WDL50
5-valued Win/Draw/Loss information can be used to decide which positions to aim for.
DTZ50′′
DTZ50 refers to the Distance to Zeroing under the 50-move rule: The number of half-moves until the next capture, pawn move, or checkmate, that keeps the optimal outcome under the 50-move rule (WDL50).
Syzygy adjusts the raw DTZ50 values with a possible offset of 100 to DTZ50′′, which can then be min-maxed to reliably make progress in favorable positions and stall in unfavorable positions.
100 ≥ DTZ50′′ ≥ 1
Winning with and without regard to the 50-move rule. No adjustment is needed.
DTZ50′′ > 100
For positions that are drawn because of the 50-move rule, the simple case is that the current endgame phase is solely responsible for the draw. In this case no adjustment is needed.
However it's also possible that one of the following endgame phases is responsible for the draw.
For example, in 8/8/2N5/8/3k4/7N/p2K4/8 b - - black promotes the pawn in 7 ply for a DTZ50 of 7, but white can hold a draw under the 50-move rule after this zeroing move. Other positions with a DTZ50 of 7 may be unconditionally winning.
To distinguish both cases, Syzygy with DTZ50′′ adds an offset of 100 whenever one of the following endgame phases is drawn. This way the number will always represent the game-theoretic value of the position: 1 ≤ DTZ50′′ ≤ 100 if and only if the position is unconditionally winning.
This is very useful in practise, but also means the original DTZ50 could be DTZ50′′ - 100 or DTZ50′′.
DTZ50′′ with rounding
To save space, there is an ambiguity in Syzygy, where DTZ50′′ values can be off by 1.
| DTZ50′′ with rounding | Zeroing move or checkmate in half-moves |
|---|---|
| 100 ≥ n ≥ 1 | n or n + 1 |
| n > 100 | n or n + 1 n - 100 or n + 1 - 100 |
If a table has no endgames that are exactly on the edge of the 50-move rule, then half-move precision is not really needed. In this case Syzygy may round to full moves.
For example, see how the given DTZ50′′ repeats after the only-move Ka6 in 8/2B5/8/k7/8/2NK4/qR4q1/8 b - -.
While rounding is never used for endgame phases where it woud change the game-theoretical outcome (WDL50), it implies that some primary tablebase lines may waste up to 1 ply.
Users need to be careful in positions that are nearly drawn under the 50-move rule! Carelessly wasting 1 more ply by not following the tablebase recommendation, for a total of 2 wasted plies, may change the outcome of the game.
The tables up to 6 pieces on this site have been generated with a patch to avoid rounding for 100 ≥ n ≥ 1.
An in-depth discussion of rounding can be found in this thread.