The value of Cylindrical Pieces?

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Ovyron
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The value of Cylindrical Pieces?

Post by Ovyron »

Cylindrical pieces are fairy pieces that are very rarely discussed, and I'm interested about knowing what their value would be, as some look much stronger than their normal counterparts.

Cylindrical pieces are those that play as if the board was a cylinder, successfully warping around the right and left edges. Here's an overview of the these pieces (In no specific order):

Cylindrical Knight:

Image

Its new powers are only apparent when he's at the right, or left edges of the board, and its advantage is that it doesn't lose half of it's mobility, like the normal knight (Here, the knight can also move to the blue circles.)

Cylindrical Bishop:

Image

Its value is enhanced because now it's as if it was always on a long diagonal, but now it also controls its diagonals properly (by having access to the half of the board it normally wouldn't.)

Cylindrical Rook:

Image

Here, the King does no longer block the rook as it can warp to the other side.

Cylindrical Queen:

Image

I wonder if this piece is too strong as to be unusable (because the game may become CQueen centric.)

Cylindrical "King":

Image

If this king is too hard to mate maybe it shouldn't be a royal piece.

Cylindrical Pawn:

Image

The new ability is only when it's around the edge, and only for capturing. This should remove it's pawn edge weakness. In this case, each pawn is attacking each other.

I guess that learning this variant may be easier for someone that has not played chess, because being used to normal chess, I kept overlooking most moves from these pieces.

I don't think these pieces are very popular, but I'd want to know if there's an easy way to figure out their values.
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hgm
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Re: The value of Cylindrical Pieces?

Post by hgm »

Unfortunately Fairy-Max does not support such pieces. They could be added easily, though, by not immediaately breaking out of the ray-scan loop when you hit the side edge, but wrapping around in stead.

The only way I know to determine piece values is play games with unequal material in the initial position (one side having more of the pieces to be evaluated than the other), and then see how much material the other side needs in compensation to score 50%.
mjlef
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Re: The value of Cylindrical Pieces?

Post by mjlef »

For what it is worth, Zillions of Games piece ratios which is calculate from scratch for cylidrical chess are:

q 9.46
r 5.5
b 4.15
n 3.3
p 1
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Ovyron
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Re: The value of Cylindrical Pieces?

Post by Ovyron »

mjlef wrote:For what it is worth, Zillions of Games piece ratios which is calculate from scratch for cylidrical chess are:

q 9.46
r 5.5
b 4.15
n 3.3
p 1
What kind of calculation does Zillions use to get these values?

For instance, a Queen in normal chess has been found to have a value of about 9.75, so its cylindrical counterpart would be expected to have an even higher value.
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hgm
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Re: The value of Cylindrical Pieces?

Post by hgm »

I guess the Pawn value is determined mostly by the fact that it can promote. (Has anyone ever measured how much non-promoting Pawns would be worth? This is perhaps something I should do with Fairy-Max, as it would be very easy there to define a new piece that moves as a Pawn (but, not being a Pawn, will not promote) in its fmax.ini file. My guess is it can't be much.)

So if the Queen value goes up, the Pawn value also goes up because it now promotes to a stronger piece. So the ratio remains approximately constant.

Or perhaps the value of Pawns is not primarily set by the strongest piece you can promote to, but by the value of the piece you have to give to prevent the promotion (i.e. the lowest-valued piece on the board). But that also goes up here.
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Re: The value of Cylindrical Pieces?

Post by Uri Blass »

hgm wrote:I guess the Pawn value is determined mostly by the fact that it can promote. (Has anyone ever measured how much non-promoting Pawns would be worth? This is perhaps something I should do with Fairy-Max, as it would be very easy there to define a new piece that moves as a Pawn (but, not being a Pawn, will not promote) in its fmax.ini file. My guess is it can't be much.)

So if the Queen value goes up, the Pawn value also goes up because it now promotes to a stronger piece. So the ratio remains approximately constant.

Or perhaps the value of Pawns is not primarily set by the strongest piece you can promote to, but by the value of the piece you have to give to prevent the promotion (i.e. the lowest-valued piece on the board). But that also goes up here.
I think that part of the value of the pawn is that it can help to prevent the opponent pawns to promote.

[d]rnbqkbnr/pppppp2/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1


I think that I prefer white here even if the white pawns cannot promote and the black pawns can promote.
Note that I expect the white pawns to be effective in preventing the black pawns to promote.
Tony

Re: The value of Cylindrical Pieces?

Post by Tony »

:)

I actually had a discussion last week with my pupils that rook and king cannot checkmate a cylindrical king.

Tony
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hgm
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Re: The value of Cylindrical Pieces?

Post by hgm »

Well, you certainly have a point; Even mere obstacles might be worth something as shields or Pawn blocks. If your choice for the above position is a wise one can only be determined by trying it out. I'll put it on the to-do list, but currently the time of my Chess PC is much in demand. I first want to test B vs N and RR vs Q values for 8x8 Chess using normal Joker, to test if I see the same effects as is 10x8 Chess, (where I more or less finished this kind of testing), and thus help determining if these effects are artifacts of the testing method, or genuine differences between 10x8 and 8x8 Chess.

After that I want to measure the effect of adding one or more orthogonal contact non-captures to the Knight. I already tried this for the Bishop, expecting that even such a single extra move (e.g. a piece that moves like B+P) would give a huge value increase of the Bishop, because it breaks the color-boundedness. But I found these extra moves are only worth about 1/6 Pawn each. I want to test now if that is similar in Knights, which are not color bound to start with.

Then I could try the non-promoting Pawn stuff, probably by repalcing 4 normal Pawns by 4 non-promoting Pawns (giving them a value of 50 cP initially), and play games. There should be Binomial(8, 4) = 8*7*6*5/1*2*3*4 = 70 ways to do this replacement, which can then be done with either black and white, for 140 independent games. That is on the low side for good statistics, but with Fairy-Max I can play them more than once, since I quite heavily randomize the first 3 moves there.
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hgm
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Re: The value of Cylindrical Pieces?

Post by hgm »

Tony wrote::)

I actually had a discussion last week with my pupils that rook and king cannot checkmate a cylindrical king.

Tony
Indeed. So perhaps the Rook is highly overestimated above. Currently I favor the theory that a large part of the R-B value is due to mating potential.

Perhaps I should also test the Dragon King (R+K) vs Dragon Horse (B+K) values. (These are two Shogi pieces.) They both have mating potential, but otherwise are pretty close to B and R. Perhaps I should make the difference even smaller by only allowing the 4 extra moves they have to be captures, so that the Bishop look-alike cannot change color that easily.
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Ovyron
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Re: The value of Cylindrical Pieces?

Post by Ovyron »

Tony wrote::)

I actually had a discussion last week with my pupils that rook and king cannot checkmate a cylindrical king.

Tony
I consider that a flaw of cylindrical chess, and that the king should not be cylindrical.