Even the pawns had a nice design which clearly indicated that movement of one square forward (normally), or attacking on the diagonal, were both allowed.

https://i.ebayimg.com/images/g/Yx4AAOSwTY9i7XeC/s-l960.jpg

https://i.ebayimg.com/images/g/AZUAAOSwuABi7XeE/s-l960.jpg

https://www.reddit.com/r/mildlyinteresting/comments/c1ri78/t...

Not all of the moves were the clearest, but it was still handy while trying to learn.

Displaying usual the moves on the pieces is certainly super-handy for beginners to understand the moves, but as you've pointed out: Chess also has other nuances.

---

I was showing off one night and, at the tail end of an end game, and promoted a pawn to a pawn once it reached the far rank. It didn't really help in that game (although I can envision corner cases where it could be helpful as a blocker, but any other promotion is equally useful a blocker), but I had a move that I could afford to burn and it was fun to do so I did it.

It was a fun game. 10/10, did repeat other fun (and absurd) chess games.

There's a lot of other versions sold under "chess teacher", this seems to be the most modern: https://www.ebay.com/itm/266236564204?hash=item3dfcef92ec:g:...

It appears that it was originally sold as "The Educator": https://www.ebay.com/itm/325899664936?hash=item4be1223e28:g:...

Not affiliated with any of those and they probably aren't the best prices (just the first ones I found), but should give you enough to track one down.

https://web.archive.org/web/20240125205710/https://i.ebayimg...

https://web.archive.org/web/20240125205730/https://i.ebayimg...

https://en.m.wikipedia.org/wiki/Art_Deco

I.e. the knight is an anti-queen.

[1]: https://twitter.com/skidbladnirr_/status/1750285122769957129

very old variants often had such compound pieces like for example: https://en.wikipedia.org/wiki/Grant_Acedrex

https://en.wikipedia.org/wiki/Hexagonal_chess#/media/File:Gl...

- n-square Chebyshev distance forms concentric squares around your starting point

- n-square Manhattan Distance forms diamonds (meaning up/down/left/right = 1 space away but all diagonals are 2 spaces away)

We could also say the Knight can go everywhere a queen can't in the 3-square Manhattan distance and this might be more useful since it is all points along that boundary except the corners! (We got an in the wild "2 problems in computer science" with an "off by 1" error :)

[0] https://chris3606.github.io/GoRogue/articles/grid_components...

I think this is something math education can improve on since we are highly visual creatures. But it is always a tough balance since that same tool to help learning can decrease generalization if internalized improperly. But that can also be said about anything and is why I dislike the common test focused paradigm of education. As I think we've been doing it long enough that students have found studying for the test -- as opposed to study for learning -- is optimal. Goodhart always wins lol

A simple matrix multiplication only performs a linear transformation. To get a nonlinear affine transformation you need to augment the matrix and vector with extra dimensions containing carefully selected extra ones and zeros in addition to the translation. The end result is still a linear transformation of the supplied vector, but looks like an affine transformation if you ignore the final dimension.

But yes, I did not pick that up in linear algebra. It wasn't even mentioned there. All the fun stuff was taught in computer graphics.

https://math.mit.edu/~gs/linearalgebra/ila5/linearalgebra5_1...

For more on the underlying geometry, see, e.g.,

https://archive.org/details/elementarymathem0000klei/page/70...

or, for a more modern, abstract formulation,

https://archive.org/details/geometry0001berg

(And apparently it would be a more _interesting_ game without castling. At least according to the game that the AIs at Deep Mind played when they trained them on this variant on a whim. Castling was supposed to speed up development of chess, but it favours the defense a lot.

So what the game's appeal wins from castling in cutting out some busy work moves, it loses in attacking spirit.)

The non-castling variant was invented by Vladimir Kramnik[2] explored by Deep Mind not on a whim but specifically as part of Vlad's exploration of whether this chess variant would help to revitalise the game given how computer evaluation has affected theory.[3] There were also a couple of no-castling tournaments played, but like chess960[4], opinions were very much divided about whether or not it was actually any kind of improvement.

[1] Even though I pretty much always fall into stalemate traps in blitz.

[2] Former world champion and lately old guy shouting at clouds about cheating

[3] https://www.chess.com/article/view/no-castling-chess-kramnik...

[4] https://lichess.org/variant/chess960

That's what I was asking - do they get to "pass" and the other side gets to move? This is how it works in the game of go for instance. In chess that would be more or less equivalent to the non-stalemated player winning, because in many stalemate positions if you had an extra move you could checkmate.

The stalemate rule adds something that the attacking player has to keep in mind and gives the defending player something to shoot for - lots of creative and tricky play arises from this, with IM Eric Rosen being the most famous exponent[1] so much so that he now has a particular type of stalemate trap named after him.[2]

I'm not seriously entertaining your Fortnite rule. That is such a radical departure from the game of chess as not to be the same at all, so you could have that as a chess variant or whatever but it's fundamentally a different game.

[1] https://youtu.be/YB_LLivPlY8?si=dWl2bEAEeRmzhBiC

[2] Defending king in the corner with the opposing queen a knight's move away and no other legal moves for the defender. https://www.chess.com/forum/view/game-analysis/the-rosen-tra...

If the only two pieces left are kings, that is a stalemate. It is not even a legal move for two kings to come within one square of each other.

[1] https://chess.stackexchange.com/questions/27815/why-does-a-k...

After one move, it can go to f4 where it can add on as a second attacker to the queen on 4 squares. After another move it can go to d3, where it can again cover squares the queen cant (e2,e5).

So I guess its both because it has a lot of alignment in doubling as an attack, and covering nearby squares the queen cannot.

This also leads to situations where two knights can be positioned amongst other pieces such that one knight is able to capture the other but not vice versa.

However in western chess, it doesn't matter what pieces are in the other 4 locations of the 3x2 rectangle.

In Chinese chess, you can only move from A to B if X is unoccupied. The locations marked "-" don't matter if they are occupied or not.

    A X -
    - - B

    A -
    X -
    - B

    - - B
    A X -

    - A
    - X
    B -

Of course, all the other pieces have their own rules as well, so it's a significantly different game. There is no queen, the elephant is sort of like a bishop but must move 2 squares at a time, the cannon moves horizontally and vertically but cannot kill without having exactly one (not zero) piece in-between, the "guards" and king all cannot leave the king's palace which is a 3x3 box, the pawns can move sideways after they cross the river in the middle of the board, etc. Come to think of it the only piece that has the exact same rules are the 2 "chariots" which are positioned in the same place as western rooks and function exactly like western rooks.

I don't know people that think or thought that horses move "one straight, one diagonal".

"Move one straight and then move one diagonal into a 135° turned direction."

"The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal."

[1] https://www.fide.com/FIDE/handbook/LawsOfChess.pdf

"the knight may move to any nearest cell not on an orthogonal or diagonal line on which it stands"

Another is that a queen, like a rook, can reach any unblocked square in at most two moves. A Knight can require up to six moves!

Add to this the ability to move and attack diagonally like a bishop, but without the restriction of staying on the same colour of squares...

The queen is immensely powerful.

Even grandmasters fall for knight forks in blitz games quite often.

(a) knights' threats are disconnected and this "flower" approach while good is maybe not ideal. You might as well use a hollow circle at that point.

(b) when we say "chess pieces can be redesigned to be..." then I think about actual physical pieces, it would not do to make these as actual physical pieces because an accidental misplacement turns a rook into a bishop or vice versa. Gotta make the bishop look like it is "sniping" along the diagonals while the rook looks more "sweeping" maybe?

(c) don't make the king a little-queen. Make the king a little square to emphasize "it can only threaten the neighboring square," then it looks more visually distinctive.

The pawns are fun though.

This was my first thought too. If the "feet" of all of the pieces were "flat", or parallel to the rows of the board, you could more easily tell their proper orientation.

I guess there is still a cultural aversion to its use, however.

...anyway so people can see it better, that actual character is a pretty close representation of the knight's movement, it's just a little hard to tell the 2-then-1 distances: https://en.wiktionary.org/wiki/%EA%96%85

This design doesn't account for many special qualities and behaviors pieces exhibit. It doesn't indicate that

* while pawns do capture diagonally (forward), they are pushed forward in straight line

* they can capture en passant

* they can move by 2 squares from their initial file, and only from the initial file

* they can be promoted to another piece

* Knight moves are not inhibited by the presence of other pieces (unlike any other piece, a Knight can "jump over" pieces)

* castling

* special status of the King (unless it's conveyed by that circle in the middle, but it's not nearly as readable a symbol as a crown)

So this design kind of works if you already have complete information from elsewhere, but isn't that great if it were your first source of info.

It also loses the poetic aesthetics of the traditional pieces, with queens and kings and bishops etc.

But I hate the way the pawns face. Makes sense! But it still reads, to me, like one of those "color, but the text is in a different color" things. Feels like the pawns should be facing the opposite direction. =/

So pawns would be

    /|\  /|\


    \|/  \|/

    ■ ■
     P

     ■ ■
    ■   ■
      N  
    ■   ■
     ■ ■
       

Edit: Though good point to the parallel commenters, the knight shape is harder to differentiate and kind of throws me off. But maybe tweaks there.

If you ask an experienced player to use a weird piece set, you will only be introducing error and cognitive overhead. If you ask someone naive to the game to use the piece set, do they internalize how the pieces move more quickly and get over the impedance when they start to use a normal set?

Going at a tangent to your idea, maybe it is possible to construct a set that aids the performance of a naive player, but which degrades the performance of a more experienced opponent. Could that handicap be as great as a club player offering pawn odds against a naive opponent?

"Tournament chessboards" are my favourites, obviously.

Magnus Carlson, considered one of - if not the - best chess players of all time has a famous video of him playing three chess matches simultaneously, blindfolded, and winning all three.

Once you get to a certain point not only the movements but also entire gameplay strategies become internalized.

That said, I'd use a square for the rooks so they don't get confused with the bishops as they get moved and maybe an L shape for the knights. It would definitely make it easy for beginners to learn how each piece moves.

Which is more or less the easiest part of the game to learn, and one which pretty much anybody will have down after one or maybe two games.

It's a clever little idea to share on Twitter but in practice I think it would make the board slower to read for advanced players, because so many pieces look similar.

Recognizing the pieces is the easiest part of chess. And distinct symbolic forms are actually easier than representational forms like these. Similarly, iconic phonetic notation not a good replacement for the Latin alphabet

https://www.omniglot.com/writing/visiblespeech.htm

https://en.wikipedia.org/wiki/Josef_Hartwig#Chess_sets

https://de.wikipedia.org/wiki/Bauhaus-Schachspiel

https://www.lijf.org/chess/DSCF1392.jpeg> https://www.lijf.org/chess/DSCF2887.jpeg>

Always loved how the shape and size of the pieces indicate their moves while still being simple and recognisable.

https://www.haiku-os.org/development/icon-guidelines/

This is why rooks are worth 5 and bishops are worth 3, despite both having apparently equal freedom of movement (just rotated 45 degrees). The bishop will be able to access strictly fewer squares than the rook even in the best case, and usually much fewer. And the bishop is stuck on one color.

Such evaluations are only a rule of thumb intended for beginners.

It's all context dependent. There are positions where a Bishop is more powerful than a Rook. Other things being equal, Bishops tend to be preferred over Knights in serious play (especially when you've got a Bishop pair, which is synergically more powerful than one Bishop times two), even though both are theoretically "worth" 3 pawns. Two minor pieces are usually worth more than a Rook and a pawn, and more often than not it isn't a good idea to exchange the former for the latter, even though the total value appears the same (3+3 = 5+1). And so on.

It brings to mind the idea that everything is ultimately a representation, even the things designed to be as straightforward as possible.

Unfortunately, I never got around to writing a good AI so you could play against the computer. At some point, I'd like to get back to that project.

I'd probably go with circle for the king, and maybe an L or a sideways H for the knight, even though they break the original design rule. Otherwise K/Q/N just look too similar.

https://twitter.com/graycrawford/status/1750248031784763639

Not that that's an exclusive list either,

    tbody tr.athing:has(.title .titleline a[href*="twitter.com"]),
    tbody tr.athing:has(.title .titleline a[href*="twitter.com"]) + tr,
    tbody tr.athing:has(.title .titleline a[href\*="twitter.com"]) + tr + tr
    {
        display: none;
    }

This will leave "holes" in the numbering of the list of items as the numbers are not calculated based on the structure of the document but are rather hardcoded. You could definitely fix this with some more funky css rules if needed.

https://i.pinimg.com/originals/79/75/8a/79758a3355c2bed372aa...

Yes, queen already had 8 point hat wide because whole board, king eight point cross, small for one step.

Bishop has a diagonal cut in its cap.

Knight as a horse, the long nose and ears are the knight move.

Castle with a plus cut in the ramparts.

Pawn is a dot for its usual move, with the ring collar for the optional second step.

I've thought about having the squares show light shades of primary colors so you could see which side is attacking a square, and the composite colors would highlight contested ones, darker shades would mean more attackers. Like red/blue/purple or yellow/red/orange.

https://i.imgur.com/mXd0L3P.png (also blue-vs-red, to give it a bit of color)

Non-colored version: https://i.imgur.com/A1Vofpz.png

Wish we had a league without castling for that sole purpose.

The pieces resemble the movements in most cases, but also pack together into a rectangle.

I don't see it. Do they really?

Lovely communicative design

The lines don't need to be so thick I think, which would allow little arrow heads to make it even more obvious. And while we're at it, they don't even need to look like actual physical pieces, so the knight could be designed to show how it hops over squares by having blank spots in its icon.