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#Post#: 693--------------------------------------------------
How to calculate the value of a piece?
DIR By: ubersketch
Date: March 30, 2018, 7:38 pm
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This question has been on my mind for a while and it perplexes
me. It would be interesting if we had a systematic way of
assigning pieces values.
#Post#: 698--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: Martin0
Date: March 31, 2018, 1:03 am
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First you take one piece (preferably a weak one) and use it as a
base to value the other pieces. You can set its value to
whatever you want, but numbers like 1 or 100 are nice numbers.
Then you estimate how much other pieces are worth compared to
that piece and set their values accordingly.
When it comes to estimating those values, I believe the best
approach is to use statistics from a large sample of games
between players of equal strength. Naturally this is easiest
done with an engine playing against itself to get that large
sample size.
Trying to find a formula for piece values that would work for
any variant on any board size is put simply not possible, but
some methods are clearly better than others. No matter what you
do it is not something that can accurately assign the values, it
will always be an estimate. And the value for a piece in
practice will always be relative anyway.
#Post#: 702--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: HGMuller
Date: March 31, 2018, 7:04 am
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Piece values are empirical quantities, which represent who has
the advantage in a large collection of positions with a material
imbalance (differing in the placement of the pieces). To measure
them you can play a large number of games starting from an
opening-like position (i.e. pieces behind a closed rank of
Pawns), and observe how much the result differs from 50%.
As a caveat I want to mention the whole concept of 'piece value'
is an approximation. In practice, how much a piece is worth
depends on what other material you have, and what material the
opponent has. Usually the corrections are small compared to the
'base value' of the piece (i.e. the value averaged over many
total-material combinations with the same imbalance). But in
extreme situations, the effect can be large. Seven Knights
consistently beat three Queens (when they all start behind a
rank of 8 Pawns, and there are no other pieces (except Kings)).
This is totally at odds with the value you would observe in
games between more similar armies, where a Queen on one side can
be almost perfectly balanced by 3 Knights on the other side. If
you take the latter as evidence that a Queen is worth 3 times as
much as a Knight, you would expect the Knight side in the 3Q-7N
game (which I named 'Charge of the Light Brigade') to be two
Knights short of equality. But in fact the Queens stand no
chance at all. A more mundane example of cooperative material
effects is the Bishop pair: a Bishop is worth about half a Pawn
more when you already have a Bishop on the other square shade.
Then there is an entirely different question: "can the empirical
piece values be predicted from how the piece moves by a
comparatively simple calculation (i.e. without playing games)".
This turns out to be very difficult. Lots of methods to
calculate this, which sound very plausible, turn out to give
values that differ very much from the empirical value. E.g. lots
of guestimates are around for the 'Capablanca pieces', the RN
and BN compounds (Chancellor and Archbishop). Because every
Chess player knows that a Rook is worth two Pawns more than a
Bishop, these guestimates almost always have the Archbishop
value ~2 Pawns below the Chancellor value. While the empirical
value difference is only a quarter Pawn. (If one side has two
Archbishops and a Pawn, instead of the opponent's two
Chancellors, all other pieces being equal, the Archbishops
usually win.) The explanation for this that I currently favor is
that moves to orthogonally adjacent squares provide some extra
value to the piece. (This also explains why the Rook is worth
more than the Bishop, even on a cylindrical board where both
have the same number of moves.)
#Post#: 704--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: GothicChessInventor
Date: March 31, 2018, 8:18 am
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--- Quote from: ubersketch link ---
>
> This question has been on my mind for a while and it perplexes
me. It would be interesting if we had a systematic way of
assigning pieces values.
>
--- End Quote ---
I published a paper on this years ago. Google for "80 square
chess" or download the paper here:
HTML https://pdfs.semanticscholar.org/330e/6cada5af2191248e09b5910527744592e10d.pdf
#Post#: 707--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: ubersketch
Date: March 31, 2018, 10:01 am
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I think it would be a good idea to create a piece with a value
of 1.
It cannot move and cannot capture.
#Post#: 720--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: HGMuller
Date: March 31, 2018, 2:33 pm
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1 what? What is your unit? And why do you think such a piece
would have value 1 on that scale? I would be inclined to think
that such a piece would have negative value. It is worse than
having a 'hole' in that place (i.e. a square inaccessible to
both players). Because you cannot go there, but your opponent
can, by capturing it. And I would expect a hole to be sort of
neutral. Although that might depend on where exactly on the
board such a hole is. E.g. a hole on the second rank might
provide a good shelter for the white King, and would just
represent an obstacle for black.
#Post#: 721--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: GothicChessInventor
Date: March 31, 2018, 3:11 pm
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--- Quote from: ubersketch link ---
>
> I think it would be a good idea to create a piece with a value
of 1.
> It cannot move and cannot capture.
>
--- End Quote ---
I think it should have a value of i, where i squared = -1, and e
raised to the power of 2 x pi x i = 1.
#Post#: 722--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: Asher Hurowitz
Date: March 31, 2018, 3:57 pm
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If it had a value of one, and it cannot move, then a piece that
can move therefore can technically move an infinite amount of
more spaces than the base piece, and thus is infinitely more
powerful, no matter the move, as 1 unit of movement is
infinitely more than 0 units of movement.
#Post#: 723--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: ubersketch
Date: March 31, 2018, 4:55 pm
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--- Quote from: Asher Hurowitz link ---
>
> If it had a value of one, and it cannot move, then a piece
that can move therefore can technically move an infinite amount
of more spaces than the base piece, and thus is infinitely more
powerful, no matter the move, as 1 unit of movement is
infinitely more than 0 units of movement.
>
--- End Quote ---
Assigning it 0 seems to make more sense. I'll call this piece
the zero piece or stone.
Also, we have to mention that the zero piece still may be useful
as it can block attackers.
#Post#: 726--------------------------------------------------
Re: How to calculate the value of a piece?
DIR By: Martin0
Date: April 1, 2018, 2:23 am
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Here is a stupid example trying to decide how much light squared
bishops are worth compared to dark squared bishops.
HTML https://i.imgur.com/Bzuk3TJ.png
In this specific case it would make sense to value the light
squared bishops as 0. Black will also be able to checkmate
white. We could try with a lot of different positions for the
dark squared bishop and kings where the bishop is not directly
lost and white is not directly stalemated and we would get the
same result.
I don't think anyone would be stupid enough to try to make
conclusions with piece values on this example, such as 1 dark
squared bishop is worth more than 32 light squared bishops, but
I sort of like it to show off how piece values really are
relative.
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