Thank you for your interest in this fairy piece ✌️
What I think is why this piece does not have that much of a synergy bonus is that it's two short ranged pieces that are joined together. A non-royal king and a knight are estimated to be roughly the same value. When these are merged, there is no particular bonus since they move relatively slowly. There is possibly some bonus but nothing major. 6 plus a smidgen.
Thank you for your interest in this fairy piece ✌️
What I think is why this piece does not have that much of a synergy bonus is that it's two short ranged pieces that are joined together. A non-royal king and a knight are estimated to be roughly the same value. When these are merged, there is no particular bonus since they move relatively slowly. There is possibly some bonus but nothing major. 6 plus a smidgen.
Okay, I made a experiment: 16 Rooks vs 16 Crowned Knights on a 8x8 board: Results:
10 Matches:
2 Wins for the Rooks
3 Draws
5 Wins for the Crowned Knights
Now I am slowly thinking how the Crowned Knights is better than the Rook, but why some people say the Crowned Knight is worth 6.75? there’s absolutely no way the Non-Royal King is worth 3.75, the non-royal king is too much of a defensive piece and its only a good offensive piece during endgame, i think the values of the non-royal king on a 8x8 are:
opening: 2.25
middle game: 2.5
ending game: 2.75
everyone forgets how slow the non-royal king is
Yes, it is certainly very slow. But scary at close range. It can also deliver checkmate with help from the real king, assuming K & Commoner versus K. It is quite adjacent to a knight in face value, yet maybe not early in the game.
Notable references:
https://en.wikipedia.org/wiki/Mann_(chess)#Value
https://www.chessvariants.com/d.betza/chessvar/pieces/wf.html
Yes, it is certainly very slow. But scary at close range. It can also deliver checkmate with help from the real king, assuming K & Commoner versus K. It is quite adjacent to a knight in face value, yet maybe not early in the game.
Notable references:
https://en.wikipedia.org/wiki/Mann_(chess)#Value
https://www.chessvariants.com/d.betza/chessvar/pieces/wf.html
Okay, I will do some experiments later with the non-royal king later
Counting the average number of moves is not a consistent method for guestimating piece values, because it does not take into account that players tend to place their pieces on good squares, rather than bad ones. That the Centaur is weak in the corners is of no import, because no one in his right mind would move it there, and the opponent cannot force you to go there. (This is a bit different for exceptionally good squares, such as the center for a Bishop, where the opponent often can force you to stay away from there.)
Another important factor is that during most of the game the board is far from empty. For a board that is populated for 50% with pieces of each color, a Centaur that stays in the central 4x4 area still has 12 moves on average; a Rook would have only 6, as it would almost never see a long free path. Unblockable leaper moves are worth a lot more than distant slider moves, which can be blocked in many places. A 'Modern Elephant', which can step one or jump two squares diagonally is worth nearly as much as a Bishop, in the start position.
As a rule of thumb on 8x8 boards leapers with 12 unblockable moves are worth about as much as a Rook (5), and with 16 moves they are worth around 7.
The Centaur is worth well over 7; like with all piece values it depends on what scale you use (Q=9 or Q=9.75). A non-royal King is quite strong because of the 'concentration' of its attacks; this allows it to attack an area from which an isolated Pawn cannot escape, or deliver checkmate. This is mostly spoiled by the fact that it is so slow, and cannot catch up with passers. In combination with longer leaps (or slides) the latter is no longer important, though. So the Centaur has the best of both worlds: it has the speed of the Knight, as well as the concentrated attack power of the King. The N and K moves are furthermore orthogonally adjacent, which is also good. That means there is actually a lot of synergy between the K and N moves.
Counting the average number of moves is not a consistent method for guestimating piece values, because it does not take into account that players tend to place their pieces on good squares, rather than bad ones. That the Centaur is weak in the corners is of no import, because no one in his right mind would move it there, and the opponent cannot force you to go there. (This is a bit different for exceptionally good squares, such as the center for a Bishop, where the opponent often can force you to stay away from there.)
Another important factor is that during most of the game the board is far from empty. For a board that is populated for 50% with pieces of each color, a Centaur that stays in the central 4x4 area still has 12 moves on average; a Rook would have only 6, as it would almost never see a long free path. Unblockable leaper moves are worth a lot more than distant slider moves, which can be blocked in many places. A 'Modern Elephant', which can step one or jump two squares diagonally is worth nearly as much as a Bishop, in the start position.
As a rule of thumb on 8x8 boards leapers with 12 unblockable moves are worth about as much as a Rook (5), and with 16 moves they are worth around 7.
The Centaur is worth well over 7; like with all piece values it depends on what scale you use (Q=9 or Q=9.75). A non-royal King is quite strong because of the 'concentration' of its attacks; this allows it to attack an area from which an isolated Pawn cannot escape, or deliver checkmate. This is mostly spoiled by the fact that it is so slow, and cannot catch up with passers. In combination with longer leaps (or slides) the latter is no longer important, though. So the Centaur has the best of both worlds: it has the speed of the Knight, as well as the concentrated attack power of the King. The N and K moves are furthermore orthogonally adjacent, which is also good. That means there is actually a lot of synergy between the K and N moves.
Okay but the Centaur stills better than the rook on a 14x14 board?
Hard to say. The Interactive Diagram has a heuristic for guestimating piece values, based on the number of moves pieces have on a 25% filled board (the average plus one standard deviation). In GigaChess II it thinks the Centaur is worth 709 and the Rook 584 centi-Pawn.
I have never measured this in games on 14x14, though; I don't have an engine that can play realistic games on such a large board. It appears to be very important to keep your pieces protected at all times on such a board as long as the opponent has a Queen; an engine that doesn't do that will find the Queen has near-infinite value, as it will keep gobbling up unprotected pieces in the late middle-game/early end-game.
Of course a more sophisticated way to value material makes a distinction between opening and end-game values; sliders like the Rook would definitely gain in value when the board empties.
Hard to say. The Interactive Diagram has a heuristic for guestimating piece values, based on the number of moves pieces have on a 25% filled board (the average plus one standard deviation). In GigaChess II it thinks the Centaur is worth 709 and the Rook 584 centi-Pawn.
I have never measured this in games on 14x14, though; I don't have an engine that can play realistic games on such a large board. It appears to be very important to keep your pieces protected at all times on such a board as long as the opponent has a Queen; an engine that doesn't do that will find the Queen has near-infinite value, as it will keep gobbling up unprotected pieces in the late middle-game/early end-game.
Of course a more sophisticated way to value material makes a distinction between opening and end-game values; sliders like the Rook would definitely gain in value when the board empties.
I used the Play-Test applet of chessvariants.com, I made a diagram with a 14x14 board and it gave a value of 577 centipawns to the rook and 683 centipawns to the centaur, btw can you help me to make a Xiangqi Cannon with Rifle capture (capturing without moving)?
HGM with all due respect. How can Centaur be above 7, which means there will be good synergy with two short range pieces combined.
Why pieces that combines one piece with more pieces always have some kind of “synergy bonus”?
HGM with all due respect. How can Centaur be above 7, which means there will be good synergy with two short range pieces combined.
Synergy an have many sources. One factor that seems to contribute to piece value seems to be the ability to attack orthogonally adjacent squares. I have never taken the effort to investigate this quantitatively in a systematic way, but it explains a number of observations:
* A Rook is significantly stronger than a Bishop even on a cylinder board, where they would have equal mobility.
* The BN compound (Archbishop), which has 16 orthogonal contacts between the B and N moves is nearly equal in value to the RN compound (Chancellor), which has only 8 such contacts. Despite the obviously higher value of the components of the latter.
The Centaur has 8 orthogonal contacts between the N and K moves.
In general there is always some synergy between moves because of 'future mobility', i.e. how many squares you could reach in 2, 3, ... moves. Because you have mixed sequences. E.g. two Centaur moves can reach all squares a Knight can reach in two moves, and those a King can reach in two moves. But also those that can be reached through one Knight and one King move, such as the (2,3) and (0,3) destinations, which neaither the King nor the Knight could. The moves of one component help you to make better use of the moves of the other.
Another example of synergy is lifting of area binding. (Pieces that do that are rerferred to as Amphibians.) Both the Alfil ((2,2) leaper) and the Threeleaper ((3,0) leaper) are severly area bound, able to reach only 8 and 9 squares of an 8x8 board, respectively. Which makes them almost worthless. But their compound can reach every square. (You can make a (1,0) step by two Alfil and one Threeleaper move, e.g. e1 - g3 - e5 -e2.) It is a healthy 8-target leaper, similar in value to the Knight.
I used the Play-Test applet of chessvariants.com, I made a diagram with a 14x14 board and it gave a value of 577 centipawns to the rook and 683 centipawns to the centaur, btw can you help me to make a Xiangqi Cannon with Rifle capture (capturing without moving)?
There is some randomness involved in the piece-value heuristic of the Play-Test Applet: it measures the average number of moves in some 100 randomly generated positions with 25% population, which would be different each time you reload the applet. But beware that these are still only educated guesses, even though the way it makes them is quite advanced. (It accounts for the general synergy as a non-linear term in the average number of moves, and for that the piece would typically be placed in an above-average good location.) But the value for the Archbishop (BN) it gets is still lower than what you get from games.
I am afraid a rifle-capturing Cannon is not yet possible with the Play-Test Applet. It would require a special interpretation of multiple 'iso' modifiers in multi-leg moves, where these would not refer to the length of the previous slider leg, but increasingly further back along the path. (Because to get back to the square of origin you need to revert two slider legs.) But this was not the original definition on XBetza notation, and thus was not implemented this way. Perhaps I will change this one of these days.
I used the Play-Test applet of chessvariants.com, I made a diagram with a 14x14 board and it gave a value of 577 centipawns to the rook and 683 centipawns to the centaur, btw can you help me to make a Xiangqi Cannon with Rifle capture (capturing without moving)?
There is some randomness involved in the piece-value heuristic of the Play-Test Applet: it measures the average number of moves in some 100 randomly generated positions with 25% population, which would be different each time you reload the applet. But beware that these are still only educated guesses, even though the way it makes them is quite advanced. (It accounts for the general synergy as a non-linear term in the average number of moves, and for that the piece would typically be placed in an above-average good location.) But the value for the Archbishop (BN) it gets is still lower than what you get from games.
I am afraid a rifle-capturing Cannon is not yet possible with the Play-Test Applet. It would require a special interpretation of multiple 'iso' modifiers in multi-leg moves, where these would not refer to the length of the previous slider leg, but increasingly further back along the path. (Because to get back to the square of origin you need to revert two slider legs.) But this was not the original definition on XBetza notation, and thus was not implemented this way. Perhaps I will change this one of these days.
okay, I will make more test with the crowned knight, but there’s things a rook can do that the crowned rook can’t do and there’s also things the crowned knight can do that the rook cant.
about the rifle Xiangqi Cannon:
I have some ideas for the Xbetza extension:
ii (initial iso) in continuation leg: slider leg has as many steps as a the FIRST slider leg. (I believe that mRpafcaiibpR or something similar would be a Rifle Xiangqi Cannon)
kd: capture friendly pieces but not the king/royal pieces
+ could be used to describe kamikaze capture: Q+ would be a Queen that captures itself after capturing a piece, R+B would be a Queen that captures without capturing itself after capturing diagonally like a bishop but it captures itself after capturing like a rook
$ (‘enemy excite’): it works the same way as the x (‘excite’) but it works with opponent pieces: $K would be a piece that moves by borrowing the moves of every adjacent opponent piece, $adQ would be a piece that can force a piece of your opponent to capture a piece of your opponent
Ö could be a atom that is a shortcut to mopabK, basically meaning a turn skip
w (‘freeze’): stops enemy pieces from moving or capturing (mQwK would be a ultima chess Immobilizer) the w modifier could also have variants:
ww: stops ANY piece from moving or capturing:
wc ('charm'): stops enemy pieces from capturing but not from moving without capturing
wm: stops enemy pieces from moving without capturing
wd: stops friendly pieces from moving or capturing
wdm: stops friendly pieces from moving without capturing
wdc: stops friendly pieces from capturing but not from moving without capturing
i also have a idea for bracket notation:
burning:
[Q:K] would be a Queen that captures all opponent pieces adjacent to it after moving or capturing like a queen
[W:F][F:W] would be a piece that moves like a king but after moving or capturing like a Wazir then it captures all opponent pieces diagonally adjacent to it, and after moving or capturing like a Ferz
the d modifier could also be used here to describe pieces that burn friendly pieces:
[Q: dK] would be a Queen that captures all adjacent friendly pieces after moving or capturing, we could also combine this with + to describe pieces from atomic chess:
[B+: dK][B+:K] would be a bishop from atomic chess
Some of these ideas are good (and sometimes already under consideration), for others there already exist alternatives.
Indicating 'burning' in the bracket notation is on the to-do list, but basically the whole bracket notation is still on the to-do list. Using a colon would interfere with the syntax of the Interactive Diagram, though. So we decided to use semicolon instead.
Move borrowing is already supported by using x in the final leg. It is true that there is no modifier for inducing moves in, or borrowing moves from enemy pieces. But there are other modifiers that suffer from lack of color specifity too (such as p). I hope to generally solve that by allowing single or double quote suffixes on modifiers for indicating friend-only or enemy-only. Specific problem for enemy induction is that in every position you would have to generate moves for the side that is not on move as well, to see if they induce something. This would slow down the AI by a factor two. So it is costly to implement, and I did not even know any variants that would need it. And even if there were: there will always be variants that are too complex to handle.
Forcing moves would be a new concept, which transcends move induction. In principle there could be many priority classes of moves, and the priorities could either apply just between the moves of one piece or globally to all pieces in the position. I think it would be too complex to cover all that in the move notation.
Spells like 'freeze' and 'charm' are not moves. Their zone of influence and selectivity could of course be defined through Betza notation, but it seems better to do that separately from the moe of a piece. Then you would not need any new notation. This is different for burning, which is a consequence of the move, and potentially could be different for different moves of the same piece.
Kamikaze moves can already be specified in the Interactive Diagram through the 'capture matrix'. There they can even be specified in a type-selective way, which would not be possible in the move notation. If only a subset of the moves should do it, the other moves can be suffixed with an apostrophe, as a general mechanism to exempt moves from whatever action the capture matrix specifies.
As to the ii: I think it would be more versatile to just look backwards through the path. So not just remember the length of the latest slider leg, but stack these lengths for any (non-i) slider leg, and then pop a length from that stack for every i leg that is encountered to know how long it should be.
In Khan's Chess there is a piece that moves like a knight but captures as a king. How would you estimate the value of such a piece HGM. Also, what about a piece that moves like a king but hits captures as a knight.
Some of these ideas are good (and sometimes already under consideration), for others there already exist alternatives.
Indicating 'burning' in the bracket notation is on the to-do list, but basically the whole bracket notation is still on the to-do list. Using a colon would interfere with the syntax of the Interactive Diagram, though. So we decided to use semicolon instead.
Move borrowing is already supported by using x in the final leg. It is true that there is no modifier for inducing moves in, or borrowing moves from enemy pieces. But there are other modifiers that suffer from lack of color specifity too (such as p). I hope to generally solve that by allowing single or double quote suffixes on modifiers for indicating friend-only or enemy-only. Specific problem for enemy induction is that in every position you would have to generate moves for the side that is not on move as well, to see if they induce something. This would slow down the AI by a factor two. So it is costly to implement, and I did not even know any variants that would need it. And even if there were: there will always be variants that are too complex to handle.
Forcing moves would be a new concept, which transcends move induction. In principle there could be many priority classes of moves, and the priorities could either apply just between the moves of one piece or globally to all pieces in the position. I think it would be too complex to cover all that in the move notation.
Spells like 'freeze' and 'charm' are not moves. Their zone of influence and selectivity could of course be defined through Betza notation, but it seems better to do that separately from the moe of a piece. Then you would not need any new notation. This is different for burning, which is a consequence of the move, and potentially could be different for different moves of the same piece.
Kamikaze moves can already be specified in the Interactive Diagram through the 'capture matrix'. There they can even be specified in a type-selective way, which would not be possible in the move notation. If only a subset of the moves should do it, the other moves can be suffixed with an apostrophe, as a general mechanism to exempt moves from whatever action the capture matrix specifies.
As to the ii: I think it would be more versatile to just look backwards through the path. So not just remember the length of the latest slider leg, but stack these lengths for any (non-i) slider leg, and then pop a length from that stack for every i leg that is encountered to know how long it should be.
Okay, but why spells don’t work on the play-test applet? and I have some pieces ideas that work with my ideas for the Xbetza Extension, like the manipulator: moves like a Queen but can’t capture anything, but any adjacent enemy piece can’t move, and the manipulator can force any adjacent enemy piece to move (without capturing your own pieces) (and even make them capture other enemy pieces) the Betza notation would be mQ$amK$adKwK
Some of these ideas are good (and sometimes already under consideration), for others there already exist alternatives.
Indicating 'burning' in the bracket notation is on the to-do list, but basically the whole bracket notation is still on the to-do list. Using a colon would interfere with the syntax of the Interactive Diagram, though. So we decided to use semicolon instead.
Move borrowing is already supported by using x in the final leg. It is true that there is no modifier for inducing moves in, or borrowing moves from enemy pieces. But there are other modifiers that suffer from lack of color specifity too (such as p). I hope to generally solve that by allowing single or double quote suffixes on modifiers for indicating friend-only or enemy-only. Specific problem for enemy induction is that in every position you would have to generate moves for the side that is not on move as well, to see if they induce something. This would slow down the AI by a factor two. So it is costly to implement, and I did not even know any variants that would need it. And even if there were: there will always be variants that are too complex to handle.
Forcing moves would be a new concept, which transcends move induction. In principle there could be many priority classes of moves, and the priorities could either apply just between the moves of one piece or globally to all pieces in the position. I think it would be too complex to cover all that in the move notation.
Spells like 'freeze' and 'charm' are not moves. Their zone of influence and selectivity could of course be defined through Betza notation, but it seems better to do that separately from the moe of a piece. Then you would not need any new notation. This is different for burning, which is a consequence of the move, and potentially could be different for different moves of the same piece.
Kamikaze moves can already be specified in the Interactive Diagram through the 'capture matrix'. There they can even be specified in a type-selective way, which would not be possible in the move notation. If only a subset of the moves should do it, the other moves can be suffixed with an apostrophe, as a general mechanism to exempt moves from whatever action the capture matrix specifies.
As to the ii: I think it would be more versatile to just look backwards through the path. So not just remember the length of the latest slider leg, but stack these lengths for any (non-i) slider leg, and then pop a length from that stack for every i leg that is encountered to know how long it should be.
Well, I think I discovered a way of making a Xiangqi Cannon with Rifle Capture (kinda of):
gafcabgafW means a piece that captures like a orthogonal contra-grasshopper with rifle capture, I decided to keeping adding af to it and I got this:
mRgafcabgafWafgafcabgafafWafafgafcabgafafafW afafafgafcabgafafafafWafafafafgafcabgafafafafafW afafafafafgafcabgafafafafafafWafafafafafafgafcabgafafafafafafafW is a Xiangqi Cannon with Rifle capture that works perfectly in a 8x8 or smaller board and mRgafcabgafWafgafcabgafafWafafgafcabgafafafW afafafgafcabgafafafafWafafafafgafcabgafafafafafWafafafafafgafcabgafafafafafafWafafafafafafgafcabgafafafafafafafWafafafafafafafgafcabgafafafafafafafafWafafafafafafafafgafcabgafafafafafafafafafW is a Xiangqi Cannon with Rifle capture that works on a 10x10 or smaller board (also works on a Xiangqi board)
I also solved some other cases:
KaKafabsKazabzKaqabzKaafKaafsKasasKafasKafsasK means a piece that moves 1, 2 or 3 times like a Mann, but it doesn’t have any locaust capture or turn skip (KaKaaK also doesn’t have any locaust capture but it has turn skip)
ucaibQQ is a Queen that has Normal capture and Rifle capture
i also discovered that pieces with burning capture can be theoretically be described using complex lame leapers, locaust captures, and hopping over friendly pieces, for example afmoabKafcabKcafmoabKcafcabKcafdaubKafdaubKafafmoabWafafcabWafafdaubWafcafmoabWafcafcabWafcafdaubW is a piece that I made that moves like a mann and like a non-leaping dabbaba and every time it moves or captures something it also captures one enemy piece in that same direction
Counting the average number of moves is not a consistent method for guestimating piece values, because it does not take into account that players tend to place their pieces on good squares, rather than bad ones. That the Centaur is weak in the corners is of no import, because no one in his right mind would move it there, and the opponent cannot force you to go there. (This is a bit different for exceptionally good squares, such as the center for a Bishop, where the opponent often can force you to stay away from there.)
Another important factor is that during most of the game the board is far from empty. For a board that is populated for 50% with pieces of each color, a Centaur that stays in the central 4x4 area still has 12 moves on average; a Rook would have only 6, as it would almost never see a long free path. Unblockable leaper moves are worth a lot more than distant slider moves, which can be blocked in many places. A 'Modern Elephant', which can step one or jump two squares diagonally is worth nearly as much as a Bishop, in the start position.
As a rule of thumb on 8x8 boards leapers with 12 unblockable moves are worth about as much as a Rook (5), and with 16 moves they are worth around 7.
The Centaur is worth well over 7; like with all piece values it depends on what scale you use (Q=9 or Q=9.75). A non-royal King is quite strong because of the 'concentration' of its attacks; this allows it to attack an area from which an isolated Pawn cannot escape, or deliver checkmate. This is mostly spoiled by the fact that it is so slow, and cannot catch up with passers. In combination with longer leaps (or slides) the latter is no longer important, though. So the Centaur has the best of both worlds: it has the speed of the Knight, as well as the concentrated attack power of the King. The N and K moves are furthermore orthogonally adjacent, which is also good. That means there is actually a lot of synergy between the K and N moves.
The scale i use is Queen = 9 Points, so the Centaur is worth 6 or more than 6.5?
Definitely well over 6.5. The average value of a short-range leaper with N unblockable moves is 32*N + 0.7*N*N centi-Pawn on the Q=900 scale (on 8x8). For N=8 that gives 301, for N=16 it gives 691. So a synergy of 90 cP, caused by the non-linear 0.7*N*N term. The Centaur benefits from concentration of its moves , and a Knight is not yet so slow on 8x8 that its limited speed is a bad handicap. (Unlike the Man.) So it is one of the better 16-target leapers. I would think about 750 cP.
Note, however, that sum-of-piece-values as evaluation is in itself already an approximation. Strong pieces devaluate when pitted against less-valuable pieces, because they have to avoid 1-for-1 trading. So 3 Queens tend to lose from 7 Knights, despite the fact that the commonly accepted piece values for Q and N suggest that you are 2 Knights short of equality. Playing only Centaurs against only Rooks could suffer from the same effect, and not really tell you how strong these pieces are in the more varied FIDE mix. Replacing one side's Rooks by Centaurs in the FIDE setup should already be enough for an almost certain win; to equalize the chances a bit you could delete one of the minors of the player with the Centaurs.
the Crowned Knight (Also called Centaur and also Called General on chess.com variants) is a fairy chess piece that combines King and Knight, and it’s not royal so it can be captured and it can move to squares controlled by your opponent
but most people say it is worth 6 points and some people say it is worth 6.75 (only 2.25 less than a queen!)
but i really don’t understand why it is worth so much:
the rook on a empty 8x8 board always controls 14 squares, no matter where it is:
And if the king ever attacks the rook then it can just move away to a square on the file or rank while it still restricts the king
Most people argue that the Crowned Knight is the combination of the Knight (which is worth 3 points) and the Mann (a fairy chess piece that moves and captures like a king but it’s not royal) the value of the Mann is mostly accepted as 3 (but everyone forgets how slow the Mann is) so i don’t think it’s higher than 2.75
I seriously need answers