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Quantifying Piece Activity

@CreativeMadness said in #3:
I included the first position as I think it's an interesting example to consider. I get you feeling that White is more active and my intuition would be similar, but one also shouldn't neglect the fact that Black's rook and bishop are currently very active and that the White knight has no good forward moves. My score is certainly not perfect, but reaching the right balance is always difficult and I don't think it's completely unreasonable to say that black is more active in the first position.

Maybe using piece table that engine used for evaluating pieces activity would give a better extimation.
What piece tables do you mean? I only know the piece value tables of the engines and that just take the position of a piece into account, not the possible moves it has.

@CreativeMadness said in #3: I included the first position as I think it's an interesting example to consider. I get you feeling that White is more active and my intuition would be similar, but one also shouldn't neglect the fact that Black's rook and bishop are currently very active and that the White knight has no good forward moves. My score is certainly not perfect, but reaching the right balance is always difficult and I don't think it's completely unreasonable to say that black is more active in the first position. > Maybe using piece table that engine used for evaluating pieces activity would give a better extimation. What piece tables do you mean? I only know the piece value tables of the engines and that just take the position of a piece into account, not the possible moves it has.

@WillSandi said in #4:
Thanks for sharing your thoughts.
There are two main reasons I didn't use any engine evaluation. First of all, I want to use such scores on a lot of different games and if you look at thousands of games, analysing each position for even half a second takes hours or even days.

Secondly, I want these scores to be more stand alone. The piece activity won't capture tactics that happen after a piece moves, but in my view it isn't supposed to do that.
The engine evaluation is also very complicated and takes everything into account. The evaluation may be better if you move a knight to a passive square because it allows the queen more freedom. But this doesn't mean that the activity of the knight was improved by this move.

Your point about controlling squares can be addressed without using engines and I tried something similar in the past. This can certainly be combined with the piece activity, as I mentioned towards the end of the post. But one big disadvantage of not using the engine is that any potential sacrifices and dynamics will be missed.

@WillSandi said in #4: Thanks for sharing your thoughts. There are two main reasons I didn't use any engine evaluation. First of all, I want to use such scores on a lot of different games and if you look at thousands of games, analysing each position for even half a second takes hours or even days. Secondly, I want these scores to be more stand alone. The piece activity won't capture tactics that happen after a piece moves, but in my view it isn't supposed to do that. The engine evaluation is also very complicated and takes everything into account. The evaluation may be better if you move a knight to a passive square because it allows the queen more freedom. But this doesn't mean that the activity of the knight was improved by this move. Your point about controlling squares can be addressed without using engines and I tried something similar in the past. This can certainly be combined with the piece activity, as I mentioned towards the end of the post. But one big disadvantage of not using the engine is that any potential sacrifices and dynamics will be missed.

@aVague said in #6:
I did something similar to what you mentioned in the past with calculating the control over squares: https://lichess.org/@/jk_182/blog/quantifying-the-control-over-squares/pqVbFlYu

Using the square control to weigh up the activity of the pieces is certainly an interesting idea for the future.

@aVague said in #6: I did something similar to what you mentioned in the past with calculating the control over squares: https://lichess.org/@/jk_182/blog/quantifying-the-control-over-squares/pqVbFlYu Using the square control to weigh up the activity of the pieces is certainly an interesting idea for the future.

@jk_182 said in #13:

I did something similar to what you mentioned in the past with calculating the control over squares: lichess.org/@/jk_182/blog/quantifying-the-control-over-squares/pqVbFlYu

Using the square control to weigh up the activity of the pieces is certainly an interesting idea for the future.
Thx for mentioning , will check it

@jk_182 said in #13: > I did something similar to what you mentioned in the past with calculating the control over squares: lichess.org/@/jk_182/blog/quantifying-the-control-over-squares/pqVbFlYu > > Using the square control to weigh up the activity of the pieces is certainly an interesting idea for the future. Thx for mentioning , will check it

@jk_182 said in #10:

I didn't consider the secondary activity, as I wanted to just capture the current activity, to see how it develops over the course of a game. But your approach to "discounting" with q makes a lot of sense.
One question about your recursive approach: would you also do the recursive calculation for the secondary squares to get a tertiary activity?

I wouldn't go that far. Then you would have to take into account enemy movements and you open a can of worms you don't want to open. I was just thinking out loud on a way to get rid of those pesky square values.

I didn't want to simply add up the squares, as this makes knights always much less active than bishops or rooks. My goal was that the activity indicates how active a piece is compared to its maximal potential activity.

Ah, OK. I thought you were trying to measure the activity of a side, not of a piece. Hard to think of a reason to compare the activity of different pieces, though. We know that some pieces are more active than others, so what does it matter that a pawn has activity 1 and a queen 25?

I also think that weighing squares differently is important. There are many closed positions where a rook has many moves on its own first rank, but it doesn't have any impact on the game as it's blocked by its own pawns. At the same time, there are situations where a piece doesn't have many moves, but it controls important squares around the enemy king to facilitate an attack.

I understand why you want to use these, but they are an average value that has no connection to the current position. What if a rook is in the corner in an end game when the board is almost empty? Surely it matters less than at start.

Anyway, those were just some instant ideas as I was reading your article, not anything I've given a lot of thought to.

@jk_182 said in #10: > I didn't consider the secondary activity, as I wanted to just capture the current activity, to see how it develops over the course of a game. But your approach to "discounting" with q makes a lot of sense. > One question about your recursive approach: would you also do the recursive calculation for the secondary squares to get a tertiary activity? I wouldn't go that far. Then you would have to take into account enemy movements and you open a can of worms you don't want to open. I was just thinking out loud on a way to get rid of those pesky square values. > I didn't want to simply add up the squares, as this makes knights always much less active than bishops or rooks. My goal was that the activity indicates how active a piece is compared to its maximal potential activity. Ah, OK. I thought you were trying to measure the activity of a side, not of a piece. Hard to think of a reason to compare the activity of different pieces, though. We know that some pieces are more active than others, so what does it matter that a pawn has activity 1 and a queen 25? > I also think that weighing squares differently is important. There are many closed positions where a rook has many moves on its own first rank, but it doesn't have any impact on the game as it's blocked by its own pawns. At the same time, there are situations where a piece doesn't have many moves, but it controls important squares around the enemy king to facilitate an attack. I understand why you want to use these, but they are an average value that has no connection to the current position. What if a rook is in the corner in an end game when the board is almost empty? Surely it matters less than at start. Anyway, those were just some instant ideas as I was reading your article, not anything I've given a lot of thought to.

@TotalNoob69 said in #15:

Ah, OK. I thought you were trying to measure the activity of a side, not of a piece. Hard to think of a reason to compare the activity of different pieces, though. We know that some pieces are more active than others, so what does it matter that a pawn has activity 1 and a queen 25?

I want to do this to see how exchanges and sacrifices change the overall activity. For example, it would be interesting to be able to measure the activity of a minor piece compared to the opponent's rook to see (part of) the compensation for an exchange sacrifice. This would at least be the dream outcome.

@TotalNoob69 said in #15: > Ah, OK. I thought you were trying to measure the activity of a side, not of a piece. Hard to think of a reason to compare the activity of different pieces, though. We know that some pieces are more active than others, so what does it matter that a pawn has activity 1 and a queen 25? I want to do this to see how exchanges and sacrifices change the overall activity. For example, it would be interesting to be able to measure the activity of a minor piece compared to the opponent's rook to see (part of) the compensation for an exchange sacrifice. This would at least be the dream outcome.

I agree with others who are opposed to averaging. The greater scope of long range pieces is why bishops have some edge over knights in a lot of end games. I would also suggest that using a static square value is problematic. Somehow, square values should be piece dependent. Like a square on one of the two long diagonals should be more valuable for a bishop than for a rook because being on the long diagonal makes it possible for the bishop to access other squares in fewer moves, but this is not the case for a rook. Something to think about anyway. I also don't understand why defending important squares in your own territory should negatively impact piece activity. This was a very interesting article. Gave me a lot to think about.

I agree with others who are opposed to averaging. The greater scope of long range pieces is why bishops have some edge over knights in a lot of end games. I would also suggest that using a static square value is problematic. Somehow, square values should be piece dependent. Like a square on one of the two long diagonals should be more valuable for a bishop than for a rook because being on the long diagonal makes it possible for the bishop to access other squares in fewer moves, but this is not the case for a rook. Something to think about anyway. I also don't understand why defending important squares in your own territory should negatively impact piece activity. This was a very interesting article. Gave me a lot to think about.

Some chess trainers encourage beginners to "improve the least active piece" as one of the ways to advance.

It makes sense to me, since it's the first principle to the more rigid "develop your pieces" rule. You might want to move a piece twice, for example, if it improves activity more than developing another piece.

Also, activity is the third out of five elements used in the K-MAPS method, starting with king safety and material advantage. Pawn structure and space advantage are less important.

So I think calculating the activity of a piece, as well as the difference in activity generated by a move, do have merit.

Some chess trainers encourage beginners to "improve the least active piece" as one of the ways to advance. It makes sense to me, since it's the first principle to the more rigid "develop your pieces" rule. You might want to move a piece twice, for example, if it improves activity more than developing another piece. Also, activity is the third out of five elements used in the K-MAPS method, starting with king safety and material advantage. Pawn structure and space advantage are less important. So I think calculating the activity of a piece, as well as the difference in activity generated by a move, do have merit.