Tactics — The Motif Curriculum 見微知著

Dan Heisman's Counting is not counting material: it is working out whether a sequence of exchanges on a given square gains or loses material. The method itself, a worked example and the five ways a correct count still loses you a piece are on Calculation, because it is a procedure rather than a pattern. What belongs here is its place in the order. Heisman's curriculum position is explicit — Counting goes "after the rules and the average values of the pieces, but before multiple square motifs like pins and removal of the guard," because beginners make trivial Counting errors far more often than they miss a pin.

The Steps Method — the Dutch Stappenmethode — arrives at the same order from an entirely different tradition. Step 1 is board and piece safety, attacking, defending, the profitable exchange, and its manual states the policy outright: "Learning how to mate is postponed as long as possible" — on the reasoning that piece safety must be automatic first. Two traditions, same ordering decision. That is convergence between two experienced curriculum designers, not evidence — but it is about as close to evidence as curriculum design gets.

You will be told 85% success, citing Wilson et al. (2019, Nature Communications), "The Eighty Five Percent Rule for optimal learning." The paper is real and so is the figure — an optimal error rate of 15.87%.

It is also a result about stochastic gradient-descent algorithms performing binary classification. The authors state that the optimum shifts with the noise distribution (85% Gaussian, ~82% Laplacian, 75% Cauchy), that extension beyond binary tasks "will likely involve more complex mappings," and that Bayesian learners with perfect memory show no sweet spot at all. Chess puzzles are not binary classification and you are not a perceptron. Take 85% as a steer away from the two obvious errors — puzzles you solve instantly, puzzles you fail four times in five — not as a constant. It also sits in unresolved tension with Bjork's desirable difficulties, which the rest of this site leans on heavily. Nobody has reconciled the two for chess.

The boundary: pattern recognition supplies the candidate; calculation verifies it. De Groot's 1946 finding is that masters do not search deeper or wider — they see the right candidate almost immediately. The seeing is tactics. The checking is calculation.

So a puzzle that resolves in one or two moves is training recognition; a puzzle that takes three minutes and four candidate moves is training calculation, and wants a different session — slower, fewer, written down. Both are worth doing. The mechanics of the second are on Calculation.

Michael de la Maza's claim: roughly 1,000 problems cycled seven times on a compressing schedule, and about 400 USCF points in 400 days, capped by winning the 2001 World Open under-2000 section and crossing 2000. He then stopped playing rated chess entirely — an ending Mindset treats as part of the same fact rather than a footnote to it.

It has not replicated. A blogging community — the "Knights Errant" — formed around doing the programme in the 2000s; the most-cited outcome among them is a participant who completed the full cycle and recorded no measurable gain. Two decades on there is still no documented case of a second person reproducing that curve with it. Heisman's position is narrower than it is usually reported: he defended de la Maza against the cheating insinuations, said he agreed with most of the general advice, and disputed the Seven Circles drilling specifically — not the man and not the whole book. Blog and forum testimony, not data, and the people who quit early left no record. But the absence of a single replicated success after that many enthusiastic attempts is itself informative.

The modern successor is the Woodpecker Method (Smith & Tikkanen). Its headline case is Tikkanen making three GM norms and crossing 2500 inside seven weeks in the summer of 2010, after a spring of the training — and to his credit he states the caveat himself: "Would I have made the same improvement with some other type of training? It's not impossible — but my playing strength had not taken any significant leap in years." One player, self-reported, uncontrolled.

What repetition demonstrably does

An observational study on one training platform logged 120,513 puzzle attempts by 1,017 users over seven weeks. Read the third column before the second: the cycle comparison rests on a far smaller group than the headline sample, because almost nobody finishes a full set twice.

The cycle-one-to-two gain is on 55 and 54 users and looks solid. Cycles three and four are ten people and four people, and the neat continuation of the curve there should be treated as decoration, not data — the four who reached cycle four are exactly the people for whom it was going well. The study also says, in its own words: "We do not have data on whether improvements on the platform transfer to over-the-board play, online rated games, or other measures of chess skill." No control group, self-selected users, heavy attrition. So: repetition reliably makes you faster and more accurate on the puzzles you repeated. Whether that is the same thing as getting better at chess is the exact question nobody has answered, and it is the same question the −0.02 volume correlation raises.

So how many repetitions does a pattern need?

Honest answer: nobody has measured it for chess. Any specific number you have been given — five times, seven, twenty — was invented. What exists is an inference, and it is worth seeing why it cannot become a schedule.

Simon (1974, Science) estimated a master's stored vocabulary at 25,000 to 100,000 chunks, and the time to fixate one new chunk in long-term memory at 5 to 10 seconds. Multiply the two ranges out: somewhere between 35 and 280 hours of pure fixation to build a master's library — so far below the observed 3,016 to 23,608 hours to reach master that the chunk model plainly describes storage rather than acquisition. Take from it the two things the learning-science evidence does support — label patterns, and space their return — and ignore anyone who converts it into a repetition count.