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I'm solving tactics on http://chesstempo.com .

One of the things that I struggle with, is tactics involving moving the Knight several times. I find it very odd to calculate Knight movement beyond the first move and often miss very simple tactics as a result.

I have an ELO of ~1600 on chess.com and still sometimes miss simple tactics involving this piece.

Are there any ways to train yourself to be better at calculating Knight movement?

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    What in particular makes Knight movements in a row more difficult than, say, any other piece? – gented Dec 28 '16 at 16:14
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    When you look at a Bishop for example, you can see its immediate movement as well as future ones simply by looking down the diagonal since immediate and future are all on the same diagonal. Likewise a Rook on a column shows you all its possible moves immediate and future possible. A Knight doesn't. The set of squares it can move or threaten now changes once it has moved. This makes projecting its influence difficult. – user34445 Dec 28 '16 at 18:10
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I've mulled this over a number of times. Here is what helps me play better with a knight. I offer it not as a general solution, but as a solution that has worked for me. I hope you find it useful:

  1. Understand how the Knight moves COMPLETELY.
  2. Understand ALL the Knight threatens COMPLETELY.
  3. Understand that the value of the Knight relative to the Bishop may change.
  4. Understand by colour, what the Knight threatens when he sits still or moves twice (Rule of Even).
  5. Understand by colour, what the Knight threatens once he moves (Rule of Odd).

Point 1. Most people know how the Knight moves described as a "L". I've found this to be inefficient since this is only visualizing one of his possible moves and it's possible to miss some of his possible moves thinking this way.

To truly see his potential a player needs to know all of his possible moves at once. Here's how I visualize it (and will try to explain clearly how I see it):

All of Knights Moves

Around the Knight is a box the corners of which match the colour he is sitting on. The Knight jumps outside of the box to the opposite colour squares touching the corners.

It is possible to look at a board and see this "box" while playing and see all of Knights potential moves at once, rather than just one. The ability to see this box rather than a single move is something of an epiphany.

Point 2. Understanding all the Knight threatens at once, rather than a single threat allows the player to understand all the pieces he can attack.

Just as above (Point 1) where seeing all of a Knights moves show his true potential, seeing all he threatens shows all of his attacking potential. Many players identify what he threatens (in a somewhat sequential manner) one threat at a time. However, this is inefficient and may inevitably miss some. The ability to visualize his box allows a player to see all he threatens which allows a player to realize his full attacking potential.

Point 3. Some theories of Chess don't assign the Knight a static value relative to the Bishop (meaning the same unchanging value). Consider this for a moment:

If the Bishop works best on an open board with far reaching open diagonals BUT the Knight can jump around pieces on a crowded board but whose reach is always limited, it stands to reason the Bishop's value increases over time as the board opens up and as the game goes on; whereas the Knight's value decreases overtime since the board opening up removes his advantage. Accordingly, consider assigning the Knight a value of 3.5 in the beginning of the game (Bishop at 3.0), and flip these values as the game goes on as it's appropriate.

Point 4. An un-moved Knight threatens the opposite colour he's sitting on (or if he moves twice).

A Knight on BLACK is threatening WHITE. A Knight on WHITE is threatening BLACK. Remember this and consider it when considering position.

Point 5. A moved Knight threatens the same colour he sat upon before moving.

A Knight moving off BLACK will threaten BLACK once he comes to rest. A Knight moving off WHITE will threaten WHITE once he comes to rest. Remember this and consider it when considering position.

These last 2 points really help in end-game situations where you're forced to chase an odious opponent around the board. If you want to threaten the same colour you sit upon, you must move. If you want to threaten the opposite colour, stay or move twice.

Good luck! Mighty Knight!

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    A nice way to remember 4. is to realise how many Knights one can place on the board so that they don't capture one other :p. – gented Dec 28 '16 at 20:15
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    This is some really great stuff! – Alex Weitz Dec 28 '16 at 22:14
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    So far I implemented step 1 and it's way easier to find ideas for Knight – Alex Weitz Dec 29 '16 at 8:11
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You suffer from "Knight Vision" problems.

:)

Do a series of visualization exercises whereby you randomly select a start square and an end square, and without looking at the board, write down all the shortest paths the knight can take to get there. Do 8 a day, every 2 or three days, always, and no more frequently than that (your brain won't absorb it all).

You WILL see improvement after several weeks.

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