Syzygy tablebases: endgame WDL/DTZ
Syzygy tablebases
Definition
Syzygy tablebases are a complete, exact database of chess endgames with a limited number of pieces on the board (typically 3–7 “men,” counting both kings). Created by Ronald de Man (c. 2013–2014), they encode every legal position in those endings and the perfect result with optimal play, taking the 50-move rule into account. Engines “probe” these files to play flawlessly once the game simplifies to a tablebase-covered position.
What they contain and how they work
Syzygy distinguishes between two complementary data sets:
- WDL tables (Win/Draw/Loss): For a given position and side to move, WDL says whether the result is a theoretical win, draw, or loss with the 50-move rule enforced.
- DTZ tables (Depth To Zeroing move): The distance in plies to the next “zeroing” move (a capture or pawn move) that resets the 50-move counter, while preserving the winning/drawing objective. DTZ guides engines to play wins within the constraints of the 50-move rule.
Because DTZ and WDL are compact and geared to practical engine decisions, Syzygy files are much smaller and faster to probe than older DTM-based sets (Distance To Mate) such as Nalimov. Typical setups include full 3–5-man WDL+DTZ, 6-man WDL (often with DTZ), and sometimes 7-man WDL. Complete 7-man coverage is very large (many terabytes).
Usage in chess
- Engine play and analysis: During search, engines query WDL to learn the perfect result of leaf positions and use DTZ to choose moves that maintain winning chances while resetting the 50-move counter when necessary.
- Adjudication: Many online platforms and engine tournaments automatically adjudicate positions with 7 or fewer men using tablebases, stopping games when the result is known.
- Training and study: Coaches and players verify endgame analysis, test fortress claims, and extract model lines for instruction. Studies are often checked against tablebases to confirm soundness.
Strategic significance
- 50-move rule awareness: Syzygy’s WDL/DTZ approach builds the 50-move rule into the evaluation. In some endgames (for example, rook and bishop vs rook), positions that are “mate with best play” in DTM terms become theoretical draws under the 50-move rule unless a capture or pawn move can be forced in time. Syzygy will show many such positions as drawn.
- Forcing zeroing moves: DTZ teaches practical winning technique: favor lines that achieve a capture or pawn push to reset the counter, even if they appear to “give up” material temporarily.
- Zugzwang and fortresses: Tablebases precisely reveal zugzwangs, stalemates, and fortresses. They confirm, for instance, that a rook pawn with the “wrong” bishop against a lone king is drawn when the defender reaches the safe corner.
- Refining endgame theory: Classic rules of thumb are validated, sharpened, or corrected—e.g., KBN vs K mates in at most 33 moves; queen vs rook is won (mate in at most 31 moves), while two knights cannot force mate without a pawn present.
Historical notes
- Nalimov tablebases (early 2000s): Pioneering 6-man DTM bases, huge and not 50-move-aware in their primary metric.
- Lomonosov 7-man (c. 2012): First complete 7-man DTM bases, computed with supercomputing resources, delivered via online access because of their size.
- Syzygy (Ronald de Man, 2013–2014): Introduced WDL/DTZ for compact storage and fast probing, quickly adopted by engines (e.g., Stockfish family) and now the de facto standard for practical endgame perfection.
- Rules and practice: FIDE historically experimented with exceptions to the 50-move rule in certain endgames, but these were removed; modern tablebases assume the standard 50-move rule, which shapes many WDL outcomes.
Examples
1) Mutual zugzwang (“Trebuchet”)—WDL flips with side to move
In this symmetrical pawn ending, whoever moves first loses. Syzygy labels one side as “loss” solely due to the move obligation.
Position (White: Kd4, Pe4; Black: Kf4, pe5; White to move loses):
- If 1. Kd5, then 1... Kf3 and Black penetrates; if 1. Kd3, then 1... Kf3 2. h4? isn’t possible, and Black wins the e4-pawn and the opposition.
- With Black to move, the mirror logic applies and White would be winning instead.
2) Wrong bishop fortress—drawn despite material edge
With a rook pawn whose promotion square is the opposite color of the bishop, the defender’s king reaches the corner to draw. Syzygy confirms WDL = draw for both sides to move.
Position (White: Kh1, Bc1, ph2; Black: Kg3; White to move, draw):
- Even with perfect play, White cannot force the king off the h-file or control h8 with the light-squared bishop. Any attempt to approach allows perpetual checks or stalemate defenses.
3) Queen vs Rook—win within the 50-move rule
Syzygy shows that KQ vs KR is a theoretical win (WDL = win) and DTZ guides precise maneuvers to avoid stalemates and deliver mate within 31 moves (no 50-move issue). The winning technique uses nets like the “W-maneuver” to corner the king.
Illustrative starting setup (White: Kg1, Qf1; Black: Kg8, Rf8; White to move, WDL = win):
- Typical plan: restrict the rook with queen checks from behind, push the king to the edge, and force a decisive skewer or mating net.
How engines use Syzygy during search
- Leaf evaluation: When a node has ≤ 7 men, the engine probes WDL to replace heuristic evaluation with the exact result.
- Move ordering and pruning: Losing branches (per WDL) can be pruned early; DTZ selects moves that maintain the winning basin and aim for the next zeroing move.
- Practical tip: On your system, store Syzygy on a fast SSD; start with full 3–5-man WDL+DTZ, add 6-man WDL next, and DTZ for the 6-man sets if space permits. 7-man WDL is enormous and mainly used by servers or research setups.
Interesting facts and anecdotes
- Name origin: “Syzygy” means an alignment of celestial bodies—apt for the perfect alignment and coordination required in endgames.
- Rewriting endgame books: Tablebases confirmed many fortress claims and unearthed remarkable mutual zugzwangs and stalemate resources previously unknown or doubted.
- Human vs. machine: Even grandmasters sometimes fail to convert theoretical wins like KQ vs KR over the board; Syzygy-enabled engines never do.
- No DTM needed: Syzygy purposely avoids storing DTM; WDL+DTZ is what engines need to convert wins under the 50-move rule efficiently and with far less disk space.