Information stored in Syzygy tablebases
5-valued Win/Draw/Loss information can be used to decide which positions to aim for.
Once a tablebase position has been reached, the Distance To Zeroing (of the fifty-move counter by a capture or pawn move) can be used to reliably make progress in favorable positions and stall in unfavorable positions.
The precise meanings are as follows:
A DTZ value n with 100 ≥ n ≥ 1 means the position is winning, and a zeroing move or checkmate can be forced in n or n + 1 half-moves.
For an example of this ambiguity, see how the DTZ repeats after the only-move Ka8 in 1kb5/8/1KN5/3N4/8/8/8/8 b - -. This is due to the fact that some Syzygy tables store rounded moves instead of half-moves, to save space. This implies some primary tablebase lines may waste up to 1 ply. Rounding is never used for endgame phases where it would change the game theoretical outcome (WDL50).
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.
A DTZ value n > 100 means the position is winning, but drawn under the 50-move rule. A zeroing move or checkmate can be forced in n or n + 1 half-moves, or in n - 100 or n + 1 - 100 half-moves if a later phase is responsible for the draw.
For example, in 8/8/2N5/8/3k4/7N/p2K4/8 b - - black promotes the pawn in 7 ply, but the DTZ is 107, indicating that white can hold a draw under the 50-move rule in a later phase of the endgame.
An in-depth discussion of rounding can be found in this thread.