How a Chess Move Calculator Works

Step 1: The Position Has to Be Exact

An engine does not see a picture of a board. It reads a position description called FEN, which records four things you cannot always tell by looking: where every piece stands, whose move it is, which castling rights remain, and whether an en passant capture is possible. The starting position is:

The most common setup mistake is the wrong side to move, and it changes everything: the calculator then answers a question about a different position. The next most common is castling rights. If your king has already moved, the engine must not be told it can still castle (the castling lesson covers exactly when the right is lost). The same goes for en passant, which is only available on the move straight after a two-square pawn advance.

Step 2: Search

From the starting position White has 20 legal moves. In a typical middlegame each side has 30 to 40. Looking just three moves ahead for both sides (six half-moves) means roughly a billion lines, so no engine checks them all. Stockfish uses four ideas to cut the tree down to something it can search:

• Alpha-beta pruning. Once one reply refutes a move, the engine stops looking at that move's other replies. With good move ordering this skips most of the tree without changing the answer.
• Iterative deepening. It searches to depth 1, then 2, then 3, and so on. Each pass tells the next one which moves to try first. That is why the evaluation on the board starts changing almost at once and keeps moving while the engine thinks.
• Extensions and reductions. Forcing moves such as checks get searched deeper. Quiet moves that look unpromising get searched less. Depth is the nominal length of the search in half-moves, not a guarantee about every line.
• Quiescence search. At the end of a line the engine keeps playing captures until the position is quiet, so it never stops in the middle of an exchange and counts a piece it is about to lose.

Step 3: Evaluation with NNUE

At the end of every line the engine needs a verdict on the position it reached. Stockfish gets it from NNUE, an "efficiently updatable neural network". The design came from computer shogi and arrived in Stockfish 12 in 2020. Since Stockfish 16 in 2023 it has been the only evaluation: the hand-written rules about piece values and pawn structure were removed.

"Efficiently updatable" is the important part. A move changes only one or two pieces, so the network updates the part of its first layer those pieces touch instead of starting again. That keeps it fast enough to score millions of positions per second on an ordinary processor, which is what lets a deep search and a learned evaluation work together. The networks are trained on billions of positions from engine games.

Reading the Numbers

The score is given in pawns from White's point of view, to one decimal on our board. Plus is good for White and minus is good for Black. Since Stockfish 15.1 the scale is tied to results rather than material: +1.00 means the engine expects White to win about half of the games from that position. So an extra pawn in a rook endgame, which is often a draw, can show less than +1.0, while a strong attack with equal material can show +2.0.

Take 1.e4 e5 2.Bc4 Nc6 3.Qh5 Nf6. The natural-looking knight move ignores the threat, and the board switches from a number to a mate score because 4.Qxf7# ends the game. A mate score is the one output you can trust without checking further.

Why the Answer Changes With Depth

A search that stops too early can end just before the refutation. This is called the horizon effect: the engine sees itself win a pawn and stops looking, one move before the reply that wins its queen. Every extra depth pushes the horizon back, which is why the move and score sometimes jump while the engine is thinking.

Two practical rules follow. When the best move has stayed the same for several depths, trust it. When two moves are within about 0.2 of each other, treat them as equally good: their order can swap from one depth to the next, and a phone reaches a lower depth than a desktop in the same time.

Why Engines Disagree With Humans

An engine plays for the best score it can prove, not for the simplest position. Three differences explain most of its surprising choices:

• It sees the concrete reply you missed. In the Two Knights Defence, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5, most beginners recapture with 5...Nxd5. That allows 6.Nxf7, forking the queen on d8 and the rook on h8, and after 6...Kxf7 7.Qf3+ Ke6 8.Nc3 Black's king is stuck in the centre. This is the Fried Liver Attack. The main line, 5...Na5 6.Bb5+, puts a knight on the rim, which looks wrong and is right.
• It does not care how hard a move is to play. A move that keeps +0.5 only if you find six exact moves in a row is worse in practice than one that keeps +0.3 with an obvious plan.
• It never gives up. Engines defend positions people would resign and find the one move that holds. When the score says a lost position is only slightly worse, it usually means there is a single narrow path.

Both lines grow out of the position after 3.Bc4, which our Italian Game page walks through, and the chess openings hub has the other main systems with their ideas explained move by move.

How to Learn From a Calculator Instead of Copying It

A best move on its own teaches very little. The point is to find out why your move was worse. This routine works at every level:

1. Finish the game first. Never consult an engine during a game you are playing.
2. Write your answer down before you look. Note your candidate moves and who you think is better. You are testing your judgement, so commit to it.
3. Compare the top three lines, not the top move. If your move is one of them and within 0.2 of the best, your move was fine.
4. Play your own move on the board. Then look at the engine's reply. That reply is what you missed, and it is the lesson.
5. Follow the line until the idea appears. Step through the suggested moves until you reach the capture, fork or mate that justifies them.
6. Turn the pattern into practice. Missed a mate? Drill the checkmate patterns. Lost a piece to a fork? Solve chess puzzles with that theme.

For a whole game rather than a single position, Pro members can paste the PGN into the chess analysis board, which grades every move and takes you straight to the ones where the score swung. On the free tier, set up each critical position in the calculator instead. Our guide on how to get better at chess builds this into a full weekly training plan.

Strength Settings: When the Calculator Plays Weaker on Purpose

Our calculator has a strength slider. At the top setting (3650) it searches to depth 22, or for 8 seconds if that comes first, and returns Stockfish's own first choice. Lower settings search less deeply and then choose among the engine's candidate moves the way a player of that rating tends to, sometimes taking a weaker one on purpose. That is useful when you want to know what a 1200 player would play, or want a sparring partner. When you want the objectively best chess move, use the highest setting you have. Guests and free accounts can use settings up to 800 (depth 3), and the full range comes with Pro.

The Limits

• A score is not a plan. "+0.6" tells you who is better, not what to do next. The line underneath the score is where the plan is.
• Depth costs time. On a slow phone the same few seconds reach a lower depth, and lower depth means more horizon effects.
• No endgame tablebases in the browser. Every position with seven or fewer pieces has been solved exactly, but those databases are far too large to load in a web page. In rare endings the browser engine can misjudge a draw or a win that a tablebase would settle.
• Locked positions. An engine can show an advantage in a blocked position that neither side can break. The score only comes down once the search runs out of ideas.
• It cannot explain itself. Engines give evidence, not reasons. That gap is what our AI insights try to close: a plain-English explanation of why the move works.

Further Reading

The Stockfish chess engine covers the engine's history and strength. How AI plays chess compares Stockfish's search with AlphaZero's learning. Stockfish ELO by level explains what the engine's strength settings really mean. To run the engine with its full controls, open Stockfish online.