Knight Moves Explained: Making a Post to Understand Them Myself

Hey. I'm Maya and I have a confession to make - whenever I'm calculating Knight moves I'm drawing with my eyes thousands of L lines on the board. If you're already eyerolling, you're obviously too experienced in chess for this post but if you're like me... well, take a sit.

Ok, but what's so wrong with drawing L's around the board?

Well, nothing. If you're casually playing with friends every once in a while, having a descent win rate amongst non-regular chess players and not playing with a clock. That was all my previous chess experience too but recently I got a bit more interested in the game and the more I dig, the more skill cracks started to show. I still think I'm a decent everyday player as long as I have all my time to think... But the moment I tried rapid, boy oh boy, my moves quality went down the toilet real fast. I don't like time pressure in general, so I got very close to just forgetting about this experience and never playing rapid or blitz ever again. But then I thought, why not embrace the misery of the ticking clock and figure out what makes me panic so bad when I have to play fast and how to improve on it. And maybe improve my classical games too. But I'm not a "just play 'till you stop hating it" kinda gal, I need to find the issue itself and attack it with a strategy. So I started thinking, what is making me so slow and stressed. One of the reasons I come up with is that I take for-fucking-ever to analyse where the opponent's Knight is going and if I need to be concerned or not. Now, make them two and imagine them both in full attack mode and ya girl is melting behind the board. So, I needed to find a way of seeing the Knights moves faster- and not just the immediate move but also the next couple of potential moves.

Here are my solutions:

First thing first, the Knight could never go to the same colour square it is currently on. Seems obvious? Well, that's because it is. But have I ever thought about it before? No. I, of course, know where the Knight could go but I never paid attention of the colour of the targeted squares. 

From this we can get a coupe of conclusions right away:
- All of our pieces positioned on the same colour square as the opponent's Knight are currently safe.
- If two important (or even not so important) pieces are currently on the same colour squares and the Knight is coming towards them, there might be a fork in the making. So we should check for any potential forks and act accordingly while still have time.
- If the Knight is, for example, on white square, each odd number move would be to a black square (1st move, 3rd move...) and each even number move would be to a white square (2nd move, 4th move...). So if our Queen is currently on a black square and is not attacked by the Knight, there is no way she would be attacked by the Knight the next move either.

Non of the conclusions are "must remember" but they could be useful while calculating opponent's potential moves. Where visualisation fails, math could do the job and vice versa.

The first move

	If we have a Knight on d5, these are all the squares it can go to in one move. Now seeing them together, they are no longer just random L's on the board - they make patterns. So, I came up with 2 ways to visualize those patterns faster while playing:
1. First one is imagining arrows pointing to each corner of the Knight square where the same colour square is the tip of the arrow and the other two - the sides/wings (?) of the arrow. The "wings" are all the squares that are currently threatened by the Knight.
2.  Second option is to "draw" diagonals from the Knight and the side squares at the end of the diagonals would be the Knight targets. Currently, I prefer this method. While in a hurry during the game, my stupid brain sometimes goes "wait, what's an arrow???" but both methods could be useful for visualizing the moves.

Oh but you still "draw" on the board to find the squares.
Yes, but now with a single "draw" I find 2 targeted squares instead of one. But lets take this a bit further:

In a real game, not all legal Knight moves are even important for us. In the example above, the opponent's Knight has moved form d7 to f6. None of our pieces are behind the Knight, so with this move, the opponent is obviously interested on potentially moving forward with the Knight in the future. So the moves we need to evaluate currently are d5, e4, h5 and g4. No need to lose any time calculating d7, e8, h7 and g8. Combining this and the visualisation methods, now we need to "draw" only twice on the board to see all relevant squares this Knight could go to next.

The second move

	If we imagine the Knight being on each of the red squares and follow the possible next squares from them, we will find all squares the Knight can reach in 2 moves. That's obviously not the fast path following I'm in need of, so what conclusions we could get from the pattern we have here that are actually applicable during the game?
Firstly, there is a very easily spotted "ring" around the Knight. One way to visualize it is by remembering that each square that is the same colour as the current Knight's square and is touching the 4 different colour squares next to the Knight is accessible in 2 moves.
The other way to visualize it is by imagining a diamond-like shape around the Knight.
	If the Knight is obviously approaching a certain direction, we can continue the diagonal we used to find the first move in this direction. The square in the middle is accessible in two moves by both one-move squares.
	If we again imagine the arrow pointing towards the Knight, the next 3 (second-move) squares are actually the arrows pointing towards the red squares.
	If we follow this direction, between the Knight and the 3 second-move squares I showed on the 2 pictures above (f1, g2, h3), the only same colour (as the Knight's square) square that can't be reached in 2 moves is the second square diagonally across the Knight (f3).

Those patterns doesn't give us all possible Knight square but are definitely saving some time.

In the game example, looking at the down-left direction, we can right away see 4 potential threats - the Knight could eventually reinforced the other Knight on b4, it could threaten our Knight on d2, it could threaten the Bishop on e3 or it could even go to c3 threatening our Queen. Meanwhile, we see no immediate threats on down-right direction.

Does that mean the Knight wants to go on d5 or e4? Not necessary, moving to g4 could threaten the Bishop on e3 and the Pawn on f2 too. Seeing more threats in one directional pattern is not enough to assume that's where the Knight is going. That being said, on the down-left we see 5 two-moves squares just by glancing at the board once. How much time it would have cost us to find all 5 by drawing L's?

Lets fill the rest

	By filling the rest of the moves on the board, we get a couple more potentially easy to spot and useful patterns. Some of which are filling the "blind spots" on the example above.
Horizontally and vertically every 1st square is 3 moves away and every 2nd square is 2 moves away.
	Diagonally every 1st square is 2 moves away and every 2nd square is 4 moves away.

Here are some screenshots from a very useful tool on Itchio that shows the number of moves the Knight needs to access any square. (Don't get fooled by the black screen, it works, it just loads a bit slaw sometimes.)

As you can see, some patterns do change when the Knight is too close to the edge or the corner. I mean, of course, the Knight can't fly from a1 to a7 in 2 moves but I had to mentioned this - the patterns are not law, they are just tools to use when applicable. And playing around with the Knight positioning helps with understanding when they are and when they are not applicable.

Where the Knight can't go?

Well, the answer is obviously nowhere. Each square would eventually be accessible for the Knight. However, in the real world we can assume the opponent is not planning to move their Knight for 4 moves straight (if it's not endgame). This means the squares further than 3 moves away are probably safe for us.

	The ones I'm particularly interested in are those 4 squares. Why? 1. They are easy to spot - they are between the "wings" of the "arrows" pointing towards the Knight 2. They are in the close vicinity of the Knight but they are safe - you won't need to draw L's to see if the opposite side of the board is safe... 3. If the Knight is yours and you want to attack one of these you'll quickly know not to bother trying to do it with this Knight
In the game, if we for whatever reason want to keep our Bishop safe from this particular Knight, one way to do it would be to move the Bishop on d4, knowing that it's one of the Knight's "blind spots". (Of course now the Bishop has the other Knight to warry about since it's 2 moves away)
And if the Knight is approaching and our piece is already on one of these squares, we know not to warry about this particular piece. Similar to how at the first game example we don't warry about the backward possible Knight squares as non of our pieces are there. Again - a potential time saver.

What to do with all of this?

Well, do whatever you want. Maybe choose one pattern to use, maybe all of them or maybe tell me I suck at chess and you love drawing L's. But my approach is, whenever I'm doing a chess puzzle and there is a Knight on the board I try to quickly imagine as many patterns possible. This is a 3-5 seconds exercise and I just get onto solving the puzzle then. All this pile of patterns looks intimidating but by doing this you will probably start seeing them mostly effortlessly in a couple of days.

Some useful sources I used compiling those methods:

1. Number of Knight moves to each square on Itchio
2. Knight Mastery: Fastest Path to Any Square with the Knight
3. A shortcut for visualizing knight moves in chess