Mate In Seven Versus Plus Nine: Reading Forced Sequences

Stockfish shows you two kinds of number. One looks like +9.40. The other looks like #7. Most improvers read both as “very winning” and treat the second as a bigger version of the first. That is the wrong model, and it quietly wrecks a lot of training time.

Here is the claim of this post: a chess engine mate score is a statement about a forced line, not about how hard the position is for a human. It says that against best defence, mate arrives in at most N moves. It says nothing about whether you could find the first move, or whether the position teaches you anything. Some mates in seven are trivial. Some +9 positions are close to unplayable. Which one you are looking at decides whether it belongs in your training set.

What the numbers actually mean

A centipawn score like +9.40 is an estimate. Stockfish’s evaluation (NNUE, in current versions) is a trained function that guesses how likely you are to win from here. The engine searches a tree, applies that function at the leaves, and backs the numbers up. The result is a prediction with error bars you cannot see.

A mate score is different in kind. #7 means the search found a line where every defender reply loses to mate within seven of your moves. No estimate is involved, just a proof relative to the search. If the engine says #7 and the line is verified, it is true, full stop.

So you have two very different objects:

Notice what neither tells you: how many moves a human would need to see to play it.

Example one: a mate in seven that a 1200 can play

Take a lone king hunted by king and queen against a bare king, or better, a typical back-rank collapse. Say White has a queen and rook against Black’s castled king with no pawn moves available, and the engine reports:

depth 24  score mate 7  pv Qh5 Kg8 Qxh7+ ...

Look at the principal variation. Every Black move is forced, one legal move each time. The “seven” is long only because the king shuffles along the edge. A human sees: checks, only one reply, checks, only one reply. The calculation tree has a width of one. You can play it with a coffee in your other hand.

Compare the actual difficulty. Depth in plies for a #7 is up to 13 plies, but the branching is close to nothing. Difficulty for a person is roughly width multiplied by depth, and here the width is 1.

Elementary endings behave the same way. King and queen versus king is a mate in at most 10 from any start. Every club player should be able to convert it, yet the engine happily prints #10 for positions a ten-year-old finishes. Putting that in a tactics set teaches nothing you do not already own, or it is a technique drill and belongs in a different folder.

Example two: a +9 you cannot play

Now the reverse. A middlegame where you are a rook and a knight up in the engine’s eyes, but the win depends on a slow positional squeeze:

depth 30  score cp 940  pv Rfd1 Qe7 h4 a5 Nb3 ...

Nine pawns of advantage looks like a gift. Yet scroll the multi-PV lines (set MultiPV to 3 in Lichess’s analysis settings or in the Stockfish UCI options) and you may find:

1. cp 940   Rfd1
2. cp  35   Rac1
3. cp -20   Qd3

Only one move keeps the win, and the gap to second best is over eight pawns. That is a knife-edge. The reason for the huge number may be a pin that dissolves one move later, or a trap where the natural developing move loses a piece. A human in this position plays the “sensible” Rac1 and walks into equality. The +9 is real, but it sits on a single narrow path, and no heuristic a club player uses will find it.

Would you want that position in your training set? Probably not as a play-it-out exercise. It is a position where the engine knows something you cannot be expected to know, and drilling it yields memorised trivia.

Three questions to ask before you save a position

When I get engine output that makes me want to add something to a study, I run through these.

1. How many legal alternatives does the defender have at each step of the PV? Set MultiPV 3 and look at the replies. If Black has one non-losing move each time, the line is easy to read even when long. If Black has four plausible defences and each needs a separate refutation, the mate is hard whatever the distance.

2. What is the gap between the best move and the second-best? In the UCI output compare line 1 against line 2. A gap under 0.5 means several moves work and the position is forgiving. A gap above 3.0, or a mate against a non-mate, means one move only. Both can be good training material, but they train different things: forgiving positions train plans, knife-edge positions train calculation.

3. Does the first move look like a human candidate? Quiet moves, retreats and sacrifices of the queen are the usual hidden ones. If the key move is a check or capture, you will probably find it. If it is Qa1 from nowhere, you are looking at engine geometry.

A quick filter you can use tonight

Run your own lost games through Stockfish 17 (or whatever your Lichess analysis uses) and collect every position where the evaluation jumped by more than 2.0 pawns, or flipped to a mate. Then sort them:

Roughly, when I did this on forty of my own blunder positions, eleven were forced mates and twenty-nine were centipawn swings. Of the eleven mates, seven had forcing PVs I should have found in minutes. Of the twenty-nine swings, about twenty were only winning through one quiet move, and those went in the bin. That left roughly fifteen worth keeping from forty, not forty.

Beware the horizon on both sides

A caveat on #7: the engine reports mate in its count, in moves for the side to win, and it can show mates it found at low depth that are not the shortest. Give it more time and #9 may become #6. This is fine for training since any forced mate is a valid mate, but do not treat the number as difficulty or even as optimal length.

For centipawn scores the problem is the opposite. A +9 at depth 14 can become +0.3 at depth 28 once the engine sees a perpetual. If you did not check depth, you did not check anything. The deeper discussion of how depth, nodes and evaluation fit together is in Reading Engine Output: Evals, Depth And Lies, and it is worth having open while you do this filtering.

What to do with the first move, not the number

Stop saving positions by their evaluation. Save them by what the first move asks of you. When you open the analysis board, cover the evaluation bar, ask yourself what you would play, and only then reveal the engine line. Write down whether your move was a check, a capture or a quiet move, and whether it won, drew or lost against the engine’s choice.

After thirty positions you will see a pattern. Most club players miss the quiet moves, not the long mates. That tells you where your calculation needs work, and it is something no evaluation number, mate or otherwise, could have told you.