My biggest improvement in chess came after comprehending The Theory of Steinitz [1]:
1. At the beginning of the game the forces stand in equilibrium.
2. Correct play on both sides maintains this equilibrium and leads to a drawn game.
3. Therefore a player can win only as a consequence of an error made by the opponent. (There is no such thing as a winning move.)
4. As long as the equilibrium is maintained, an attack, however skilful, cannot succeed against correct defence. Such a defence will eventually necessitate the withdrawal and regrouping of the attacking pieces and the attacker will then inevitably suffer disadvantage.
5. Therefore a player should not attack until he already has an advantage, caused by the opponent's error, that justifies the decision to attack.
6. At the beginning of the game a player should not at once seek to attack. Instead, a player should seek to disturb the equilibrium in his favour by inducing the opponent to make an error - a preliminary before attacking.
7. When a sufficient advantage has been obtained, a player must attack or the advantage will be dissipated."
It assumes both players are as highly skilled as it is possible to be (e.g. they can see right to the bottom of the decision tree in every variation).
If the players are less skilled than this, i.e. they aren't going to play the best move every time, then any analysis you want to make about whether the starting position is a theoretical draw becomes moot because they aren't going to play the theoretical best moves anyway.
But if you assume the game is a theoretical draw from the starting position, then any game you lose is ultimately down to you playing at least one suboptimal move (otherwise you would have been able to force a draw), and any game you win is ultimately down to your opponent playing at least one suboptimal move (otherwise he would have been able to force a draw).
As it happens, I've just got home from playing a chess match in the local league. I lost, which means I made at least one suboptimal move, although I'm quite confident I made many!
Fundamentals can be hard to define concretely because they can even underly the principles of how people talk about playing the game. Take, for example, the age-old advice in chess "control the center." To an absolute novice, this is interpreted as 'have your pieces in the center.' To more experienced players control can be more fluid. In some cases, it's as much about protecting a position as it is about occupying it.
To give an example from a game I love dearly: Halo. The number one fundamental isn't aim, or knowing sick trick nades, or masterful timing of power weapons. It's positioning. Positioning controls where your opponents respawn, it controls where your team respawns, and it is the single most impactful part of "map control." Good aim means nothing if you stand in the wrong places at the wrong times. Power weapons are useless if you get yourself back-smacked by opponents getting split-spawned that you weren't aware of.
Fundamentals are (somewhat) unique to a game, and they typically reveal themselves either once you've intuitively started applying them, or through thoughtful analysis.
Fundamentals -- let's go back to the fundamentals of fundamentals (cognition)!
Cognition and agency in the real world is often hierarchical in nature. You learn a task by breaking it down into simpler tasks, and if necessary breaking down the simpler tasks into yet simpler. This is due to nothing more than algorithmic efficiency (when at all possible -- it usually is IRL), divide and conquer.
The fundamentals are the basic tasks which higher level tasks rely on. Sometimes (quite common really) the nature of this (inverted) tree is such that the higher level tasks have a sort of soft max-min relationship: your overall skill will only be about as good as your weakest subskill. An example that comes to mind is manual driving. You could be the most brilliant, strategic, high-reflex rally race car drive in the world, if you miss most of your stick shifts you will likely be a mediocre driver, if even competitive. Shifting properly and quickly makes a significant difference. So much that it's almost completely futile to practice those higher skills unless you've nailed down the basics.
When you're just having 'fun', learning something intuitively, without the sharp focus on improving, it's easy to neglect those fundamentals. They are likely areas where you have some natural relative difficulty, which can lead to shying away from them (in larger contexts sometimes this is even wise -- you want to use what you're good at afterall!) -- it could be because they're uncomfortable, painful, repetitive, boring, too difficult (break it down!) and so on. Compensating for weaknesses exists I believe, but in high levels of competition it's something extremely subtle; again risking generalizations almost every high skill individual will have fundamentals mastered.
Most of my activity is academic, and I have some anecdotes in this regard. I feel like I've really evolved when (a) I've focused on learning the basics of my field really well (going down to the math foundations and axioms) (b) focused on improving weaknesses. It wasn't intuitive to me that this attention to fundamentals could yield so much.
edit: It should be noted (as others noted) that identifying what are the fundamentals can be something difficult itself. Common tools here are reviewing your games/production/etc, or asking others (teachers, peers, etc).
In Chess, you can learn techniques used by players a few hundred points above your rating, but still make game-losing blunders (hanging a piece totally undefended, not knowing how to finish a winning endgame) that are easy to spot (if you are careful). Patiently eliminating blunders will do much more for your rating than learning myriad openings variations and complex combination moves.
In FPS, aiming moving and ducking are like learning how to move the pieces in chess. And sure, those are the basics to even play.
But when people talk about "fundamentals" they are talking about the emergent things that come from those skills and are usually unique to the game. In chess, this is stuff like don't hang your pieces, tactics like spotting skewers or forks, understanding endgames, and later general strategic goals like controlling the center or develop your pieces to "good" squares.
In FPS games, this often deals with understanding the flow of a map (choke points vs open areas, cover and sniper locations), proper navigation (efficient pathing!), role synergy, and how a match develops (at about 30 seconds I should expect an opponent, if they went straight path A, to show up around this corner).
MOBA games moving and attacking and using a skill are the language. Fundamentals involve map awareness, ganking, vision control, wave management, etc.
Fighting games move, jump, attack, block is the language. Understanding zone control, the Rock-Paper-Scissors of strike/block/grapple, how to manage your health and special meters, character movesets/matchups are the fundamentals. Picking character X against player Y is the meta.
Once you have all of that squared away, you can start doing "meta." That is figuring out optimal picks vs particularly optimal setups, researching your opponent to build a specific toolkit against them, etc.
The fundamentals are about positional elements and strategic principles.
For example: Relative value of the pieces, Control of the center, Pawn structure, Tactics, Initiative, Tempo, Opposition, Keep the position balanced, Develop multiple ideas/areas (strategy), Control open lines (files/ranks/diagonals) and crossings
In Starcraft, the one that gets hammered on the most for lower-level/newer players is "constantly make workers and spend all your money". The most basic rule of thumb is to not stop making workers until you hit 70 or so.
If you do that in silver league, you're going to stomp 99% of your opponents even if your scouting and strategizing and unit compositions are all awful. You could do nothing but make a single unit type and still win.
Of course, if you do this at least somewhat well you'll rapidly "level up" in the ranking system to the point where you'll need to actually start scouting and reacting.
And it's actually really hard (from personal experience) to keep this up and have your money all spent and controlling your units all at the same time. So simply practicing this one simple rule makes you better at many aspects of the game because you're forced to scramble and keep up.
I actually had games where I was too focused on this where I hadn't made a single aggressive move, the opponent pushed and saw my massive army and just quit.
Yeah, I was never amazing, but I played a decent amount of Brood War back in the day. So I had build orders, I knew of the importance of making workers and staying broke and expanding early.
We had my ex-wife's brother living with us for a while and he wanted to play StarCraft. I was like, "Sure, we can play 2v2 against the computer until you're comfortable". He was like "Nah, I've played Age of Empires, I know how RTS works, let's play 1v1." I tried to tell him, "StarCraft is fast". He insisted. So we played.
I built workers, sent a scout across the map, found his base. He was hoarding mineral until he could afford a barracks. I was pumping out workers. I built a secondary base in his expansion area, a barracks and a factory and staged a bunch of siege tanks along his opening, then drop-shipped several marines, firebats, and medics behind his mineral line.
He had just started building his second barracks. He sent his troops to try and handle the situation, then I pushed my siege tanks in from the other side and ruined his barracks.
I tried to find the original comment on HN, it was very informative, but some chess master (grandmaster?) commented on here that until you are highly rated (say 2200), the only thing you should focus on to improve at chess is to improve your ability to notice tactics in games. He went into more detail but I can't find the post :(
Not quite. First you need to eliminate your own hung piece blunders and look for opponents'. But that gets you to 1000-1500 then you need to notice tactics.
There is overlap, in that the simplest single-move tactics (forks and skewers) are almost the same as catching immediately hung pieces.
