Endgame tablebases

Endgame tablebases

Definition

Endgame tablebases are exhaustive databases that contain the exact outcome (win, draw, or loss) and perfect play for every legal chess position with a limited number of pieces on the board. For each position, a tablebase can tell you whether the side to move can force a win against best defense, and often how many moves it takes to achieve a decisive event (such as mate or a capture/pawn move). Modern public tablebases cover all positions with up to seven pieces (including kings). Because they are built by retrograde analysis from all possible mates backward, their guidance is mathematically perfect.

How they are used in chess

  • Engine accuracy: Chess engines “probe” tablebases when the position has seven or fewer pieces. The engine then plays flawlessly in that endgame, instantly knowing the result and the best moves.
  • Training and study: Players consult tablebases to learn exact defensive resources (e.g., fortress holds) and winning techniques (e.g., KBN vs K). They also check whether a position is a theoretical win or draw.
  • Adjudication: Online servers and some tournaments adjudicate positions that are within tablebase scope. If the position is a tablebase win or draw and the claim conditions (like the 50‑move rule) are met, the result may be declared.
  • Correspondence chess: Under modern correspondence rules (e.g., ICCF), using engines and tablebases is typically allowed, so endgames within tablebase range are played perfectly.
  • Endgame theory: Composers and theoreticians use tablebases to test studies, discover new resources, and refine or overturn traditional endgame evaluations.

History and milestones

  • Early foundations (1980s–1990s): Ken Thompson’s work produced the first complete 5‑man tablebases, proving many classical endings and revealing hard defenses.
  • Nalimov tablebases (circa 2000): Eugene Nalimov’s format popularized 5‑ and 6‑man tablebases, widely used by engines and analysts.
  • Lomonosov 7‑man (2012–2014): Computed on the Lomonosov supercomputer (Vladimir Makhnychev and Konstantin Zakharov), these were the first complete 7‑piece tablebases, uncovering wins that require hundreds of optimal moves.
  • Syzygy tablebases (Ronald de Man): A highly efficient, engine‑friendly format that split data into WDL (win/draw/loss) and DTZ (distance‑to‑zeroing move), now standard in top engines. Syzygy

Key metrics you’ll see

  • WDL: Win/Draw/Loss outcome under optimal play (usually respecting the 50‑move rule via reset‑aware metrics like DTZ).
  • DTM (Distance to Mate): Number of moves to mate with perfect play, ignoring the 50‑move reset constraint.
  • DTC/DTR: Distance to Conversion/Repetition; older metrics measuring moves to a capture/pawn move (conversion) or repetition state.
  • DTZ (Distance to Zeroing move): In Syzygy, the number of moves to the next pawn move or capture (which “resets” the 50‑move counter) or to mate if sooner. DTZ guides engines to maintain winning chances within 50‑move windows.

Strategic and rules significance

  • 50‑move rule pressure: Tablebases revealed many positions “won” in principle but drawable due to the 50‑move rule unless the attacker can engineer a capture or pawn move to reset the count. This created the notions of “cursed wins” (objectively winning, but drawn by the rule) and “blessed losses.”
  • Fortresses and resources: Many surprising fortress holds and stalemate ideas are confirmed. Conversely, some long‑assumed fortresses were overturned by perfect play.
  • Guiding technique: Tablebases show the fastest routes and critical “only moves,” sharpening human endgame technique, e.g., precise maneuvers in rook endgames or the winning net in KBN vs K.
  • Rule evolution: FIDE retains the 50‑move claim rule and added a 75‑move automatic draw rule (no pawn move or capture in the last 75 moves). Tablebases helped quantify just how long some wins can be without resets.

Examples

  • “Wrong rook pawn” fortress (draw):

    With a bishop that does not control the promotion square of a rook pawn, the defender can draw by reaching the corner. For instance, imagine White: Kg6, Bf5 (light‑squared bishop), pawn h6; Black: Kh8, no other pieces. Even with the extra pawn, White cannot force the king out of h8 because the h8‑promotion square is dark and the bishop is on light squares. Moves like 1. Be6 (threatening Bg8) are met by 1... Kg8 and any attempt to escort the pawn leads to stalemate motifs. Tablebases confirm a 100% draw with best defense once the king reaches the corner.

  • KBN vs K (win in up to 33 moves):

    Tablebases certify that K+bishop+knight vs K is a theoretical win, with a maximum DTM of 33 from the worst initial placements. The technique uses triangulation to drive the king to a corner controlled by the bishop (e.g., mate patterns in a1/h8). Example plan: 1. Nd6+ Ke7 2. Ke5 Kd7 3. Bb5+ Ke7 4. Bc4 Kd7 5. Bb5+ Ke7 6. Bc6 Kd8 7. Ke6 Kc7 8. Bd5, etc., squeezing the king. The exact route is tablebase‑perfect and often counterintuitive in its waiting moves.

  • Troitsky line in KNN vs K+P:

    Human theory (via A. A. Troitsky) predicted a boundary beyond which two knights can win against a lone king plus a pawn. Seven‑man tablebases largely confirmed and refined this “Troitsky line,” showing exactly which pawn positions allow mate and which are drawn because the defender can sac the pawn to avoid zugzwang. For instance, with the defending pawn blockaded well behind the line, the knights can force zugzwang and eventual mate; if the pawn is too far advanced, the defender sacrifices it and reaches a known draw (KNN vs K is drawn).

  • Long wins that exceed 50 moves:

    Some 6‑ and 7‑man wins (e.g., certain bishop/knight vs minor‑piece endings or complex rook and pawn configurations) require more than 50 moves to reach mate without any capture or pawn push. Tablebases thus classify them as winning in principle (DTM shows “mate in hundreds”) but, under the 50‑move rule, they are drawn unless the attacker can orchestrate a timely capture or pawn move to reset the count. Practical winning technique revolves around forcing such “zeroing” events at key moments.

  • R+B vs R (draw, but tricky):

    Five‑man tablebases confirm that rook and bishop vs rook is a theoretical draw with best defense, yet it is notoriously hard to hold practically. Tablebases map the defensive methods (e.g., the Cochrane Defense and the “second‑rank” setup) and the attacking try with triangulations to create mating nets. Many top‑level saves in this ending align with tablebase “only moves.”

Interesting facts and anecdotes

  • Hundreds‑move truths: Seven‑man tablebases uncovered wins requiring several hundred moves to mate with perfect defense—astonishing by human standards.
  • Underpromotion surprises: Tablebases sometimes choose rare underpromotions (to a knight or bishop) to avoid stalemate or to keep winning chances within the 50‑move window.
  • Zugzwang catalog: They provide a definitive list of mutual zugzwang positions in small endgames, useful for study and composition.
  • Engine synergy: Modern engines combine search and tablebases; they steer toward WDL‑winning positions while timing captures to reset the 50‑move counter as advised by DTZ.
  • Influence on classic theory: Many celebrated studies have been verified, corrected, or even refuted by tablebases, leading composers to craft positions that remain sound against perfect defense.
  • Historical match context: From the 1990s onward (e.g., Kasparov vs. Deep Blue, 1997), top teams have integrated endgame databases into their preparation; today, every elite engine ships with Syzygy probing.

Practical tips for players

  • Track the 50‑move count. If you’re winning a tablebase endgame over the board, plan a capture or pawn push before move 50 to preserve winning chances.
  • Know the landmarks: Philidor and Lucena positions, Vancura defense, “wrong rook pawn,” and KBN technique are all perfectly mapped by tablebases—study the critical setups and “only moves.”
  • When defending, aim for fortress coordinates flagged as drawn by tablebases (e.g., rook in Vancura, king in the “wrong corner,” or setups that force stalemate nets).
  • In correspondence or analysis, consult 7‑man tablebases for absolute truth, but remember that in practical OTB chess, clock, nerves, and the 50‑move rule shape real outcomes.

Related terms

  • Syzygy tablebases (WDL/DTZ format used by engines)
  • 50-move rule and the 75‑move automatic draw rule
  • Fortress and Zugzwang in endgames
  • Troitsky line (two knights vs pawn theory)
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Last updated 2025-08-30