Improvement

Compound Interest in Practice: Unlocking Layered Tactical Combinations

A step-by-step representation of how knowledge compounds to help you find the winning move

“The strongest force in the universe is compound interest.”

- Albert Einstein (maybe)

Opening

I’m far from the most tactically gifted player. I love endgames, positional grinds, and long-term strategy. I quite regularly find myself on the wrong end of some hard-to-swallow tactical motifs, particularly in faster time controls. Frustrating to be sure — but just about every powerful stretch of learning begins with a blend of frustration, uncertainty and outright failure. If you already knew everything, there would be nothing to be frustrated about — and nothing to learn.

Over time, I’ve rapidly seen myself grow stronger and stronger when it comes to board visualization and in spotting these sorts of concrete move sequences (albiet not Queen’s-Gambit-on-the-ceiling nonsense — even the world champion has stated he doesn’t visualize a 3D board like that). This progression isn’t news to chess players per se, but no matter your profession, the compound interest of quality reps and thoughtfully organized, methodical study is the recipe for lasting progress.

What’s amazing about chess is that a common phrase like, “do something to improve 1% each day” can be visually represented. As with many of the concepts I’ll try to articulate in this series, chess has a unique capacity to symbolically illustrate an everyday piece of wisdom through the language of its pieces.

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Middlegame (part i)

To exemplify the concept of compounding knowledge, I’ll use a single position from one of my more recent games. In walking you step-by-step through precisely how each element of knowledge contributes to a final decision (i.e. my move choice), I hope you’ll not only enjoy that individual move, but that you’ll be able to reflect on how you might bring patterns or skills from your own life to bear on your current life and work.

Now for the fun stuff:

Step 1: Take stock of the position and time situation.

This was a somewhat faster game than the others I’ve been covering: I had only two minutes to play out the remainder of my moves. My opponent was sitting on three-and-a-half minutes, amounting to a sizeable advantage. He’s also up a pawn, but material is less relevant here as I’m trying to put some pressure on his position. His king isn’t obviously vulnerable and incidentally every single piece in his position is guarded — for now. What to do?

Step 2: Use the patterns you know to begin your search

Mastering individual skills unlocks opportunities to combine those skills. If an architect understands multiple ways to design space, and has a deep background in both material science and physics, he or she is able to recruit each of those mental assets to create a physical structure that incorporates some or all of them. Remove any of those underlying knowledge sets or practical understanding, and creativity is constrained by their absence.

This is all to say that a lightbulb started to flicker in this position (completely unconsciously) because certain patterns were visible to me. Let’s start with the simplest.

1. My queen is x-raying his queen, creating some hidden danger for black’s most valuable piece
2. My knight can give check on a6 or d7, and should a piece be deflected from guarding those squares, black’s king and his defenders could be in some trouble

3. I also took note of the fact that my rook is uncontested on the e-file, making it a valuable asset in a potential attack

4. My bishop on h3 is similarly uncontested along the h3-c8 diagonal, and controls some valuable squares near black’s king

5. My king looks relatively safe for the time being, and black has no available one-move checks or material-winning threats to speak of

These patterns are all relevant, but the trick is knowing which ones matter more, which matter less, and whether there is opportunity to combine them. Rarely do tactics or meaningful ideas derive from the brute-force application of a single, isolated concept or area of knowledge. Integration is everything.

Step 3: Experiment

Start playing with various ideas — some will be silly, some will be boring — but some might be winning. Here are a few combinations that don’t work, but instinctively flashed across my eye in a second or two. Keep note of them though, because it’s these initial misses that led me to the winning idea.

It should also be noted that, prior to beginning any analysis, there is a huge advantage simply by knowing I’ve “set up a puzzle”. When I was playing this game in real time, I had no clue as to whether there was an immediate “solution”. That’s part of it too, but also why mental heuristics and high-confidence skillsets are essential to ever finding a win in the first place.

Here’s bad idea #1:

Nd7+ — this move is terrible, but creates the possibility of a counter-blunder by my opponent. Notice the exposure of the black queen. Should the rook re-capture my knight, the white queen would recapture black’s queen with check!

The back rank is exposed and mate will follow. Naturally, in the initial position, black would have just captured my knight with his knight and gone for a stroll.

How about another idea? If I could find a way to infiltrate and create a threat on black’s king, my knight could eventually help in a material-winning or checkmating attack. Notice that if black moved his knight, I would immediately checkmate the black king on b7. These moves would never be played without the assistance of major-league substances, but if the black knight moved anywhere, the following mate would ensue:

Now we’re getting somewhere. Is there anything else that would create a similar effect? After white moved his queen in our initial position (below), black’s pieces are surprisingly restricted in their ability to restrict the white king. I could create a similar attack on the white king if I ever got my queen or rook to the seventh rank, and create a decisive attack on black’s b7 pawn:

In all, we’ve established the following through a few hypotheticals and miniature sequences:

1. Black’s queen might not be as safe as it seems (e.g., if the rook no longer guarded it)
2. There are nested checkmating threats on black’s king
3. Black’s pieces might have trouble defending the b7 pawn
4. The 7th rank or b-file might be useful in delivering a checkmating attack.

Middlegame (part ii)

So with each component idea in mind, what’s the move I decided to play here?

Re7!! A wild move. At first glance, placing one of your most valuable pieces on a square where it’s completely undefended looks like a mouse-slip. Did I mean Re5 or something? No — Re7 is the purest combination of every idea above:

1. It directly threatens the b7-pawn
2. It brings another piece into the attack and further restricts black’s pieces in the defensive task
3. It subtly highlights the black queen’s potential exposure via knight check
4. If b7 cannot be defended, the rook, knight and queen stand an excellent chance of finishing off the black king

First question: why can’t black touch the rook (i.e. take it with his queen? I’ve hinted at this at several points, but the knight would immediately give check, giving white the black queen in exchange for a knight and rook, while ruining black’s pawn structure.

If black chooses to bite the bullet here and enter this position, he’ll soon find himself completely lost. Black’s king is simply too weak, white has a material advantage, and there are too many simultaneous threats in the position:

This position is hopeless, and my opponent immediately realized my rook was not for sale. He didn’t take it, instead sidestepping with Ka8…

But this gives me the one tempo I needed, and he’s forced to part with the valuable b7 pawn (below):

Unfortunately for my opponent, this attack continued to prove much stronger than meets the eye. I took the pawn, and my opponent desperately tried to make a move that didn’t lose on the spot. But the attack is already decisive. After black played Qe8 (game link again here), the white rook decides to make it buy one, get one free:

Ra7+! (above) Sacrificing itself for a second time — but now for checkmate. If black goes back to b8, it’s mate in one (queen takes knight). So black takes the rook, but the white queen, bishop and knight combine to control all the king’s escape squares and forge a mating net. The king can only walk the plank:

The king must fall back to b7 as its entire army stands on the sidelines:

26…Kb8. 27. Qxb6+, Ka8. 28. Qb7# (checkmate)

Endgame

The purpose of in-game combinations like these extends far beyond showing a cool tactical sequence; it’s an attempt to visually represent the often elusive concept of compound interest. Building individual skills, internalizing meaningful patterns and having the patience to search for combinations of those skills and various forms of recognition are the building blocks of creative output. This often feels like intuition (I played the move after less than 15 seconds of thought), but that’s an illusion. Ten years ago, Re7 would have never even crossed my radar. I simply didn’t have the resources to think it up, let alone under time pressure.

Finding ways to reflect upon what kind of work you’re doing to get just a bit better each day is about as powerful an exercise as you can perform. Just today I was able to beat another player with a considerably “higher rating” than me because I slowed down and unpacked a variety of patterns that I’d seen in a few games I’d been reviewing from the 2016 World Championship. In an incredible twist of fate, I found myself playing at one of the tables Magnus Carlsen and Sergey Karjakin used for that same World Championship during the tournament’s second round.

It’s not always possible to voice how or why certain concepts collide to make something new, and often people chalk it up to great memory or some other innate “talent”. That’s fundamentally wrong. Memory helps, but I (and many chess players) find themselves harkening back to a game’s storyline much more than a specific move order.

With a game that has more possible positional combinations than there are atoms in the observable universe, the only way to extract meaningful applicable lessons is by understanding the story-esque why behind particular moves. You build an internal archive that feels more like “when it’s cold out, I should probably throw on a jacket”, not [input = january 17th and mental code says every January 17th at 2pm, me wear jacket].

Those stories come together and their lessons manifest themselves in sometimes common, sometimes completely unexpected places. Learning a theme or principle with the potential to extend across a near-infinite permutation of real-life instances will almost always trivialize human attempts at memorization.

In my view, the most exciting bit of all this is that it’s something that can be done with just about every area of life. Writing, fitness, work, woodwork, you name it. If you want to get better, you can get better — a lot better. One of the essential ingredients is reviewing what you do today, assessing the goods and bads, and incorporating new techniques slowly and steadily to improve your craft. Learn from people who are better than you and those who came before you. Lose more than you win. And then lose some more.

Originally published at https://chessforlife.substack.com on February 4, 2023.