DTM: Depth to Mate in Chess

DTM

Definition

DTM stands for “Depth (or Distance) To Mate.” It is the minimal number of half-moves (plies) required to force checkmate from a given position with best play by both sides. Some interfaces report DTM in plies; others render it as “M#” (mate in # moves), where M7 corresponds to DTM 14 plies.

Example of equivalence: DTM 6 plies = M3 (mate in 3 full moves). Engines typically display “M3,” while endgame tablebases often store or can derive the underlying DTM value.

How it is used in chess

• Engines and GUIs: When an engine proves a forced checkmate, the numerical evaluation is replaced by a mate score, e.g., M8. Internally this reflects a concrete DTM line.
• Tablebases: Classical Nalimov endgame tablebases (up to six pieces) store DTM in plies. Modern Syzygy tablebases emphasize a related metric (DTZ50), but many GUIs still display or reconstruct a DTM for won/lost positions.
• Practical play: DTM tells you how long a forced win takes with perfect defense. It informs technique (e.g., whether you must drive the king to a corner first) and time management (forcing lines vs. “easier” but longer wins).
• Composition and studies: Problemists label solutions “mate in N,” which corresponds to a DTM of 2N plies under perfect defense.

Strategic and historical significance

DTM revolutionized endgame understanding. With the advent of Nalimov (6-man) and later 7-man tablebases (e.g., Lomonosov), analysts discovered that some positions require surprisingly long, precise maneuvers to force mate—sometimes hundreds of plies. This sharpened our knowledge of “theoretical wins” versus practical draws, especially under the 50-move rule.

Historically, chess laws briefly allowed special extensions for certain endgames (like bishop+knight vs king) due to their known but lengthy DTM. Modern rules do not grant such exceptions: a player may still claim a draw after 50 moves without a pawn move or capture (and there’s also a 75-move automatic draw), so some DTM wins are not practically convertible without resetting the counter.

Related metrics you will see

• DTZ (Distance to Zeroing move): Minimal plies to the next pawn move or capture that resets the 50-move counter. Syzygy tablebases store DTZ50 (respecting the 50-move rule). DTZ-oriented play often seeks a timely capture or pawn push before continuing the winning plan.
• DTC (Distance to Conversion): Minimal plies to reach a simpler, known won endgame (e.g., promoting a pawn or winning material decisively), not necessarily checkmate.
• WDL (Win/Draw/Loss): The basic tablebase verdict ignoring length—useful for a quick outcome classification before consulting DTM/DTZ.

Examples

• KBN vs K (bishop and knight vs lone king): The win is forced, but in the worst case it can take up to 33 moves (M33, i.e., DTM 66 plies). The technique involves driving the defending king from the “wrong” corner to the “right” corner (matching the bishop’s color) before executing the mating net.
• KQ vs KR (queen vs rook): With best play, mate can require up to 31 moves (M31, DTM 62). Defensive techniques like the Cochrane or second-rank defense resist for a long time, and the winning side must avoid stalemate tricks while making progress.
• Two knights vs pawn (KNN vs KP): Without a pawn, two knights cannot force mate against a lone king. With a pawn on the board, mating nets can exist—but many require more than 50 moves (very high DTM). Because of the 50-move rule, a theoretical DTM win may be a practical draw unless a capture or pawn move resets the counter at the right moment. This is a classic example of why DTZ and practical rules matter.
• Seven-man extremes: 7-piece tablebases uncovered wins requiring well over 500 plies (DTM > 500) against best defense. These are mathematically exact but practically irrelevant in tournament play unless frequent zeroing moves occur.

Interesting facts and anecdotes

• “M#” parity: If an engine shows M7, that’s 14 plies—your opponent will be mated on your 7th move from now. Engines often flip from numeric (+5.3) to “M#” only when a forced mate is conclusively proven within search bounds.
• The 50-move rule can “break” long DTM wins. Many tablebase wins (especially in minor-piece endings) need precision plus timely zeroing moves; otherwise, despite a winning DTM line, the defender can claim a draw.
• Discovery through retrograde analysis: DTM values are computed by working backward from checkmated positions. This layered propagation explains why deeper tablebases took years of computation and storage to complete.
• Practical resignations: In master play, opponents typically resign long before an engine would show a large M#, because the path to mate is obvious or material losses are unavoidable en route to a trivial mate.

How to read DTM in practice

• If your GUI shows M5, expect five of your moves (and four of your opponent’s replies) before the final checkmate—assuming you keep to the best line.
• If you see a tablebase DTM but the sequence contains long stretches without pawn moves or captures, verify whether a DTZ-aware plan exists to reset the 50-move counter along the way.