Learning Through Comparing Similar But Different Situations

The temptation is very great, for both a learner and a teacher, to try to go fast through a lot of material, when learning a subject such as chess, because there is so much that is known. This is not a problem specific to chess: in fact, it is a problem for students of cooking, running, law, computer science, medicine, you name it. We all feel the burden of the accumulated knowledge of all of human history. Educators everywhere face the challenge of somehow distilling more and more knowledge, wisdom, and practical technique into less and less time. Unfortunately, there is no shortcut for deep learning. Just flipping through a chess book or even working through a set of exercises is no guarantee that when you sit down across the chess board, you will remember or know how to apply what you learned.

In my attempts to improve my own lifelong learning as well as my teaching, I have found that comparing similar but different situations is a technique that can be very useful in making learning more efficient, and even more interesting. Instead of trying to focus too much on “this is how to do things”, it is better to have worked through several similar ideas that do or don’t work, and know why. It is like in martial arts where you must learn how to fall, in addition to how to strike.

Fundamental endgames are a great place to notice both patterns and differences between them. Little things can make a big difference in endgames. It is a great mental exercise to understand fundamental endgames and learn to appreciate the importance of detail, and the unexpected beauty of peculiar features of chess positions. For example, consider the following Rook and Pawn endgame position, White to move. Can White win or is it a draw?

One way to win

The answer is that it is a win for White. The key insight is that in order to Queen the a7-Pawn, White must reach a position in which

  • Black cannot check White’s King forever.
  • White has time to move the Rook with check in order to free up the a8 square for Queening without losing the a7-Pawn (if Black’s Rook is on the a-file always threatening to take it).

The tricky part of winning is finding out how to deal with all possibilities and obstacles while keeping in mind the key insight.

One way to win is to move the King all the way to the left, perpetually uncovering Black’s King and therefore threatening to check it. This forces Black’s King to move in the “shadow” of White’s King; if the King does not move but the Rook checks instead, then White can simply bring the King near the Rook eventually and stop all checks and then be in position to check Black’s King and Queen the a7-Pawn.

Once Black’s King is pushed all the way to b1, and White’s King at b3 prevents a Black Rook check, White has the tactical trick of moving the Rook to the right and simultaneously threatening Queening and checkmate on the first rank!

Changing the problem

Unfortunately, teaching this way to win, although instructive in its own right, can cause a failure to generalize. This is a special case kind of winning plan. To prove this, move the pair of Kings up one rank:

Here, if White blindly follows the plan of trying to box Black’s King down, then it becomes clear at the end of the King march that the original tactical idea no longer works: there is no back rank mate.

I believe that it is extremely instructive to allow the student to try a generalization that fails, to solidify the understanding of what is going on, rather than treat endgame knowledge as a mechanical memorization of particular move sequences. Then after trying out some possibilities, we can finally reveal a key idea: White has another tactical trick, based on reaching a position in which White can still move the Rook away and allow Black to capture the a7-Pawn, but in return, White can perform a discovered check that wins the Rook. So White’s King should, at the first opportunity, start a diagonal march straight to the a7-Pawn.

By presenting first the back rank trick, and then the discovered check trick, we allow the student the opportunity to learn a more general lesson than if the back rank trick had not been mastered first: that the goal is to be able to move the Rook with an appropriate tactic in mind, not just checkmate or a discovered check.

A variation that still obeys the pattern

It’s always useful to show how a pattern can in fact be applied to a slightly different position, without substantial change. Move the Kings up more: the discovered check still works.

A variation that does not work

And, of course, it is necessary to show a variation of the initial position in which White cannot win, otherwise the student might get the wrong idea and again fall into mechanical memorization habits.

Here, the Kings are so far forward that Black has boxed in White’s King so that it has no shelter and is far away from Black’s Rook, so Black can keep on checking White for a draw. Note that a careless student might try to mechanically apply the discovered check tactic with Rc8 only to find that after losing the Pawn on a7, there is no win of the Rook, because Black’s King is close enough to protect it! Again, allowing the student to fall into this trap is important, to prevent complacency and really nail down the nature of the discovered check tactic, which requires a nice combination of

  • White’s King being close enough to the a7-Pawn to get there in two moves, including one “free” discovered check move if necessary.
  • Black’s King being far enough away from the a7-Pawn not to be able to cover the a7 square in one move.

Conclusion

Even elementary endgames provide quite a rich amount of material for setting up ways for a student to discover the reasons for what works and what doesn’t work in a line of reasoning and a general plan.

Franklin Chen

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About Franklin Chen

Franklin Chen is a United States Chess Federation National Master. Outside his work as a software developer, he also teaches chess and is a member of the Pittsburgh Chess Club in Pennsylvania, USA. He began playing in chess tournaments at age 10 when his father started playing in them himself but retired after five years, taking two decades off until returning to chess as an adult at age 35 in order to continue improving where he left off. He won his first adult chess tournaments including the 2006 PA State Game/29 and Action Chess Championships, and finally achieved the US National Master title at age 45. He is dedicated to the process of continual improvement, and is fascinated by the practical psychology and philosophy of human competition and personal self-mastery. Franklin has a blog about software development, The Conscientious Programmer and a personal blog where he writes about everything else, including his recent journey as an adult improver in playing music.