What does +1.5 mean in chess?

+1.5 means White is ahead by about a pawn and a half. An engine like Stockfish scores a position in pawns. A plus sign is good for White, a minus sign is good for Black, and 0.0 is level. The score is a verdict on the whole position, so +1.5 can be an extra pawn and a safer king, or no extra material at all.

dxc4 always gives the score from White’s side. The analyzer’s chart is White’s chance, and a solved best-move puzzle ends with a line such as Stockfish: White +7.1.

Pawns and centipawns

Inside the engine the unit is the centipawn, a hundredth of a pawn. Stockfish reports 150 and the screen shows +1.5. A pawn used to be the whole definition, but Stockfish’s neural-network evaluation is much less tied to material than the old one was.

Since version 15.1, Stockfish ties the scale to results instead. At +1.0 it wins about half its games against itself at a fast time control, and at 0.0 nearly every game is drawn. The Stockfish FAQ has the curves. Real odds depend on the opponent and the clock: at bullet fewer games are drawn, and against a weaker player even a minus score can win.

Mate scores

When the engine finds a forced mate it stops counting pawns. +M3 means White mates in three moves whatever Black does, and -M3 means Black mates in three. Other programs write the same thing as #3. On dxc4’s chart a forced mate is 100% when White delivers it and 0% when Black does.

Depth, and why the score moves

Depth is how far the search went, counted in half-moves. Stockfish does not look at every line to that depth: it cuts unpromising moves short and follows checks and captures much further. The analyzer’s chart searches each position to depth 15 or for one second, whichever comes first.

A longer search can change its mind. When we checked the best-move puzzles, 14 of 60 lines that passed at one million positions searched failed the same check at four million, and 10 of the next 46 failed at sixteen million. A score is the best estimate so far, not a proof.

The win-probability chart

The analyzer turns each score into White’s chance with one curve, 1 / (1 + e^(-cp/400)), where cp is the score in centipawns. It is gentler than Stockfish’s own scale, and 50% means an even position, which at a high level is mostly draws. Read it as White’s share of the result rather than the odds of a win.

The move list marks a move by how far it moves that line. A swing of 20 points or more against the player who moved is a blunder, 10 a mistake and 5 an inaccuracy. The same swings in their favour are brilliant, excellent and good.

Near the ends of the curve a big change in score is a small change in chance. Falling from +10.0 to +6.0 takes White from 92.4% to 81.8%, a mistake rather than a blunder, and the position is still won.

Common questions