
- Best moves: Some formats store only the result and distance, and engines reconstruct a line; others can also supply one or more optimal moves directly.
How tablebases are built (retrograde analysis)
Tablebases are generated by working backward from terminal positions. The process starts with all checkmates and stalemates (whose outcomes are known) and iteratively marks any position as winning if it can move to a losing position for the opponent, or as losing if all legal moves lead to winning positions for the opponent. This “retrograde analysis” continues until every legal position in the material set is assigned a result. Variants of the algorithm compute distances like DTM and DTZ along the way.
Usage in chess
- Engine strength: Modern engines probe tablebases during search to replace evaluation with perfect knowledge when the position has few enough pieces. Syzygy tablebases are widely used in Stockfish and others for WDL/DTZ guidance.
- Training and study: Players and coaches consult tablebases to verify theoretical results, practice technique, and study defensive resources in tricky endings such as rook and bishop versus rook.
- Adjudication: Correspondence chess and engine tournaments often adjudicate late endgames via tablebases to save time once a result is proven.
- Compositions and studies: Composers check soundness of endgame studies and sometimes discover new ideas or corrections using tablebase truth.
- Anti-cheating considerations: Because tablebases provide perfect moves, accessing them during rated play where external assistance is forbidden is considered engine assistance and violates fair-play rules.
Strategic and historical significance
Endgame tablebases have resolved many long-standing theoretical questions, confirming classics like the Lucena and Philidor positions and uncovering surprising resources such as fortresses, underpromotions, and long zugzwangs. They quantify how “fragile” a win may be under the 50‑move rule and show that some positions are winning in principle (mate is possible) but drawn in practice because no capture or pawn move can be made before 50 moves elapse. This has influenced practical endgame technique: winning sides aim to engineer timely pawn moves or captures to reset the counter, while defenders strive to avoid allowing any “zeroing” move.
Historical milestones
- 1980s–1990s: Ken Thompson pioneered 4‑ and 5‑man tablebases via retrograde analysis on Belle and later systems.
- Early 2000s: Eugene Nalimov’s 6‑man tablebases (DTM) became the standard reference and were integrated into many engines.
- 2012–2013: The 7‑man Lomonosov tablebases were computed on a Moscow State University supercomputer, offering full 7‑piece DTM results.
- 2013 onward: Ronald de Man’s Syzygy tablebases, optimized for WDL and DTZ50 probing from disk, became the most widely used format in top engines. Public 7‑man Syzygy sets followed, practical in “tens of terabytes.”
- FIDE rule context: Historically, there were temporary exceptions to the 50‑move rule for certain endgames (e.g., KBBKN, KNNKP), later repealed; tablebases helped clarify the true landscape of such endings under modern rules.
Examples and instructive positions
Below are typical positions whose theoretical status is confirmed by tablebases. You can load them to explore best play.
-
Lucena position (won with correct “bridge-building” technique):
With White to move, tablebases confirm a forced win by building a bridge to shield the king from checks and promote the a‑pawn.
-
Rook and bishop versus rook (R+B vs R): Theoretical draw with perfect play
Tablebases show that while many positions are drawable, practical winning chances exist if the defender is forced into the “Cochrane” or “second-rank” defenses’ pitfalls. Strong players press for 50 moves trying to induce a concession; defenders aim for known drawing zones.
-
Two knights versus pawn (KNN vs KP): Conditional wins
Without a pawn, KNN vs K is a theoretical draw; with an enemy pawn, tablebases confirm Troitzky’s analysis that many setups are winning—but only if the pawn is sufficiently blocked and mating nets avoid stalemate. The 50‑move rule often decides whether the theoretical win can be realized.
-
Queen versus rook (KQ vs KR): Theoretical win for the queen’s side
Tablebases give exact mate distances and the critical nets (e.g., “W‑maneuver”). In practice, technique and awareness of stalemate tricks are required; tablebases remove any doubt about the winning path.
Famous games and moments
- Carlsen vs. Karjakin, World Championship 2016 (Game 3): Ended in rook and bishop vs rook. Tablebase analysis confirms long phases are drawn with best defense, illustrating how the 50‑move rule and precise technique interact.
- Engine events (various TCEC seasons): Matches are routinely adjudicated by 6‑ and 7‑man tablebases once a known result is reached, saving compute time and preventing pointless shuffling.
- Corrections to endgame literature: Classic manuals occasionally contained errors in rare positions; tablebases have helped refine the canon, confirming or revising lines in endings like KRP vs KR, R+B vs R, and some minor-piece fortresses.
Reading tablebase outputs in practice
- If an engine shows WDL=Win but DTZ=“—”: You’re likely not probing DTZ files. Add DTZ files so the engine can maintain a winning plan that resets the 50‑move counter when necessary.
- DTM (mate in N) is educational but can mislead under the 50‑move rule. Prefer DTZ50 guidance for practical play.
- Probe only when few pieces remain: Engines automatically fall back to evaluation and search before the probe threshold is reached.
Practical tips for players
- Use tablebases to check key textbook positions (Lucena, Philidor, Vancura) and to practice defensive techniques in R+B vs R and KQ vs KR.
- Remember the 50‑move rule: Even “winning” positions can be tablebase draws if no capture or pawn move occurs soon. Plan to engineer a reset.
- Study “critical zones” the tablebases reveal—squares and piece placements that flip a position from drawn to lost or vice versa due to zugzwang or stalemate motifs.
Interesting facts
- 7‑man tablebases completely solve all endgames with 7 total pieces. Storing them in practical formats still requires many terabytes of disk space; compressed online probing makes them widely accessible.
- Some 7‑man positions have astronomical mate lengths (hundreds of moves ignoring the 50‑move rule). DTZ50 ensures engines avoid “illusory” wins that violate the rule.
- Syzygy separates WDL and DTZ files; many users keep only the small WDL set for faster probing during search, adding DTZ files for endgame play/analysis quality.
- Tablebases have uncovered beautiful underpromotions and precise triangulations that are nearly impossible to find over the board without assistance.