8 ms·
For me the most surprising observation from this thread is this tweet [1] showing that the knight's moves are exactly the squares that the queen can't get to wi
by infogulch 3y ago
For me the most surprising observation from this thread is this tweet [1] showing that the knight's moves are exactly the squares that the queen can't get to within a 2 square manhattan distance.
I.e. the knight is an anti-queen.
[1]: https://twitter.com/skidbladnirr_/status/1750285122769957129 https://twitter.com/skidbladnirr_/status/1750285122769957129
- fasteo 3y ago>>> I.e. the knight is an anti-queen. The complement-queen I would say
- sicariusnoctis 3y agoA very interesting property: Knights have odd-even parity, i.e., they attack only opposite colored squares. Pop quiz: How many knights can you place on a board so that they don't attack each other?
- bell-cot 3y agoWell, since a knight on a white square can only attack knights on black squares, and half of the 64 squares are white...
- aurelwu 3y agoSome non-orthodox chess variants have a piece which combines Queen+Knight: https://en.wikipedia.org/wiki/Amazon_(chess) https://en.wikipedia.org/wiki/Amazon_(chess) very old variants often had such compound pieces like for example: https://en.wikipedia.org/wiki/Grant_Acedrex https://en.wikipedia.org/wiki/Grant_Acedrex
- porphyra 3y agoThere's also the knook that combines the Knight and the Rook, which was hilariously invented as a meme on /r/anarchychess: https://anarchychess.fandom.com/wiki/Knook https://anarchychess.fandom.com/wiki/Knook
- goriv 3y ago[flagged]
- Izkata 3y agoHere's a whole page of chess variants, many of which include such invented pieces: https://en.wikipedia.org/wiki/List_of_chess_variants https://en.wikipedia.org/wiki/List_of_chess_variants
- klyrs 3y agoWherein the hex-knight is the anti-hex-queen. https://en.wikipedia.org/wiki/Hexagonal_chess#/media/File:Glinski_Chess_Knight.svg https://en.wikipedia.org/wiki/Hexagonal_chess#/media/File:Gl...
- lovecg 3y agoThis is why in some rare endgames you might want to promote to a knight instead of a queen to avoid a stalemate!
- MaxikCZ 3y agoI dont get it. Queen can do everything a knight can, and then some. How can electing a knight instead of queen can be of any usefulness? Or do you mean it avoids stalemate by making it harder for the elector to defend/attack, and loose? I dont see any advantage there, isnt stalemate always preffered to loosing?
- have_faith 3y agoA knight can attack squares the queen cannot. There are positions that promoting to a knight is checkmate, but a queen would lose.
- mtlmtlmtlmtl 3y agoSometimes it's tactically crucial that the promotion is a check, and in these cases you might need a knight. Making a knight to avoid stalemate is actually extremely rare, because very often a knight isn't enough to win. Making a rook is more common there, but even that's rare.
- PeterisP 3y agoPromotion generally happens when there are very few pieces on the board, and often the opponent's king is the only piece they can move, and it often is close to the promotion square since it was likely trying to block it. If the promoting piece can't check but immediately blocks the last movement squares for that king, as a queen may easily accidentally do, the player who has only the king gets a stalemate draw out of a technically lost position.
- eru 3y agoChess would be a more elegant game without the stalemate rule. (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.)
- dheera 3y agoIn Chinese chess, the horse behaves like the knight in western chess except that (a) it cannot jump over pieces, and (b) the definition of jumping over is that it first move horizontally/vertically 1 step and then diagonally 1 step. It cannot first move diagonally. 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.
- zelphirkalt 3y agoMost people think of the knight move as one straight and then one diagonal. However, this is still ambiguous. Imagine one up, then one down left for example, resulting in the square left to the original square. A better description is moving 2 squares straight, not diagonal, into one direction, then moving 1 square into a 90° turned direction.
- tmtvl 3y agoForward two steps and the knight falls off his horse.
- paulddraper 3y agoMost people think of the knight moving 2 and then 1.
- zelphirkalt 3y agoChess players do, yet experience of basically any non-player I have ever heard describing it as "one straight, one diagonal" tells me otherwise. Also "moving two and then one" is ambiguous and would allow moving 3 squares into the same direction.
- bmacho 3y agoThis probably _heavily_ depends on the country where you live. I don't know people that think or thought that horses move "one straight, one diagonal".
- blauditore 3y agoI thought that was the main deal about knights...
- andoando 3y agoTo add to that, this also makes a knight and queen a very strong attacking combo, because they can uniquely cover the most squares.
- V-2 3y agoIt also enables some powerful, well-known attacking patterns, like a smothered checkmate with Queen sacrifice (or Philidor's mate).
- tasuki 3y agoGiven... they stay... in the same... square?
- seanhunter 3y agoThere was a big discussion of this topic on chess stackexchange[1]. It used to be just universally believed to be true but some modern analysts challenge the idea. [1] https://chess.stackexchange.com/questions/27815/why-does-a-knight-combine-better-with-the-queen-than-a-bishop-does https://chess.stackexchange.com/questions/27815/why-does-a-k...
- andoando 3y agoIn the image above, imagine a knight on H3, which covers g1, g5. Neither a bishop, a pawn or rook can help that way. 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.
- ComplexSystems 3y agoYou mean a 2-square Chebyshev distance, I think (the Linf norm). A 2-square Manhattan distance (the L1 norm) wouldn't include any of the squares that a knight can get to.
- deleted 3y ago[deleted]
- godelski 3y agoFor those that want a visual description there's a blog I serendipitous recently ran into[0]. If you're too lazy to open: - 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/measuring-distance.html https://chris3606.github.io/GoRogue/articles/grid_components...
- mananaysiempre 3y agoThat's very much a picture that you learn on the usual mathematics route of learning about these things, yes. More generally, there's a fair amount to be said about how you can derive shapes of unit balls from distance functions and vice versa (in functional analysis in particular).
- godelski 3y agoI think, unfortunately, not many get visual descriptions when learning about these topics. To be fair, these visualizations can harm one's intuitions about how the metrics work in higher dimensions, so I can understand arguments against visualization. But in another example, I think even many people can come out of a Linear Algebra class and not understand that a matrix operating on a vector always performs an affine transformation on that vector (yes, I know we can abuse and get other forms but let's keep general due to context). 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
- zeteo 3y agoYup that's how they designed it in hexagonal chess: https://en.wikipedia.org/wiki/Hexagonal_chess#Rules https://en.wikipedia.org/wiki/Hexagonal_chess#Rules "the knight may move to any nearest cell not on an orthogonal or diagonal line on which it stands"
- JCharante 3y agoI have no source for this but that is the definition for a knight's valid moves, it goes where the queen cannot within that distance
- lgeorget 3y agoThe official definition, as per the FIDE laws of chess [1], article 3.6 is "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 https://www.fide.com/FIDE/handbook/LawsOfChess.pdf
- FartyMcFarter 3y agoThat's a horrendously hard to parse definition. Couldn't they say "3 squares away but not on the same rank/file/diagonal" or something a bit easier?
- lgeorget 3y ago"3 squares away" is not entirely obvious though. The definition as it stands is mathematically unambiguous. Obviously, it's not how you teach the rule to a beginner, but that's irrelevant.
- FartyMcFarter 3y agoIf "nearest" is unambiguous then "3 squares away" is also unambiguous. The nearest squares are 1 square away, the ones nearest to those are 2 squares away, etc.
- dudul 3y agoI'm not a master or anything, but I've always found it interesting that the queen is usually thought of as the most powerful piece while I think it's the knight. Yeah the queen can move everywhere, but she's "predictable". The way a knight moves makes it more difficult to defend against IMO.
- Agentlien 3y agoA huge difference is that a queen, like a rook, can attack a whole row and column, making it possible to box in an opponent's king. A knight has limited reach and can never attack a square the same colour as the one it is occupying. 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.
- filleduchaos 3y agoKnights are useful but are very much not as difficult to defend against as a queen.
- FartyMcFarter 3y agoKnights are objectively nowhere near as powerful as queens. However they're underrated in blitz chess, where their visually hard to see moves often catch people unaware. Even grandmasters fall for knight forks in blitz games quite often.
- sebzim4500 3y agoTry playing a game where your opponents knights are replaced with queens. I suspect you will change your mind very quickly.
- V-2 3y agoKnights tend to be overrated at lower levels of playing strength, where their irregular moving pattern is indeed challenging for the players, and as a result, Knight moves often get overlooked. However, once a player becomes more proficient, not only the obvious superiority of the Queen, but even of the Bishop (other things being equal, Bishops are thought to be actually somewhat more valuable, especially as a pair) starts becoming apparent.