The Value of Chess Pieces 

The values are dynamic. In a closed position knights fare better than bishops and in open it's the other. Rooks are pretty useless in early and midgame but become extremely valuable in endgame. Especially for the side winning.

Another method is "How Many is required to force Checkmate." . Three Knights, a Bishop and a Knight, Two Bishops, One Rook, and One Queen suffice.

The Knight gets extra value because it is harder to block in. A single bishop can't cover dark and light squares, a knight can.

I think perhaps the knight was so overvalued over the bishop because you should have halved the Bishop’s average influence value. You averaged its squares influenced value over what it could influence on the light squares, but technically it has 0 influence on the dark squares (and the dark square bishop has 0 influence on the light squares). Had you halved the bishops average, it would have been comparable to the knight, though both would have been undervalued.

That was an interesting analysis. Prior to neural networks, tables would provide values for each piece depending on where it was on the board, thus a white pawn on the 7th rank is worth a lot more than on it starting 2nd rank, and a knight on the rim is dim etc. Furthermore these values would be adjusted for the end-game. Ultimately, assigning static values to pieces is not going to work well in practice.

Knight vs bishop: the Knight's influence can never be blocked, it always influences that number of squares. The Bishop's influence (like Rook and Queen) stops at the next piece.

The pawn's influence should be adjusted to account for the fact that it is the only piece which cannot capture on 1 (and occasionally 2) of its influenced squares. This would explain why normalizing to the pawn's influence left the queen, rook, and knight undervalued compared to the standard model, as well as all four (non-pawn) pieces relative to alpha-zero. Basically, I believe that the 2.916 value is too high considering that the pawn's influence is not the measuring the same thing.

The knight has a super power. It can attack all other pieces on the board without being in danger from the piece it's attacking ─ which makes it the only piece that can attack the queen.

A good next step might be to compare the pieces occupancy rates on particular squares during / after common openings instead of treating all squares as having an equal chance. I also feel certain pieces lose their value in the late game especially the knights, they’re more useful for capturing rooks and queens early game. Definitely a very interesting topic!

Great job Animated Chemist! Very interesting on lots of levels and always great to see new analysis of the game!

Great video, but as a mathematician, I think the main challenge is define what you mean by "influence" and "value". As others have noted here, there are difficulties in comparing the influence of pawns versus knights versus bishops, rooks and queens. Pawns cannot take forwards, and cannot move diagonally with taking; knights can jump over pieces and fork, but bishops, rooks and queens can pin and skewer. In my view the material value of individual pieces and their positions is most critical in the endgame. In the middle game, coordination of pieces is also very important, whereas in the endgame, it is only the local coordination of pawns that is significant (doubled, isolated, protected, passed), so estimating material value here is crucial. The goal in the middle game is to develop a stronger attack than the opponent in order either to deliver checkmate during the middle game, or reach the endgame with a material advantage. Since engines rarely fall for checkmate in the middle game, they are estimating a combination of activity (attacking potential) and endgame material value.

The first bishop is worth more than the second.

The value of pawns is way more fluid than anything. You must check if the pawn is passed, if it is connected and protected, if it is on the 7th rank (only 1 square away from promotion) instead of say 3rd rank, if it is on the edge of the board and the opposing team has only the wrong bishop left, how solid is the base of the pawn island, etc etc. I think these considerations must skew a bit the value of the pawn and therefore the relative value of all other pieces

The reason why your bishop and knight values are so off, is because you're valuing influence on every square equal. In the centre of the board, the knight attacks 8 squares, and the bishop attacks 13. However, 4 of those squares the bishop attacks are on the edge/corner of the board. You could weight influence, giving greater weighting to squares controlled in the centre.

One thing I find interesting is comparing the value of pawns. Obviously the value is 1 by default, but by looking at the other values, we can see that influence values pawns more than standard because the other numbers are lower and vice versa for AlphaZero.

I think that really the only thing that needs to be added to the “classical” picture is that having the bishop pair is worth about 0.5-1 pawns. It explains why trading one bishop for a knight is bad (you lose the bishop pair), and why trading your second bishop for a second night is almost always dubious (you lose the ability to force a trade between your “twin-less” bishop and one of your opponent’s pair).

everything is slightly under which can be explained by the fact the pawn is off. it considers all pawn moves as equal but it usually doesnt have 3 moves since its rare for a pawn to have both captures and forward be available. a pawn wont always have a capture and can easily be blocked meaning it can even have 0 possible moves sometimes and the knight has special powers such as attacking a queen while not being attacked itselt and jumping over pieces which is not considered

Here is the intrinsic (note 1) piece value system I use and have taught: P = 3, N = 10, B = 10 or 11 (note 2), R = 15, Q = 29, K = 13. As you can see, if you exchange a N & B for 1 R and 1 P, you give up 21 to get 18. Not good! But if you get 1 R and 2 Ps (21), now we're talking! Also we can see that 2 R = 30, a bit better than 1 Q. Note 2: 2 Bs = 21. Which B is worth 11? The first one to leave the board. This may seem cumbersome, but with a bit of practice it's very easy. Primarily use this when making exchange decisions. Note 1: the actual value of any piece changes with its role or position. A white N placed on an out[post on e5 for example, is usually considered to be as strong as a R. The K is a fighting piece in the endgame so use it as such!

I would question the approach of only dividing the bishop's value by the total number of squares it can influence (32) rather than the total number of squares on the board (64), given that it is the only piece on the board that is limited to half of the squares (and given that this means that its value is -- I would argue -- more than halved by not acting as a pair).

I also believe that the number of pawns on the board, and their ability to move, devaluese the bishop when the pawns are on it's color. This also increases the value of the knight. Closed positions favor knights, open positions favor bishops.

Maybe split the evaluation into max mobility count and max attack count. E.g. the bishop can attack max 4 pieces, while the knight can attack max 8 pieces. This would bring them closer together. Also, the pawn is currently overvalued as it should be much worse when ignoring its promotion ability.

Many things not accounted for, like the value of a pawn changing into a queen, or how near it is to changing to a queen, or how a bischop en pawn can auto/mutual defend itself, these are also very valuable properties.

A few things: 1. The pawn's influence is extremely overestimated. When we say that a pawn can influence 3 squares, it cannot actually capture or move to all of them. Pieces that move and capture differently are difficult to analyze. 2. Leaping pieces are far less likely to be blocked than sliding ones. In reality, a rook on one side of the board on the middlegame has basically no chance to make those cross-board 7 square moves. This can be shown by the fact that a jumping rook is pretty much a fair alternative to the queen. 3. Movement direction and the ability to jump over pieces or defended squares have quite a bit of influence on value. One reason that a knight is more useful in the early game than a non-royal king is that a knight has 4 ways to make forward progress and two of them completely bypass a row of pieces. One reason a pawn is useful at all is that all of its moves point toward the enemy and the promotion squares. A pawn with no forward bias in its movement pattern would be absolute hot garbage. 4. Pieces are more likely to be on good squares than bad squares even after moving randomly. For example, if you jump a knight around the board at random, it's much more likely to end up in the middle of the board than in the corner, because there are many more squares that a knight can move from to reach the middle of the board than the corner, and this applies recursively too. Low mobility due to board edge effect is way less important than placing pieces on random squares suggests, as in reality everything but a rook is more likely to be in the center even if moved by a monkey, and human or engine play tends to compound this effect, not negate it, since random play assumes you're equally likely to open with Nf3 or Nh3, while grandmaster level classical and rapid games played Nf3 as their first move literally one thousand times more often than Nh3. Real humans do not like moving pieces to low mobility squares even when the option is available, and even a random move agent will avoid those squares most of the time because low mobility means for pieces that move symmetrically they are also difficult to get to. The "correct" average influence of a knight is much higher than 5.25. Likely over 6. With a random move agent you could argue that knights are more likely to end up sitting still and not moving on the rim than in the middle, but that's a rather moot point unless you actually plan on using a random move agent. 5. A piece that doesn't develop anywhere can't really do much other than sit there and defend. This is part of the reason why the Ferz (1,1 leaper) is stronger than the Wazir (1,0 leaper) despite being more influenced by the board edges and also colorbound. The reality is that if you have a Wazir, marching it to the middle of the board is almost never gonna be a good use of 5 moves in a row. But marching a Ferz to the middle of the board in 3 is a different story, and bringing out a knight attacks the middle immediately. Being able to quickly and efficiently bring a piece to attack or defend an important square is very much needed for attacking. It is one reason that the King does not feel stronger than the Knight in practice outside of the endgame even if you make it not royal. The king moves significantly slower. 6. Colorbound pieces usually suffer somewhat if there are some parities of them which aren't available. 7. Move synergies often have important effects on a piece's strength. A queen has a power that neither the rook nor the bishop has. That is, the ability to move like one and attack like the other. A king can reach a square a knight's hop away in 2 moves, while a Wazir takes 3, and a Ferz can't do so at all. Another advantage that the Knight has over the king is that it has substantially more synergistic movement than the king. That is, a king can attack 25 different squares including its initial square should a knight can attack 41 (of which 8 require it to remain in place, a knight cannot "triangulate," unlike a king). Meanwhile, a pawn can only attack 4 squares unless it captures, and 2 of them require it to stay in place. It cannot attack its own square either. This is significant because making a non-capturing move to threaten a square is probably the vast majority of moves made in chess, and even if they are not made, they force your opponent to consider them. The fact that a rook or queen can instantly decide to attack any square on the board in a sufficiently late endgame is quite valuable. And the fact that the queen can potentially fork or pin most of the combinations of squares on the board is hugely valuable as well.

I think the fact that the knights are unobstructed by your own pieces, or your opponents pieces, needs to be considered. The board is rarely fully clear. I would have liked to see this but considering the number of pieces you would typically see on the board and the influence of the pieces in those positions. I.e., knight is more powerful at the bigging of the game and less so at the end, assuming that the board is open.

I think its notable that the pawns value is a lot more than its sake covering, having the highly nonstandard ability of promotion

a knight can attack other pieces without supports (like you can chase the queen with a single knight while other pieces need at least one cover). It can also move better in close game.

Woah, the influence section gave me a huge realization: Knights are known as being the powerhouses in a closed position (a position with many pawns that aren’t able to move on the board. The knight cant be obstructed except by same color peices, so it can still make of it’s moves and captures. However the bishops lose their advantage worse than the knight. My hypothesis is that if you had an application running that calculates turn-by-turn influence of each peice, the knight’s avg influence would be higher for closed games, or games where you put it on a “good square.”

Only going off of legal moves on any given square is not the best way to evaluate piece value. You need more factors than that. For example, the number of squares until promotion is a significant factor in determining the value of a pawn. A couple of connected pawns on the 7th is usually more valuable than a rook.

There’s a fundamental flaw in your calculations: the pawns can’t go backwards once they’ve moved, but they can turn into different pieces, and a pieces value is also determined by its compatibility with other pieces.

I came across this issue when trying to create my own heuristic for a chess bot. We often hear that a rook is valued at pieces in a open board but what about a closed position? I tried providing two heuristics: A control "Frontier" that explores the squares it directly controls, and a hard value. The intuition is that the hard value is a long term evaluation of how desirable it is to preserve this piece and acts as a value "floor" when computing trades. This way, a trapped queen doesn't immediately get traded for a knight. Unsurprisingly enough, the rook had the largest hard value, reflecting the discrepancy between the early game and the late game.

I can sac a king *for a bishop! Yay!

The knight can ALWAYS reach EVERY square he can move to, but a bishop is almost always restricted by intervening pieces of either color.

Even if the true valuations are wrong due to a variety of factors, just the "influence" grid is interesting to see, and probably useful for all beginning chess players to try to maximize their coverage/utility of pieces.

I think the most crucial aspect in your underestimate of Knights (or overestimate of long range pieces) is the fact the long range pieces can be blocked in by enemy or even your own pieces. As a crude example, at the starting position, none of your long range pieces actually have any available moves, while Knights have two possible moves.

A couple rational steps to improve the influence rating could be to factor in how likely it is in a real game for a piece to be on that square and be able to move to the squares it can see with rational play. Another step could be to factor in how many moves it would take for a piece to get to each square on the chess board

In terms of power, the king has classically been determined as 2.5. Knights can access 64 squares. Bishops only 32.

You also forgot the fact that you can castle making 2 extra moves for the rook and king, and en passant.

I was always taught that the Knight was sligtly higher value then a Bishop (3.1 to 3) due to its superior attacking and area influencing potential. The Knight retains its threat on all squares it can reach irregardless of the pressense of pieces which would otherwise block every other piece type, while the bishop can only each reach half the board. I think you would find that statistically knights are moved more then Bishops are and are only the pieces most likely to put the king in Check.

I think considering the number of squares covered by two moves into would be fairer on the knight, it doesn’t reach the bishops level, but it does double its influence for most squares it can land on, whereas the bishop at most adds 3/4s of its own and lowest doesn’t add anything

All pieces except the pawn can attack on all counted squares; the pawn can either capture or occupy an empty space without fighting. It seems to me that the pawn was overrated based on the squares. But a pawn can become a piece, this is not taken into account at all, there is a slight underestimation here. The knight is also noticeably undervalued, since its moves, unlike all other pieces, cannot be blocked by enemy pieces. Your own or someone else's piece on the bishop diagonal blocks all the squares behind it. Same with other figures. This does not happen with a knight; blocking each of its cells only blocks that one.

counting a pawn positioned one step from promotion as the same influence as being one step away from starting position is wild.

I would argue that a piece only "influences" the squares it attacks, so for the pawn only the diagonals should be counted giving an average of 1.75

bishops are usually considered having more value than knights but a piece has a different value depending on the scenario of the game. At times, a knight pair can be stronger than a bishop pair but it is rare. Knights are not long range pieces,which is one of the reasons they get weaker in end games or open games. but some times a bishop can be stronger than a rook, depending on the game. I have been playing chess for a long time and I am pretty good at it so I sort of think about this practically.

To the table makes sense to add price of a move. How much one tempo worth.

Outstanding co ordination between maths and chess o should say...loved it❤❤❤❤

check mate is usually worked by surprise! In my opinion, the Knight has the great advantage of stealth, valued in the same way as the `assist` to a goal scorer. The value of a football `striker` is huge in comparison to a great winger of midfielder, BUT without that pass made to the striker, the striker would be pretty useless! This is why I personally value the knight highly because he can creep up all of a sudden from out of nowhere, to afford the glorious queen her checkmate move.

The main flaw with just looking at number of squares is that being unable to switch colour seriously hurts its point value. In an endgame you can just move every pawn and your king off of that colour. This obviously applies to the bishop, but this principle holds true for a lot of alternate and historical chess pieces too. An alternate version of the bishop that is just given the ability to step one to the left or right to switch colours goes up almost to the value of a rook (like 4.5 points or something). The "Camel" which is a variant on the knight that can jump 3-1 (instead of the Knight's 2-1 jumps) ends up stuck to one colour and therefore ends up with a value of around 2 instead of the value of 3 for the knight. The same way the queen is a hybrid bishop/knight, there are historical hybrid knight/rooks and bishop/rooks, and they actually end up with very similar piece values to each other because once again the bishop gets a lot stronger when it can switch colours--which knight movement allows. (These compound pieces are worth like 8 and 8.5 respectively). With just standard pieces, there is often a point bonus that is given for owning the bishop pair, because both bishops together can cover every square (the bonus is roughly half a pawn).

Here from agadmator 😊 nice video 😀😊 really nice calculations 🙂

And it was in this position, at 9:59 , that a shout out to the great Agadmator was made and there is nothing more to be done.

this is a very nice video, I enjoyed the video a lot!!

I like the general idea, but I feel there are a few flaws with the concept. First of all, I guess it's obvious that pieces can only influence all these squares if the board is empty. Which isn't the case. The fact that the knight can jump over pieces and therefore ALWAYS influences the numbers written on screen whereas a bishop's will nearly always be reduced is something that should be accounted for. Secondly, by only averaging over the squares the piece can land on, you are overvaluating certain pieces, i.e. the pawns and bishops. Overall, they can influence less squares, but since we are only averaging over the ones that they can access, this disadvantage is not taken into account. It seems a bit weird to use a system like that and then don't account for these things at all. Which gives the feeling that you searched for a way to get close enough to the standard values and then worked your way backwards from there. Because if you included the squares the pieces can not control, the bishop would already be weaker than the knight. And we haven't even taken into account that the knight can jump at this point. Which I feel already shows that the system isn't really telling you much about the pieces' values.

well one thing is that most pieces are blocked by other pieces. So the bishop can only hit the first piece in every direction, and it's rarely covering behind it, whereas the knight always covers all squares it can reach and is good at covering backwards. If you counter the max number of square a knight control it's 8, but for both a bishop and a rook it's 4 if you account for being stopped by other pieces of course that's not a good way to look at it either, just a way to point out that the board coverage without other pieces on board isn't always a good metric.

The main issue with this analysis is that it assumes the chess board is empty, negating the main advantage the knight has over all the other pieces. If we counted the average available squares in positions from real games, you'd get a much higher number for knights as, unlike bishops, rooks and queens, they don't get stuck between other pieces.

The value of pieces depend upon its position and forking ability of the Knight gives an upper hand to Bishop.

I have also believed that the opposing bishops of opposite colors are friends. They can never capture each other.

The influence of all pieces but the knight can't go through other pieces except via x-ray attacks and fossilizations. That's probably the biggest thing that this video didn't cover. because if you factor in that most of the pieces trajectories will be blocked in some way, the knight then regains its status as being very similar in value to the bishop

I like the Kaufman values (can be found on the Wikipedia page the video mentioned near the end

Your "averages" are calculated based on the total number of squares any piece *could* move to *IF* there are no obstacles (such as its allies in the way; enemies in the way; or tempo issues such as checks, pins, and opponent's attacks on higher-value pieces). But the true value of a piece is intrinsic to what can do in the current position, extending to its realistic potential. I would submit that the value of a piece is a very dynamic number. We've all seen games where a single pawn becomes more valuable than everything else on the board, simply because its next move results in checkmate, and the opponent cannot prevent it.

Idk if u r gonna update this video ever with the feedback. But the value of the queen is bigger because it can cause "draws" from losing positions via perpetual checks. And its the only piece that can do this by itself

If I am playing a Benoni type I am killing my bishops for their knights. Same with closed Dutch. Typically - I like more open games and with that I will throw my knights away to kill their bishops. One thing with your analysis. Take any board position on any move. Calculate the influence for that piece, on that move. Very early in the game, the pawns and knights have more spaces. Bishops, queens, and rooks are useless. So you can make an argument that early in a game - pawns are important at impeding influence of competing pieces. And since knights can jump, this helps their mobility. Meaning… The time of the game can have an influence on value. The type of game (open/closed) can create a skewed value for knights over bishops/rooks. So time of game is a big deal. An end game wide open- queens and rooks rule, with bishops the next important and knights the last.

Why knight’s ability to fork the king and the queen is overlooked? I mean , its the only piece that can fork the two most important piece on the board and eat up the most valuable piece (queen) without being in the danger of being captured. Sure , the bishop , the rook and the pawn can fork the king and the queen but they cant do it on their own. They need a supporting piece to do the royal fork. The knight OTOH dont need any piece. The royal fork by the knight is considered as game over for 99.9% of the players. Its also really really tough to understand what the knight’s intention are when he is on F5. A protected knight on F5 is definitely worth a queen as it has great chances to fork A, The Rook and the Queen B , The rook and the king C, The queen and the king D, The Queen and an unprotectable Bishop These forking adds lots of value to the knight.

nice material, thanks

The Anitmated Chessist.

Assuming that reach (or influence, as you call it) is a good measure for the value of a piece… the number of surviving pieces on the board limits reach.; Your own pieces even more so than opponent pieces, since you cannot take your own pieces. So if the pieces were randomly distributed (which they aren‘t), you‘d need to adjust each piece‘s value by how many white and black pieces are left at any given moment. The knights would be the least negatively affected by this analysis, which explains why a) your analysis undervalued them and b) why they are relatively more powerful on crowded boards (which correlates with closed positions). There are additional complexities stemming from the caveat that pieces indeed aren’t randomly distributed, particularly at the beginning of the game. However, the conclusion that the value of pieces changes over the course of a game as pieces get eliminated - even before considering their position on the board - will be familiar to every chess player.

the bishop and knight is same value because i think knight does some movement and attacks surprise locations and bishop can only move on one color

What if influence was calculated not by what they can move to, but on a given square, how many ways could a piece move to that square? What about captures? Considering that pawns can only capture in certain directions but they can move in a different directions, would it be better to evaluate the influence based off of their threat or defense to a square if they were in every board position? Idk.

I think the flaw in the Influence scores is that they do not take into account the fact that the knights can jump. At any one given moment your opponent can block the full range of moves open to any of your pieces. Not so the knight. So this adds to its value - though not sure how one could use maths to factor this in ...

Philidor's estimations are impressively accurate

Should also be noted that AlphaZero's point values for pieces are conditional on its strategy. The points are not applicable for any random player

This was an extremely interesting video! I'd like to echo what some other comments have said in that I believe the reason bishops and knights are rated as equal in the standard system is their value compared to each other is determined largely by the position as a whole. They're equal by standard, but the player elevates them or hinders them with their handling of the position. Did you put all your pawns on light squares? Well your dark squared bishop DEFINITELY is now worth more than your knight, but your light squared bishop may be worth less than one. Excellent video though, seeing piece value expressed as influence is something I need to consider more in my own games.

My understanding of Alpha Zero is it determines values off pieces, moves, and positions on the probability of winning.

Love the phrase upper lower middle value ELO player

Every endgame up to 7 pieces has been solved. The results of the endgame table bases confirms that in most endgames, the bishop outperforms the knight by far, especially when there are two of them. Two bishops can even outperform 3 knights. There’s an article that has all of the data called “Bishop vs Knight”. While the knight is very handy in the early game, I believe trading it for a bishop is typically a good idea.

I think the conditional moveset of the pawn and the jumping of the knight was overlooked in the final calculation

Is there a way to take those those tables and that influence value and create the Piece Value Tables the chess engines use to determine where pieces are best positioned?

You again forgot that pawns can promote at the end, allowing them to turn into any of the pieces

Knights have an ability to jump so it can't be restricted. Its influence always stays the same. If you put other pieces on the board, knight still can move the same however bishop movement can be restricted highly. So, your measurement has a big flaw.

Could the seconf spring have moore value then the first, wich pawn is worth the most? Is the white bishop moore worth then the black bishop etc!

It should be a weighted average; the influence of a piece in a position of the board should be weighted by the probability that it will be there in the first place - which naturally changes across time, and the probability that it's influence will be neutralized by surrounding pieces. This is a calculation only the sophisticated neural net of an AlphaZero is able to do.

I expected that stockfish evaluates a bishop distinctly above 3, but I was most surprised when the rook had a value above 5.6. Shows that endgame really is everything, huh.

You just don't put your knight on the edge of the board and rotate them wisely and it's around 3 and bishop is likely 3.3 or around that

How is there only such a small amount of people who had seen this amazing video

I would argue that a pawn’s value slightly increases the further it goes, and if it is paired with additional pawns.

The knight is the only piece that retains those numbers regardless of the position. So I'd give it a plus point for that

The most unintuitive thing to me as a chess player is that Stockfish values rook+pawn higher over a knight and bishop or two knights and approxilately as much as two bishops.

Two bishops should be considered as 7 points of material.

Great video!

I like the concept here, but in practice these values are way off. And that is because the board is not empty. With pieces in the way, a lot of those pieces will have far fewer squares they can really go to in practice than if the board were empty. It should also be considered that the total possible influence is not necessarily linear with respect to actual value. As in, sure a queen can move as much as a bishop plus a knight, but even the standard values for a queen give it more value than a bishop plus a knight. There's also another flaw in that pieces are not in all places on the board an equal amount of the time. As in, knights rarely end up in corners so that shouldn't really count against them. But queens can choose to stay near the center of the board and influence a ton of spaces. Anyway, I'd recommend doing an analysis of averaging the influence over like 1000 real game situations. And then also giving a score from those games based on who won and with which piece differences, or based on a comparison with stockfish evaluations to those positions or something.

I'm a little confuser. What is the point of the video? I came up with my own value system for the pieces, but everyone says it is wrong, and actually so do I? The reason the horse is more valuable is because it can hit every square, not just half of them like a bishop. It can also smother mate. It is the best piece for attacking a queen. It cannot be blocked. It can get in and out of high traffic areas by jumping over them, where rooks, bishops, and queens need higher clearance to pass through. If it is harder to anticipate, so many people get tricked by simple forks that they would easily see from another piece. It is also the only piece, othe than a pawn, that can start a game, giving it high stretegic importance. It is harder to master, but it can be extremely useful if honed carefully.

What's missing from your assessment method is the fact that the knight, as you said, moves uniquely, any piece it attacks cannot take it. For undefended pieces, the Queen can take any of them except for the knight, to give an example. Also a king can never capture a cheking knight, altough a king might be able to capture any other checking piece. This is one of the reasons your knight was ranked to low relatively to the gameplay and experience based assessment that's 'default' today.

Seems a convoluted way to calculate piece value. I figured it would be “maximum amount of squares a piece can attack while in the enemy camp divided by 2”

"Hello Everyone" Agadmator is that you?

just some further things to note that would improve your rating: - pawns moves are attacking *or* moving, whereas the other pieces can do either in those squares [meaning the pawn is overvalued] - knights moves can always happen, whereas sliders can be blocked from a piece in the way blocking it from going behind [meaning sliders are overvalued especially in closed positions] - pawns have value in promotion, although this is niche and only valued in the endgame and normally ignored unless you have a passer [meaning the pawn is a bit undervalued on average, but severely undervalued in the endgame] - doesn't include tactics, like the knight being able to fork in a lot of situations because the squares it goes to are valuable and generally leave it untouchable to the major pieces its attacking, or bishops being able to pin pieces on a diagonal [bishops knights and to an extent all pieces are undervalued] - pawns can naturally defend themselves, defensive wasn't taken into account [pawns and to an extent all pieces are undervalued] overall i think those are just a few things that would make it closer to the generally accepted rating. [when i say under and overvalued here I'm talking about before scaled to have pawns be 1]

Half the time one of the two bishops is a “bad bishop”. Knights are never trapped

Rook much less than Bishop + Knight...even Rook+Pawn for N+B is a bad idea, barely 2 pawns compensate

Counting the squares of pawns who can just move without taking OR just take the same way like the other pieces who can do both, must be incorrect.

My guy, the reason the knight's valuation comes out as lower is because this system doesn't consider that other pieces are usually locked in or prevented from actually having access to all of their squares they could theoretically reach because of the pieces on their respective side.

5:36 for the bishop’s value, I disagree, it should be 1/2 of 8.75 = 4,375. I think we should considerate the full 64 squares and say that he has a 0 influence value on half of them.

When i was scrolling i saw this video and i read the value of cheese pieces so i clicked on it wondering what the heck cheese pieces are until he said chess pieces in the video lol

You actually miscalculated the average for the bishop. You divided the sum of influences by 32 not 64. you are just ignoring that a bishop cannot change color at all