Comments by vickalan

Hi Aurelian and Greg, just to throw in my opinion, I don't think draws are a problem in chess. It's just a 3rd possible outcome.

Games can still be intense and filled with interesting and spectacular play. Here's a good example of an interesting game that ended in draw:

See Kasparov shaking his head.

Greg: Btw, I've been enjoying your ChessV program. Excellent work!

Thanks for the update. Also, I think it's usually better to work on one game, and release it, rather than two at once.

Also (btw), I think games are fine even if they aren't in ChessV.

ChessV is awesome because you can play games against it, as well as see your moves analyzed. On the other-hand, if you play chess on-line with long time-control, you may always be worried your opponent might be using ChessV to help.

So some games not being in ChessV is good.

Also, we have to keep Greg busy with programming!!

One of the last places where he left comments is here:

<< Mullers Short-Range Leaper Law >>

It's a short but useful thread to explain how leaping piece values can be estimated with a formula. I also did some work to try to "disprove or prove" the formula, and I found it to be very accurate (comparing the value of a guard and knight to that of a bishop for example). The formula now takes the name "Muller's Short-Range Leaper Law".

Btw, I like your idea of playing cyborg chess. It is currently being used in one game of "Chess on an Infinite Plane" but unfortunatelly, the computers don't help much because the game has not been well simulated by any code.

Thank Fergus,

(Q1) Playing eight games concurently with time-control (4 moves/week) is playing an average of 4.6 moves per day. Obviously it would be good to learn all the games rules before-hand. That's a bit much to learn "on-the-fly".

(Q2) Thanks for the answer.

(Q3) Thanks. Someone on one of these forums once mentioned cyborg chess, and I wasn't sure if that was the format. A format (human + computer) vs (human + computer) could be fun too. I just wanted to know for sure (better to know the rules before the game starts rather than in the middle of the game).

Playing eight games concurently is a bit much for me with my other commitments, but sounds fun. Good luck!!

Thanks Greg for the clarifications. I'll sit this tournament out, but it does look like fun.

Some time I would like to play an engine-assisted game. Might be interesting for a game on a large board, like chess on a 12x12 board. I've always been curious if a flank attack (attack from behind the king) can be well-executed. It takes extra moves to get there, but the defense from that angle might be weaker.

Have fun in the tournament.:)

Thanks for the info. I did suspect that this game for a few reasons is pressing the limits of what variant chess engines can play. (Games will always be ahead of engines, if for no other reason that nobody makes an engine before the game. Plus, I'm sure programming is not a fast easy task, especially for chess).

HGMuller: Keep us up-to-date when HaChu is released!

Greg: I didn't know that a link to ChessV is in the "Play" menu. In an internal (CVP) search for ChessV, results for both pages come up (plus less related pages). Users will have a 50/50 chance of finding a useful page on the first try.

About "Chess and a Half". This board is 1.5x as wide as a normal chessboard - is that why it's "Chess and Half"? At this size it has 144 squares, so has 144/64 = 2.25 times as many squares. Not counting the new pieces, I think this is massivelly more complex than ordinary chess. Btw: I like how you kept the tradition "queen starts on her own color", and I also like how each of the two knight face in opposite directions. Even late in the game, when there's just one knight of a color, you can know which one survived.

Even the minutiae appears to be well-thought out. Great work!

Maybe rules 5, 7, and 8 should just be eliminated. Then the game would have the quality that the graphics are clean, crisp, and interesting, and the rules are simple and concise.

Only the game is mathematically complex (due to large size and extra pieces).

I believe it just means that that the Cat and Star-Cat can capture pieces within its intermediate move pattern. So for example a Star Cat on d4 can capture pieces on e5, f6, and g7 (in one move).

But being optional is interesting. I think it would be uncommon for one of the cats to not want to capture a piece while jumping over it. But there may be situations, for example to leave an opponent's pawn in place if the pawn is blocking a slider from attacking a more valuable piece.

I just realized it also probably means that Fairy-Max can't play this. And my estimate for the value of a Star-Cat may be low, due to multi-capture ability.

But since it's not a long distance mover, I don't think it has overwhelming power, and would still play perfectly in this game.

Kevin, thanks for your information about piece values. Your comment about a queen being more powerful on larger boards is interesting, and a good point.

A few months ago I used HGMuller's Fairy-Max to play a bunch of games to estimate the value of a guard (to confirm or dispute HGMuller's earlier work). I did it on a 10x8 board, and used the 4 extra squares for pieces to add guards and/or minor pieces. From these tests, I found that a guard is very nearly equal to a bishop, and slightly superior to a knight. (let me know if anyone would like more info about test details).

Nicolino, I hope you don't get rid of any of the Star Cats just because of their power.

This is a big board, so there's room for a few powerful pieces. Opponents have plenty of room to maneuver, create defenses, avoid attacks, and to create counter-attacks.

Btw, even though HGMuller's formula applies only to short-range leapers, I suspect it still might be good for pieces which jump up to 3 squares away when played on a large board.

Long range jumpers on a small board have the problem that long jumps go "off the board". But on a large board, attack points are more likely to useful, possibly helping the formula to remain accurate.

Maybe within a week or two, I'll calculate the "power density" of this game. It's a method I've used to determine the relative power of all pieces as a ratio to board size, and compare it with other games. I believe it's a useful measure of how "dynamic" the play can be expected to be. I'll update here if/when I finish the calculation.

Joe Joyce (and others interested):

Here's the details of my tests to estimate the value of a guard. Using Fairy-Max, I set up games on a 10x8 board. Pieces on each side placed as: RXNBQKBNXR.

X represents a variable piece, which was always different between black and white.
For example, black might have X = two knights and white has X = two guards (or vice-versa). Then I ran games (engine vs. engine with long time control) and kept track of scores. In all cases the armies were switched (W/B) so that half the games were each way. (scores are based on win = 1, draw = 0.5, loss = 0).

First, one problem in setting up a test is that Fairy-Max requires all pieces to have an assigned value, and going into a test the assigned value of a guard is unknown.

The first approximatelly 200 games were to "hunt" for the guard's best assigned value. I found guards play best with an assigned value between 300 and 375. Within this range games were not sensitive to their assigned value. But if the assigned value is lower (tested 250) or higher (tested 400) then guards don't help their side to play well (and these results are discarded from the final summary).

An Overall Summary of only games where guards have this "optimal" assigned value (300, 350, or 375):

asymmetry: [2 guards vs. 2 bishops]
guards win (score) = 40/80 = 50.0%

asymmetry: [2 guards vs. 2 knights]
guards win (score) = 46/80 = 57.5%

asymmetry: [2 guards vs. 1 bishop and 1 knight]
guards win (score) = 101/200 = 50.5%

Conclusion (on a 10x8 board, with other FIDE chess pieces):
A guard's value is:
1) equal to a bishop.
2) slightly superior to a knight.

If any questions or comments feel free to leave a message.

HGMuller's formula is interesting, and it's good to see there's a way to expand its scope by using ELC. Muller presented the formula as:

  value = 33*ELC + (33*ELC)*(33*ELC)/1584)

I prefer it a little more as:

  value = 33*ELC + 0.6875*(ELC)^2

In this form the variable occurs once for its linear component (33xELC) and once for its polynomial component (0.6875*(ELC)^2).

But this is just a minor stylistic preference. More generally, it's very interesting that a rather simple formula can be quite accurate for a wide range of leapers. Not sure if there's any future possibility (by Muller or others) to ammend it for longer range leapers. Of course, work like this always requires a lot of engine analysis, and follow-up evaluation of the data.

Good work on the formula!

Btw, do we know that Lasker's estimate of a king's value in an endgame (4) might not be too far off? The study that I did (which basically just confirmed previous work by Muller) was to estimate the value of a guard/commoner for the entirety of a chess-game (10x8 board).

From my study alone, I cannot dispute Lasker's estimate. As far as I know, it might be possible that a non-royal king might be worth a little more on an 8x8 board, and yet a little more in an end-game only situation.

As mentioned before, I completed a calculation of the "Material Power Density" for "Chess and a Half".

First, to explain what this ratio is - it is simply the sum of the value of all chess pieces on the board, divided by the playing area (number of squares).

This paramater may give some prediction of the style of play that can be expected from a game. Higher density usually means pieces have more attacking possibilities, and games can enter into dynamic attacks quickly - requiring fast responses from the other side. A lower density means that the opening development may last longer, with a stronger focus (for example) on the placement of pawns.

From lowest to highest is the "Material Power Density" of several games I've analyzed, with "Chess and a Half" now added in the list.

                     Board         Number   Piece    Power    Ratio to
                     Size (sqs)    of Pcs.  Density  Density  Classical Chess
———————————————————— ————————————  ———————  ———————  ———————  ———————————————
Classical Chess      8 x 8 =  64   32       50%      1.34     1.00
Infinite Plane(1)            360   76       21%      0.56     0.42
A Chess Endgame(2)   8 x 8 =  64    7      (11%)     0.64     0.48
Chess and a Half     12 x 12= 144  48       33%      1.04     0.78
Bulldog Legacy Chess 10 x 8 = 80   36       45%      1.10     0.82
Bulldog Chess        10 x 8 = 80   40       50%      1.31     0.98
Bulldog Chess(Witch) 10 x 8 = 80   40       50%      1.35     1.01
Janus Chess          10 x 8 = 80   40       50%      1.53     1.14
Capablanca Chess     10 x 8 = 80   40       50%      1.55     1.16
Seirawan Chess(3)    8 x 8 =  64   36      [56%]     1.88     1.40
Musketeer Chess(4)   8 x 8 =  64   36      [56%]     1.88     1.40
Chu Shogi            12 x 12= 144  92      [64%]     1.91     1.43
Amsterdam Chess      11 x 8 = 88   44       50%      1.95     1.46
Waterloo Chess       10 x 10= 100  60      [60%]     2.72     2.03

(1) - Chess on an Infinite Plane: Play is assumed to be in an 18 x 20 range. This is the horizontal span and 2 ranks less than the vertical span of the outermost pieces (starting position). Little play is presumed to take place in the outermost ranks except for pieces moving inward.
(2) - A chess endgame: A sample 7-piece ending with KQRR vs. KQR.
(3) - Seirawan and Musketeer Chess: Data assumes all pieces are on board. Some pieces are introduced early or later in the game.
(4) - Musketeer Chess: Assumes game with archbishop and chancellor played as the new pieces.

Chess and Half (4th in list) is interesting in that is has a very low piece density (48 pieces on 144 squares), and the material density is 78% compared to that of chess (100%). This is in the range of games that have become my favorite to play. They usually feature an opening with time for tactical development, rather than the players always reacting only to exact threats from the opponent.

I've seen plenty of variants where the dynamics suffer from too much power concentrated into a normal size chess board.  I would really like to try this game sometime, and as mentioned, if it's ever withing the scope of a chess engine, see if a human can win, or how two engines do against each other.

I agree that the concept of power density involves some assumptions that might cause the value to be an approximation. As you mentioned, it does assume that pieces have fixed values, even with a different mix of pieces, and different board sizes.

I do believe that if every game has a mix of pieces (as they do), such errors would tend to cancel out. For example, as board size changes, some pieces might gain slightly in value, while others lose value.

The only way to overcome such possible errors is if there was an accurate way to identify a piece's value based on the specific board size. I'm not aware of any work that has been completed to do this for a range of board sizes. At best, maybe we know the rough difference in value of a few pieces when they go from an 8x8 to 10x8 board. To my knowledge, there is no piece which has its value altered by such a large amount that it would render power density as grossly innacurate.

I believe the biggest error currently found in the power density table is the data for Chess on an Infinite Plane . Here a board size of 18 x 20 was assumed because it's the approximate span of pieces in the starting position. But the bulk of the dynamics in actual play is usually found in a much smaller area.

In fact, the tendency of pieces to try to "fight for the center" might be a phenomenon seen in all games, so the stated "board sizes" themselves might be an opportunity for refinement. But I'm reluctant to complicate the formula based only on conjecture. As we learn more about piece valuations for variant chess, I certainly can plan to refine the formula when there is merit to do so. For now, it's based on the theory that "Simple and approximate" is better than "Complex with speculation".

There may have been some differences in the test setup, for example HGM's test may have been on an 8x8 board where one side had the bishops removed altogether, and replaced by guards (commoners).

Maybe an army likes to have bishops and guards working together, but if the bishops are removed and replaced with guards, the army is slightly worse than the one that still has the bishops? Maybe HGM will shed some light on his specific test set-up, or the scope of his conclusion.

Note all tests by me were done with HGM's Fairy-Max engine, which is very well-designed for playing these types of pieces.

Oh Thanks. Sorry I didn't notice. Congratulations to all the players!

I'll probably check back occasionally - this is interesting!