The value of Cylindrical Pieces?

[hgm]

You have a point, but it is kind of difficult to estimate how important this is. On a true cylinder board, where every piece would wrap around, there obviously is no center in the lateral direction. But when most pieces do percieve the edge (in particular most of the opponent's pieces), they would be off better in the center, and your cyclindrical Knights would then be better positioned in the center as well, despite the mobility of the Knight not being any better there, just because it covers more squares that are important for the opponent there. Note also that I did never find a strong effect of the internal evaluation of a piece on the score achieved when having such a piece. This is true even when changing a large term such as the piece value used in the evaluation. I guess this is caused for a large part by the fact that both sides use the same evaluation. So if one side attaches an unrealistic advantage to having its cylindrical Knights in the center, the opponent will fear it too, and (usually succesfully) prevent the Knights from settling there. So as often as not the Knights end up on other squares (unjustly thought inferior) anyway.

I should stress that I am doing this in Fairy-Max, in which centrlization only accounts for a fairly small part of the evaluation. (The difference between a1 and e4 is 25 cP. The difference between a4 and e4 only 16 cP.)

The final result of my test was 65.5% for the cyindirical Knights as white (84 games), and 58.8% as black (108 games). Averaging away the color bias then leaves an advantage of 62%, which is about 2/3 Pawn. (Note that statistical errors are still of the order of 3%, about 16 cP.) So the advantage of a single cyclindrical Knight is about 1/3 Pawn (33 +/- 8 cP).

Note the difference between having white and black in this test was 6.7%, which in an equal-material game would translate to a 53.35% score for white. That is about what it is supposed to be (1/6 Pawn).

[Ovyron]

But when most pieces do percieve the edge (in particular most of the opponent's pieces), they would be off better in the center, and your cyclindrical Knights would then be better positioned in the center as well, despite the mobility of the Knight not being any better there, just because it covers more squares that are important for the opponent there.

But a cylindrical knight in the center is just a normal knight, maybe that accounts for not being much stronger than the normal knight (if it spends most of the time in the center, it's just a normal knight most of the game.)

[hgm]

Yes, this is why cylindicity is not really a very important trait on the Knight. It only makes it better in a very limited part of the board, and with a normal Knight, you avoid that part. So a normal Knight does not suffer from the edge as much as you might think.

This is why counting the average number of moves of a piece (mobility averaged over all board suares) is not really an accurate measure for the piece value. The average might be suppressed by a few very bad squares (such as corners for Knights), but in practice you don't go there because there is no real need to go there. Wat you really would need is a weighted average, weighted by teh importance to be on each square.

This is why Camels and Zebras are such worthless pieces. Not only does their larger step reduce their mobility already at larger distance from the edge, but the large step also hampers their manoeuvrability. The only way to displace them a littel is firs move far away and then move approximately back. And even in the center, the first move always brings you very close to the edge. So you have to be on edge squares a lot, with those pieces, or you cannot move around in the center.

I am trying cylindrical vs normal Queen now. This seems to be a far larger difference. So much that I have given the cylindrical Queen Pawn odds. Nevertheless, it seems to score still slightly more than another Pawn odds. So the difference seems to be about 200 cP. But no good statistics yet.

[Ovyron]

I wonder if you can post the games on the future? I'm looking forward to seeing these pieces in action as you are testing them.

[hgm]

Well, I have been saving all the games, but there are hundreds of them, and they are probably quite low quality, as I am playing 40/2' on a slow machine (1.3GHz Pentium-M).

If you want to see good cylindrical action, the best way is probably just to download cylmax.exe and fmax.ini from my website, and play a game with it (or have it play itself) at a longer time control.

If you really want to play with mixed cylinder / non-cylinder pieces, I can give you a game description for in the fmax.ini file that does that too. (You would have to play it as /variant=fairy in WinBoard_F to be able to use all the extra needed piece symbols in the FEN for the initial setup.)

[Ovyron]

If you really want to play with mixed cylinder / non-cylinder pieces, I can give you a game description for in the fmax.ini file that does that too. (You would have to play it as /variant=fairy in WinBoard_F to be able to use all the extra needed piece symbols in the FEN for the initial setup.)

Yeah, I don't have much experience with Winboard or its text files, so a guide on how to do it would be appreciated.

[hgm]

Well, the simplest way is to download:

http://home.hccnet.nl/h.g.muller/alpha.tst

(and save it as winboard.exe in a new folder). Then download the two files

http://home.hccnet.nl/h.g.muller/cylmax.exe
http://home.hccnet.nl/h.g.muller/fmax.ini

and save them in the same folder as where you put WinBoard. Go to that folder, right-click the WinBoard icon (should look like a black Knight), and choose "create shortcut". Windows will put the shortcut in the same folder as WinBoard, (same icon), but you can drag it to the desktop, if you want.

Then right-click that shortcut, and choose "properties". You will get a pop-up dialog box, with the path-name of the winboard.exe in the "target" field. Behind this path-name, type a space and "/variant=3checks" (without the quotes), as this is the name I gave to cylinder Chess in the fmax.ini file. (WinBoard allows you only to enter variants it knows, and it does not know cylinder Chess, so I had to hijack the name of another variant.

Double left-click the shortcut icon to start WinBoard. You will get a startup dialog box that asks you what you want WinBoard to do. Tick the first option ("play against a chess engine"), and type "cylmax" (with or without quotes) as name for the first engine. Then click "OK".

WinBoard should now come up as an 8x8 board with normal piece setup. Use the pull-down menu "Options -> Time Control..." to set the time control you want. Use "Options -> General" to tick the options "Show thinking" and (very important!) untick "Test Legality". (Next time you play WinBoard will remember all these settings, so this is something you only have to do the first time.) You are then ready to play: If you want to play white, just move. If you want to play black, use the menu "Mode -> Machine white". If you want to see automatic play, you should have typed "cylmax" as both the first and second engine in the startup dialog, and you can then use the menu "Mode -> Two Machines". If you get tired of typing the engine names, you can set them in the shortcut by also typing (next to the /variant) in the target field

/cp /fcp=cylmax /scp=cylmax

Clicking the shortcut will then skip the startup dialog, so you can play immediately. (But you won't be able to use it for other engines, though.)

[hgm]

I ended the Q* vs Q+P test (I will from now on designate the cylindrical pieces by a '*') after 191 games. The Q* was leading by 67% at that point, which is nearly as much as Pawn odds (equal to it within the statistical error).

So it seems Q* = Q + 200 cP (opening value).

I have now started a B* vs B test, where I gave the side that has the two B* Pawn odds, as I anticipate that the difference between B* and B might be quite large. (Compared to that between N* and N; I don't really expect B* to be wirth as much as a Rook, because it still has no mating potential.)

[Ovyron]

Thank you, I got it rolling, and it seems Chess* is a lot more dangerous than normal chess, Cylmax mated me in five moves on my first try:

1. e4 c6 2. d4 Nf6 3. e5 b5 4. Be2 Ne4 5. Nf3 Qd8xf2#
{Black mates} 0-1

My guess is that computers will be more stronger against humans in this than in normal.

I'm going to figure out fmax.ini to try to mix pieces* and normal pieces. I'm also interested to the possible enhanced value of the Bishop* pair.

[hgm]

OK, depending on how much flexibility you want, there are several (progressively more complicated) ways to do this. In all cases you will have to modify the fmax.ini file. Open it with notepad (or your favorite text editor). At the bottom of the file there is the description of all variants Fairy-Max is configured to play. The one starting with

Code: Select all

Game: 3check

is the one that you currently play as cylinder Chess. You will see that it only has definitions for the pieces P, N, B, R, Q and K, but that they are all defined as cylinder pieces: their move descriptions have all 0x10 prepended for the 3 or 7 that you would see in the corresponding normal pieces.

Now if you want to play a game whre certan piece types are normal, and others are cylindrical, just replace the line with the description of the piece you want to be normal by that of a normal piece (from another game, or by editing away the 0x10 everywhere). You can make a copy of the entire game description first, and give it another name (e.g. "suicide") so that "3checks" remains the pure cylindrical variant. But if you would put "/variant=suicide" in the shortcot you would play this modified variant.

If you want to play games were one side has a normal piece, say N, and the other has a N*, you can add a line behind the last piece (which is Q* in the 3check game) describing that piece. This is then piece number 8, and you would have to replace the 4 (the number of piece type N*, as it is defined as the 4th piece, after p, P, K) by 8 in the lines giving the opening array (3rd line of the game description for white, 4th line for black). Note that WinBoard will not be aware in this case that some of the Knights are different; it will display them all as Knights, as it is thinking you are playing suicide Chess. Even if the 8th piece you defined has another letter as first character on its definition line, you could not use that letter to indicate it in a FEN, as WinBoard does not accept other letters than PNBRQK in a FEN for suicide Chess.

If you want to be able to paste FENs into WinBoard involving more than 6 different piece types, you should set it to /variant=fairy. (This is mandatory if you want to give Pawn odds, as the fmax.ini can only define the opening array of Pieces; Fairy-Max always assumes a closed rank of Pawns.) WinBoard can then really display X and X* differently, which is less confusing if you play the same side with both an X and an X*. To do this add the following game description to the fmax.ini:

Code: Select all

Game: fairy
8,8
6 4 5 7 3 5 4 6
6 4 5 7 3 5 4 6
P:74 -16,0x24 -16,6 -15,5 -17,5 
p:74 16,0x24 16,6 15,5 17,5
K:-1 1,0x34 -1,0x34 1,7 16,7 15,7 17,7 -1,7 -16,7 -15,7 -17,7
N:259 14,7 31,7 33,7 18,7 -14,7 -31,7 -33,7 -18,7
B:296 15,3 17,3 -15,3 -17,3
R:444 1,3 16,3 -1,3 -16,3
Q:851 1,3 16,3 15,3 17,3 -1,3 -16,3 -15,3 -17,3
E:50 30,7 34,7 -30,7 -34,7
W:175 1,7 16,7 -1,7 -16,7
F:200 15,7 17,7 -15,7 -17,7
M:-1 1,0x34 -1,0x34 1,0x107 16,7 15,0x107 17,0x107 -1,0x107 -16,7 -15,0x107 -17,0x107
A:370 15,0x103 17,0x103 -15,0x103 -17,0x103
C:951 1,0x103 16,3 15,0x103 17,0x103 -1,0x103 -16,3 -15,0x103 -17,0x103
H:290 14,0x107 31,0x107 33,0x107 18,0x107 -14,0x107 -31,0x107 -33,0x107 -18,0x107
G:444 1,0x103 16,3 -1,0x103 -16,3

This describes PNBRQK as the normal pieces, but describes H=N*, A=B*, C=R*, G=Q* and M=K*. You can then use HACGM in FENs to set up a position. (Note that currently Fairy-Max ignores the actual letter you give in the piece descriptions, and that E is always the 8th piece in the game description, etc. I still want to change this one day.) The HACGM pieces will be displayed in WinBoard by fairy-piece symbols, so you can distinguish them from the normal ones. NOTE THAT THIS WILL ONLY WORK IN BOARD SIZES "Middling" and "Bulky", as I did not make bitmaps for fairy pieces in other sizes yet, in WinBoard_F.