Decoding: The crux move

​As a young chess player studying under Grandmaster Yan Teplitsky, one lesson that sticks out in my memory is that great players don’t just focus on how to make the best move, but also when to make the best move. I.e. there is a crucial moment in each game, long before checkmate, where the winner and loser are decided. It’s crucial to recognize this moment so you can slow down and invest the time to be precise. I refer to this phenomenon as the Crux Move: a crucial moment in a series of decisions or actions where the accuracy of your move will disproportionately affect the final outcome. In essence, it's the subset of decisions that convert hard problems into easy ones. 
This blog post is about the nature of Crux Moves, provides common examples, and discusses their relevance not only in games, but in various problem-solving contexts, including surgery, rock climbing, and even relationships.

Part 1: Defining the Crux Move

I originally came across the Crux Move from a book on problem solving — which I have unfortunately long forgot the title and author of. It poses the following famous challenge: connect these nine dots by drawing four straight continuous lines.
If you’ve never encountered this problem, go ahead, give it a try. I will disclose the answer below.

After a few tries, it quickly becomes evident that simply drawing lines between dots will never solve the problem. Until, either through creativity or perhaps even a mistake, leads you to draw outside the confines of the nine dots. Here’s the solution.

The decision to draw a line that passes beyond the dots is what the author referred to as the "crux move”. Their definition of crux move was the decision beyond which solving the problem becomes easy. I am going to propose my own, slightly modified definition.
Crux Move: a crucial moment in a series of decisions or actions where the accuracy of your move will disproportionately affect the final outcome.
Examples of other Crux Moves
I decided to make this change because besides games chess and connecting dots, this phenomenon is present in many disciplines. For example, research has shown that as surgeons become more experienced, they transition from equally distributing their time between moves to move quickly through the majority and spending a lot more time on a single Crux Move, that is more likely to determine the outcome for the patient. The research even showed that veteran surgeons who have different philosophies or approaches to a certain surgical objective, will converge on the same bottleneck in the solution where they will slow down and invest more time and focus to get it right.
When I googled the term Crux Move, it turns out it’s actually a common term used in rock climbing and bouldering, where it refers to the hardest point in a course or route. In this case, it is the limiting factor in determining what skill level is required to complete the course.
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Part 2: Understanding the Crux Move

While all these contexts offered slightly different definitions and perspectives, I felt there was a unifying connection and wanted to tie them together. In this process I made the following observations.

1. The Crux move is only relevant when the challenge is proportional to the skillset. If someone is a terrible rock climber, then it actually doesn’t matter what a professional might consider to be the Crux move — perhaps they will fall on the first boulder.
2. A Crux Move has to be detectable before it happens, after all, the chess player’s goal is to identify it before investing the time.
3. In some cases, the Crux Move is make or break (e.g. surgery, or rock climbing), in others, like chess, it can potentially be recovered.
4. Even with the knowledge that a Crux move will occur in a game or series of decisions, it is not obvious when it is happening.

This has led me to believe there are actually two sub-types of Crux Moves.
Type I: an incorrect move which leads to immediate and obvious issues. E.g. the surgeon knows if the Crux move was botched, the patient may be going critical, or a rock climber may fall instantly.
Type II: a more subtle error that is only later discovered by running into insurmountable obstacles. e.g. after a Crux move in chess, the player with the advantage will slowly creep onward gradually compounding their advantage. In this case, the opponent may review the game and not even know where they went wrong.
I think this distinction is crucial. Type I are mundane; most journeys have a particular challenge where you are likely to fail. More interesting is the insidious Type II, where back-breaking stakes are combined with the deceptively trivial appearance.
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Part 3: Making Crux Moves

Now that I have defined the notion of a Crux move, and I have provided examples of where I see it, and even a model of different sub-types, I want to discuss some places where I think each of these is relevant to our everyday lives.

1. Choosing meaningful work
   I obsess over choosing what to work on. It is my personal belief that it’s far more important to work on the right problems than to work overtime. While some may say my fixation on this problem is excessive, I stand by the claim that choosing work is a Crux Move, and should be considered very carefully.
   My framework for thinking about this Crux Move relies on one of my favourite books So Good They Can’t Ignore You, by Cal Newport (see my summary here). The TLDR is that having rare and valuable skills gives you the leverage to exchange them for the triad of ideal jobs (autonomy, creativity, and positive impact) which research indicates is the source of career satisfaction. Having the triad, as well as being valuable to your employer, will prime you to have the passion and dedication to do great work. This creates a feedback loop where you become more valuable, which in turn gives more freedom (if you avoid the traps outlined in the book) and ultimately makes it easy to love your job. Conversely, if you end up in a tyrannical, mundane, or aimless job, you are doomed to suffer.
   This decision is clearly a Crux Move. Positioned well, it gets easier over time to love your job and find fulfillment and positioned wrongly, you could potentially fight a 30 year uphill battle.
   This isn’t narrowly referring to your job title either; it can also refer to how you frame your challenges. For example, if your job as a teacher is to please your principal and school board, that’s a tyrannical job. If instead, your goal is to insert your own interests and passion into your teaching, that’s a colourful and tasteful pursuit that will impact hundreds of students over your career.
2. Engineering your environment
   For whatever your desired outcome is, it’s much easier to engineer your environment to induce the behaviour you want, than it is to change yourself to overcome the surroundings.
   Examples:
   • it’s easier to diet by controlling your grocery purchases, than resisting a cookie jar.
   • A bag of flossers on your night table is a better cue than trying to remember every day.
   • A primed work environment is better than the intent to focus.
   • Spending time with friends who promote the kind of person you want to be is better than trying to be a black sheep in a friend group you’re used to but not aligned with.
   There are surely countless more, but I think this is extremely relevant to across all dimensions of self-improvement.
3. Communication in Relationships
   I wanted to end this blog with a personal example. I recently had a conflict with my partner where she was travelling for a couple weeks, while I was going through a particularly stressful and isolating period.
   Before she left, we had scheduled out a month leading up to a day of two final exams on April 4th. Given I have a full-time lab commitment, ongoing projects, and applications — this meant that the whole week preceding the exam was going to be hell-week, ending on April 3rd as a doomsday. There’s never enough time and so even with hard-core scheduling, I ended up pulling a dawn-to-dusk workday with only a total of 120 minutes carved out to eat my three meals. I decided to divide my lunch break in two and use half of it to run on the treadmill and call my girlfriend to talk after days of being isolated while working at my desk.
   I sent her my schedule for the day and when I got to the treadmill I gave her a call. Unfortunately for me, she had plans at that time and so I wasn’t going to get to connect with her. I hung up frustrated.
   Later, we continued sparse communication over text since the rest of my day scheduled out. And by the end of the day, miscommunications had compounded, and I ended up feeling really hurt.
   As part of my journey through grief and mental health, I have been seeing a wonderful therapist, Lori, through the U of T student support (for free by the way, if any other U of T students are reading this).
   When I was explaining this whole situation back to her trying to get some clarity on my own emotions and how things got so out of hand, she identified something that moment on the treadmill as a crucial moment.
   “Rick, you failed to identify and communicate the significance of that moment on the treadmill, and given the context your partner was in, it wasn’t obvious to her. This marks an inflection point which led to a lot of frustration on your end.”
   Sound familiar?
   I think that in interpersonal conflict, there are often Type II Crux Moves that may go unnoticed. In this case, I was too wrapped up in my own thoughts and feelings that I didn’t mark the importance of the moment, and plant a flag to communicate that significance.
   Had I done a better job: “I know you were looking forward to your plans, but I am struggling and I need you right now, can you please find a way to talk?” Obviously, any reasonable partner would do what they can to make that happen, and I think the rest of the story would have been drastically different.

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Conclusion

Crux Moves are everywhere: in your career, relationships, habits and everyday problems. Their implications are compounding and their effects are significant. When faced with one, I will ask myself "instead of making this decision, how can I invest in this decision?" Thinking about Crux Moves also works in the negative case too. If you are over-optimizing a solution, ask yourself if it's a Crux Move. If it's not, as my friend Arth puts it, maybe the juice isn't worth the squeeze. 

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Thank you for reading! This essay is part of my 2024 series of my blog "Decoding Waves". If you enjoyed it and would like to stay up to date with new posts, I finally figured out how to properly keep a mailing list! (see below) 

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