Why Chess Knight teaches the way it does

Chess Knight turns the mistakes in your games into lessons. Each part of how it teaches comes from research on how people learn. That research holds a surprise: the method that works best often feels worse. Here is each idea, with a true story from the research and what it found.

Practice with your own games, not only more games

In the 1940s, a Dutch psychologist, Adriaan de Groot, did a simple test.¹ He showed chess masters a position for only five seconds. Then they rebuilt it from memory, almost perfectly.

In 1973, William Chase and Herbert Simon did the test again, with a twist.¹ Each player saw a position from the middle of a real game for five seconds. Then the player put the pieces on a board from memory. A master put about 16 pieces on the right squares. A strong club player put about 8, and a beginner about 4.

Then came the twist. Chase and Simon showed the players boards with the pieces in random places. Now the master did no better than the others.

The master did not have a better memory. He saw groups of pieces that he knew well, and he remembered each group as one thing. Chase and Simon called these groups chunks. A chunk is a group of pieces that you see as one picture. (The study was small, with one player at each level.)

Four panels of a puzzled woman who stares at chessboards covered in arrows — It is hard to see every piece and every attack at once. Strong players see groups of pieces instead.

So what makes a player strong? In 2005, a team asked two large samples of tournament players how they spent their chess time.² In both samples, one thing matched skill best: the hours of serious practice alone.

Grandmasters hold the top title in chess. In their first ten years of serious chess, they did about 5,000 hours of this practice. That is nearly five times as much as players of middle strength. The hours came from the players’ own memory, so this shows a strong link, not proof.

Every lesson on Chess Knight is this kind of practice. It uses positions from your own games, at the move where you made the mistake. The same patterns return again and again: a piece with no defender, a king with no cover, a fork. (A fork is one piece that attacks two pieces at once.) The aim is that you see each one as a single chunk, too.

Find the move yourself before you see the answer

In 2006, two researchers, Roediger and Karpicke, gave students two short texts to read.³ One was about the sun, and one was about sea otters. Then the students read one of the texts again. For the other text, they wrote all they could remember, without the text in front of them.

Some students took a memory test five minutes later. They remembered 81% of the text they read again, and 75% of the other one. Other students took the test a week later, and the result flipped. Now they remembered 56% of the text they tested themselves on, and only 42% of the other one. Students who read a text again also felt more sure, even though they remembered less.

So a lesson never shows you the answer first. You see the position from your game, and you find the move on the board. The effort to remember is the practice. When you read the answer again, it only feels like practice.

Spread your practice over many days

In 1885, a German scientist, Hermann Ebbinghaus, wrote about tests on his own memory.⁴ He used syllables that meant nothing, each one a vowel between two consonants. He learned lists of 12 of them by heart. Later, he learned the same lists again. He found that 38 times through a list over three days helped as much as 68 times on one day.

In 2006, a team checked the results of 317 experiments.⁵ Most found the same thing. Practice spread over time led to much better final scores than practice all at once. Of 271 comparisons, only 12 found no gain, or the reverse.

In a book from 1972, Sebastian Leitner gave a simple plan for flashcards in boxes.⁶ When you know a card, it moves to a box that you review less often. In the classic version, a card that you miss returns to the first box.⁷

Chess Knight uses the same idea, as a pawn on a walk to the far side of the board. Each position from your games has its own pawn, on a walk of seven squares. Each time you solve the position, its pawn moves one square forward. Each square means a longer wait: one day, then 3 days, a week, 2 weeks and a month.

Solve the position after the month, and the pawn becomes a queen. You know that position now. If you miss it on the way, the pawn returns to the start.

When you miss, try again a few minutes later

In 2009, Nate Kornell asked students to learn hard word pairs with flashcards.⁸ Each student tried two ways. Some cards were in one big stack of 20. Other cards were in four small stacks of five. In a big stack, more cards come between two looks at the same card.

Across three experiments, the big stack worked better for 90% of the students. But most of them believed the opposite. After the first session, some students thought that one way worked better than the other. Of those students, 72% chose the small stacks.

Another study found that a hard success helps more than an easy one.⁹ When it is hard to remember an answer, and you still get it right, the memory gets stronger.

So when you miss a position, Chess Knight does two things. Its pawn returns to the start. And the position goes to the back of today’s set, in random order with the rest. It returns until you solve it. Then its pawn moves one square forward, to tomorrow.

After a miss, the “Do it again” button lets you play the position again at once. It is good practice, but your pawn does not move. Here is why. In a 2011 study, people tried to remember the same items, with different gaps between the tries.¹⁰ Three tries in a row helped no more than one try. Long gaps between the tries gave a 200% gain in long-term memory.

It did not matter if the gaps grew or stayed the same. Only the size of the gaps mattered. Just after you see the answer, you do not have to search your memory for it. You only repeat what you just saw.

Mix different kinds of positions together

In 2008, Nate Kornell and Robert Bjork showed people paintings by 12 artists, six paintings each.¹¹ For some artists, all six paintings came one after another. For other artists, the paintings came in a mix with the rest. Then the people saw new paintings and named the artist of each one.

For artists in the mix, people named the right artist 61% of the time. For artists one at a time, they got only 35% right. Yet 78% of the people said that one artist at a time worked as well or better. They said so even after their own test showed the opposite.

Math works the same way. In another study, students practiced math problems.¹² Some students practiced one type of problem at a time. Others practiced a mix of types. During practice, the one-type students did better: 89% against 60%. But on a test a week later, the mix students scored 63%, and the one-type students only 20%.

So Chess Knight shuffles every set. It mixes positions from different games and from different parts of the game. Each position starts as it did in your game, with no clue about what kind of problem it is. A mix feels harder while you practice, and it works better later.

Do a small set every day, and sleep well

Picture a player who starts 10 new positions today. Each new position returns at least five more times on its way to a queen. So those 10 positions bring at least 50 reviews over the next two months. If the player starts many more each day, the reviews soon become a pile that nobody can finish.

The flashcard app Anki gives the same advice.¹³ New cards add reviews in the days that follow. So Anki says your limit for new cards should usually be 10 times smaller than your review limit, or more.

So a day on Chess Knight is one set of up to 15 positions. New positions join the set only when there is room. Up to 10 join each day, fewer as your reviews grow, and none while a full day of reviews waits.

There is one more reason to practice a little each day. A major paper on sleep research describes sleep as a state that helps the brain store new information in memory.¹⁴ So each day of practice gets a night of sleep before the next one. Sleep is part of practice.

Good help starts with a hint and talks about the move

In 2000, Vincent Aleven and Kenneth Koedinger checked how students used a computer tutor for geometry.¹⁵ When a student asked for help, the tutor gave hints in levels. Each hint said more than the last one, and the last hint gave the answer.¹⁶ Students often took that shortcut. On 82% of the steps where they asked for help, they did not stop until the last hint.

Researchers have a name for this problem: the assistance dilemma. How much help should a tutor give, and when should it give less?¹⁶

Chess Knight’s coach gives help the same way. First it tells you where to look, for example that there is a knight fork. Next it gives a closer hint, for example which of your pieces is in danger. Only then does it show the move. But only your first try moves your pawn. So a hint can help you find the move, but it cannot turn a guess into a pass.

The “I’m not sure” button shows the move at once. It counts, honestly, as not solved yet.

The words after a move matter, too. A large paper that combined research on feedback found that praise about the person is the weakest kind.¹⁷ Praise such as “Great effort” tells you little about the task. The feedback that helps is about the task, and about how to do it.

So the coach talks about the move, not about you. When you find the move, it says what the move does, for example that it wins a rook. After a mistake, it says what your move did, for example that it lost your advantage. When your move is as good as the coach’s choice, the coach says so. Any move that solves the problem counts, not only the first choice of the engine (the chess computer).

The coach says less, and it says the specific thing

In 2012, Elan Ruskin of the game company Valve gave a talk.¹⁸ He showed how the characters in the video game Left 4 Dead choose what to say. Each line has a rule: a list of facts that must all be true. When several rules fit, the game uses the rule with the most facts. A rule with more facts is more specific.

General lines come last, when nothing else fits. The game also remembers which lines it used, so it does not repeat them.

Chess Knight’s coach does the same. It says the most specific thing it can about your position. It remembers what it said. It speaks an instruction once in a session, and after that it only writes it. The written form gets shorter each time you see it. Most moments get a reaction and one fact or hint, no more.

Trust the results, not how a method feels

Think about the stories above. Students felt more sure after they read a text again, but they remembered less. In two other studies, most people judged the worse way to be as good or better. Chess Knight follows the results, not how a method feels. That is also why your numbers leave out any game where you had help. They show how you play on your own.

Sources

Chase & Simon, “Perception in chess,” Cognitive Psychology, 1973. Page 55 describes Adriaan de Groot’s experiments from Het denken van den schaker (1946; in English, Thought and Choice in Chess, 1965). Free PDF · DOI ↩︎ ↩︎
Charness, Tuffiash, Krampe, Reingold & Vasyukova, “The role of deliberate practice in chess expertise,” Applied Cognitive Psychology, 2005. DOI ↩︎
Roediger & Karpicke, “Test-enhanced learning: Taking memory tests improves long-term retention,” Psychological Science, 2006. Free PDF ↩︎
Hermann Ebbinghaus, Memory: A Contribution to Experimental Psychology, 1885, chapters 3 and 8. Free translation: chapter 3 · chapter 8 ↩︎
Cepeda, Pashler, Vul, Wixted & Rohrer, “Distributed practice in verbal recall tasks: A review and quantitative synthesis,” Psychological Bulletin, 2006. Free PDF · DOI ↩︎
Sebastian Leitner, So lernt man lernen, Herder, 1972. Library record ↩︎
University of York Library, “The Leitner system.” subjectguides.york.ac.uk ↩︎
Nate Kornell, “Optimising learning using flashcards: Spacing is more effective than cramming,” Applied Cognitive Psychology, 2009. Author’s PDF · DOI ↩︎
Pyc & Rawson, “Testing the retrieval effort hypothesis: Does greater difficulty correctly recalling information lead to higher levels of memory?” Journal of Memory and Language, 2009. DOI ↩︎
Karpicke & Bauernschmidt, “Spaced retrieval: Absolute spacing enhances learning regardless of relative spacing,” Journal of Experimental Psychology: Learning, Memory, and Cognition, 2011. Free PDF · DOI ↩︎
Kornell & Bjork, “Learning concepts and categories: Is spacing the ‘enemy of induction’?” Psychological Science, 2008, experiment 1a. PubMed · DOI ↩︎
Rohrer & Taylor, “The shuffling of mathematics problems improves learning,” Instructional Science, 2007, experiment 2. DOI ↩︎
Anki’s deck options, the help text for “New cards/day.” github.com/ankitects/anki ↩︎
Diekelmann & Born, “The memory function of sleep,” Nature Reviews Neuroscience, 2010. PubMed · DOI ↩︎
Aleven & Koedinger, “Limitations of student control: Do students know when they need help?” Intelligent Tutoring Systems, 2000. Free PDF · DOI ↩︎
Koedinger & Aleven, “Exploring the assistance dilemma in experiments with cognitive tutors,” Educational Psychology Review, 2007. Free PDF · DOI ↩︎ ↩︎
Hattie & Timperley, “The power of feedback,” Review of Educational Research, 2007. DOI ↩︎
Elan Ruskin, “AI-driven Dynamic Dialog through Fuzzy Pattern Matching,” GDC 2012. GDC Vault · Slides with notes ↩︎