Conversion distance (DTC) – chess endgame metric
Conversion distance
Definition
Conversion distance – more formally “Distance-to-Conversion” and abbreviated “DTC” – is an end-game tablebase metric that counts the minimum number of moves required, with best play, for the side to move to convert the position. A conversion is reached the moment a move is played that irreversibly improves the material or structural balance:
- a capture is made,
- a pawn advances (thereby resetting the 50-move counter), or
- a pawn is promoted.
In practical terms, DTC tells you how many moves it takes before the winning side can “cash in” its advantage for something tangible – usually a simpler won ending or a position that is trivially mating. The metric was introduced by Ken Thompson in the early Belle tablebases (1980s) and is sometimes called the Thompson metric.
How it is used in chess
Although club players rarely speak of “conversion distance” over the board, the concept is embedded in almost every modern engine and online tablebase. When you load a 5-, 6- or 7-piece ending, the engine may display “+0.00 (DTC 17)” or similar, meaning nothing material changes for 17 moves. Its main applications are:
- End-game analysis: Helps players understand why the engine continues to shuffle pieces instead of forcing mate immediately. A high DTC warns that patience (and precise maneuvering) is needed before the breakthrough.
- 50-move-rule compliance: FIDE’s draw rule declares the game drawn if fifty consecutive moves pass without a pawn move or capture. A winning line with DTC ≥ 50 is therefore not winning in practical play unless an exception is granted. For this reason some tablebases and GUIs also show DTZ (“distance to zeroing” – the newer, rule-aware metric) alongside DTC.
- Engine tuning: Authors choose different metrics (DTM, DTZ, DTC) to guide a search algorithm. Using DTC encourages engines to find the quickest decisive conversion rather than the quickest mate, which is often more human-friendly.
Strategic significance
In classical manuals you will often read that a side must “convert the advantage” before the opponent builds a fortress, reaches stalemate resources, or can claim the 50-move draw. Conversion distance quantifies this race. Knowing that a position is “+5.00” is abstract; knowing that “nothing improves for 38 moves” tells you you must manoeuvre with surgical precision for more than an hour’s play.
Examples
Two illustrative cases are given below. Load them in any 7-piece tablebase and look at the DTC value shown.
Example 1 – KBBKN (Win, but long DTC)
[[Pgn|1. Be3 Kc6 2. Bd3 Kd5 3. Bc2 Ke5 4. Bd2 Bg2 5. Bc3+ Ke6 6. Bb3+ Kd7 7. Bb4 Bf3 8. Ba4+ Kc7 9. Bc5 Bg2 10. Bb5 Bb7 11. Bd3 Bd5 12. Bf8 Bb7|fen|8/8/2k5/3kp3/8/8/7B/7K b - - 0 1]]The tablebase reports DTC = 32. White cannot force a capture or pawn move for 32 moves, yet the ending is completely won. Over-the-board, however, White must keep track of the 50-move counter.
Example 2 – Kasparov’s missed conversion (Kasparov–Leko, Linares 2003)
In the famous end-game after 39…Qg2, Kasparov had a study-like win. Engines calculate DTC = 6; he needed only six moves before converting by force-mate on the h-file. Missing one precise rook lift, the game drifted to a draw. This shows how a modest conversion distance can still be difficult for humans at the board.
Historical notes & anecdotes
- The longest 7-piece win currently known has DTM = 549 moves, but its Distance-to-Conversion is “only” 115 moves – still far beyond the 50-move limit, making it a theoretical win yet a practical draw.
- During the 1990s FIDE temporarily extended the 50-move rule to 75 and 100 moves for specific endings (e.g., KBBKN) precisely because tablebase research revealed huge conversion distances. The exceptions were rescinded once technology allowed arbiters to check tablebases on the spot.
- Online servers such as Lichess display DTZ by default, but hovering over the value reveals the underlying DTC. Many players first encounter the phrase “conversion distance” there.
- Some chess engines print a “C” symbol (e.g., “+3.14 C23”) in the principal variation to denote an imminent conversion inside 23 moves.
Key takeaways
Conversion distance measures the patience required before a decisive, progress-resetting move appears. For competitive players it underlines why apparently “won” end-games can still be drawn if you do not create a pawn move or capture in time; for programmers it is a vital heuristic guiding engines toward human-sensible play.