Calculation — The Thinking Process 三思而行

This is the skill that separates rating bands more than knowledge does. It is also the area of chess training where the gap between confident advice and actual evidence is widest. Both of those things are true at once, and this page says so throughout rather than once at the bottom.

Hope Chess and Real Chess

Dan Heisman's distinction is narrower than most people who repeat it realise. It is not about effort or about caring. It is about when in the sequence you look at the opponent's reply.

Note what it is not. Heisman is explicit: "Hope Chess is not when you make a threat and you hope your opponent does not see it." That is a legitimate practical decision. Hope Chess is a structural failure of the thinking process, not an attitude.

He splits the failure in two, and the second half is the one that catches serious improvers. Basic Hope Chess is moving with no attempt at safety at all — players who "make moves and make no attempt to see if their move is safe." Passive Hope Chess, which he puts in the 1200–1700 band (again without saying which pool), is worse because it is invisible from the inside: you believe you are checking. Nothing pattern-matches to danger, so you move. His word for it is "insidious." You are scanning, not analysing, and a scan only finds tactics you already have patterns for — which is the calculation-side version of the finding on the Tactics page. Pattern inventory is not the bottleneck. Procedure is.

The safety check, in full

The Ladder gives three questions. Here is what each one actually decomposes into. This is the procedure; run it every move until it runs itself.

Counting

Heisman's definition: "seeing if pieces are safe from capturing sequences; the tactic that determines if any forced sequence of captures on any square or squares will gain or lose material." He wrote a whole book on the question (Is Your Move Safe?, Mongoose Press, 2016), and puts it ahead of the named motifs in the teaching order — the argument for that ordering, and the second tradition that independently reached it, are on Tactics. Most material loss below 1200 is a counting failure, not a missed combination. That is our claim, not a measured one; nobody has published a breakdown of beginner material loss by error type, and Sources lists the invented figures that circulate instead.

The method

A worked example, in words

White has a pawn on d4. Black attacks it twice: a pawn on e5 and a knight on c6. White defends it twice: a pawn on c3 and a knight on f3. Black to move.

Track Black's running material: +1 (won the d4 pawn), 0 (lost the e-pawn to the recapture), +1 (won the d4 pawn again), −2 (lost a knight for it). Black stops after move two, at zero. Two attackers, two defenders, nothing to be had. The pawn is safe.

Now delete the c3 pawn. Two attackers, one defender. 1…exd4 and White is simply a pawn down, because 2.Nxd4 runs into 2…Nxd4 and he has given a knight for a pawn. That is the whole of counting: the count decides it, and value decides the order.

Candidate moves — and the long argument about them

Alexander Kotov introduced candidate moves to chess literature in Think Like a Grandmaster (Batsford's English edition, 1971; the Russian original is a year or so earlier). The sound part is the diagnosis: without structure you oscillate. His own description of the failure is still the best one — you look at the rook move, go a move deeper and "pull a long face," switch to the knight move, come back to the rook, and then: "My goodness! Already 30 minutes gone on thinking whether to move the rook or the knight." Whereupon you play a bishop move you never analysed at all. The contested part is the prescription: build the tree, and examine each branch once and only once.

What to actually do

• Two or three, written down, before you calculate any of them. Not the four to six usually quoted as the norm. Most players below 1800 calculate the first move they thought of, deeply, and never look at the second — the fix is a short list, not a complete one.
• Generate them forcing-first: every check, then every capture, then every real threat, then the quiet move you were going to play anyway. Checks are about 4% of legal moves and captures about 7% — same single Lichess analysis as above, so treat the exact figures as a ballpark — but on any plausible number the enumeration is cheap.
• Then generate one more, deliberately. Aagaard's use of the technique: the list exists to surface the move that did not occur to you. A list containing only moves you already liked did no work.
• Go back to the start position when you find something new. Kotov's rule says do not. This one is our call rather than a quotable consensus: Dvoretsky, Tisdall and Aagaard all abandon the single-pass discipline in one way or another, and none of them defends it. Break the rule.

How deep, and when to stop

Cheng Yi's gloss, carried in Zhu Xi's 集注, is why this belongs on a calculation page: 至於再則已審，三則私意起而反惑矣 — "by the second thought the matter is already settled; at the third, private inclinations arise and one becomes confused instead." Note the direction of travel. 三思而行 survives in modern usage as approving advice — think it over properly — but in its source text it is the thing being trimmed, and the corrective is Confucius's. So is Nunn's, below.

Two textual notes. Zhu Xi writes 程子曰, "Master Cheng said," which formally could be either Cheng brother; the standard attribution for this gloss is Cheng Yi. And Cheng's remark is about moral deliberation, not chess — the analogy is ours.

Stop at a resting position. Engines call it quiescence: a position reached in analysis with no further checks, captures or threats likely to change the evaluation. Heisman uses the same word. A line that ends mid-capture-sequence has not been calculated, it has been abandoned. This is Principle Ⅵ's third gate, 慎思之 — calculate to a resting position, not to an impression.

The horizon effect, in human terms. Hans Berliner named it in 1973 for computers: everything past your search depth is invisible, so a threat you cannot see looks like a threat that is not there. The human version is worse, because it has a direction. You stop calculating at the point where your line looks good. Nobody stops one move after their combination collapses. If all your variations happen to end on a pleasant square, that is the horizon effect wearing your face.

The blunder check is a separate step

It must be a distinct action with a distinct trigger, not a feeling of having been careful — feelings of having been careful are exactly what Passive Hope Chess produces. This is Principle Ⅳ applied in-game: you are testing not whether you know the position, but whether your confidence in it is earned.

One correction worth having: Heisman's classic advice was to write your move down before playing it and then look again. That has not been legal since 2005 — Article 8.1.2 of the FIDE Laws reads "It is forbidden to record the moves in advance, unless the player is claiming a draw according to Article 9.2, or 9.3 or adjourning a game." GM Noël Studer's version above — record the opponent's move, then write down their clock time while you ask the question — achieves the same interrupt legally, and he says so explicitly. The idea survives; the mechanism had to change.

Visualisation training

Our reading: drill three earns real time because it is not transfer at all — it is the game task under game conditions. Drills one and two are cheap enough that a fortnight costs nothing even if the effect is small. Drill four is for people who enjoy it. Nobody at 1200 should be spending an hour a day on blindfold work; the return on the same hour spent analysing your own games is not close.

Time inside the game

The same 10.7-million-game Lichess analysis, restricted to non-blowout positions, found this.

Finding	Number
Average centipawn loss with more than 7 seconds per move remaining	25.2
…with 2 to 7 seconds remaining	29.7
…with 2 seconds or fewer remaining	39.6
Marginal value of each of the first ~5 seconds on a move	≈100 pts
Point where extra seconds stop buying much	~20 s

Same caveat as before, and it applies to every number in that table: one author, one blog, one platform, no replication, no peer review. The three centipawn-loss figures are the solid part — they are simple descriptive averages over an enormous sample. The "100 rating points per second" figure comes out of a fitted model, so it carries the model's assumptions as well as the data's.

Read those together and the practical rule is not "think longer." It is: the first few seconds are worth enormous amounts and the twenty-first is worth almost nothing. The failure mode this describes is not being too fast overall — it is being instant on ninety percent of moves and then burning eight minutes on one. And when you do burn the eight minutes, the cause is usually not calculation at all but a decision you are refusing to make; the rules for that are on Mindset.

Prophylaxis — the 1500 to 1800 gap

Note the order — 知彼, know the other, comes first. Giles's familiar rendering ("you need not fear the result of a hundred battles") is loose; 不殆 is "not endangered," a more modest claim. Sunzi is promising safety, not victory. So is prophylaxis.

Everything above is about calculating your moves accurately. Prophylaxis is asking "what does he want to do?" before "what do I want to do?" — and in our judgement it is most of the gap between 1500 and 1800. That is a coaching claim, ours and many other people's, with nothing measured behind it. Aagaard's positional method is three questions, and the third is the one that matters here: where are the weaknesses; which is the worst-placed piece; what is your opponent's idea? Quoted from Grandmaster Preparation: Positional Play via a secondary summary, not the book.

Why this sits on the calculation page rather than the strategy page: it is the same asymmetry the Tactics page documents — puzzles train you to find your tactics, blunders come from missing theirs — but the fix is procedural, not a pattern you can drill. It happens at the board, once a game.

What to run at each rung

Rung	Every move	Drill of the week
Under 900	Counting; "what did their move stop defending?"	Square colours; count attackers and defenders aloud on ten positions
900–1149	Full safety check, all three questions	Enumerate their checks and captures, in writing, for one whole game
1150–1449	Safety check plus a named plan for the move	Blindfold knight walk; calculate from static diagrams, hands off
1450–1749	Two or three written candidates before calculating any	Prophylaxis drill once a game; always to a resting position
1750+	Candidates, comparison, deliberate blunder check	Pieceless puzzles; DAUT — find one game where you took the messy line for no reason

Every figure on this page is listed with its weaknesses on Sources. The claims most likely to need revising: the 1700 barrier (one coach's impression, and he never says which rating pool); the blindfold pilot (tiny, self-flagged sample, with one reported figure we openly disbelieve); the blunder and time-management statistics (one unreplicated analysis of one platform); and the Tisdall and Soltis rows in the disagreement table, neither of which we have checked against the book.