Comments/Ratings for a Single Item

But why would you want to play it with Shogi pieces?

I don't see why Grant Acerex or Tamerlane Chess-like rules would make the game any better, though. If promotion choice must be restricted for practical reasons, it would be best to restrict it to Queen for all the Pawns.

You appear to have misunderstood me. I was referring to how you talked about using your in development Shogi engine, which you called HaChu to play this game. You mentioned how Shogi games already have multiple promoting pieces, as well as pieces with multi-capture capabillity. Then, you said the only problem was the promotion choice of the pawn. My post was thinking of solutions to such a problem.

With the rule changes I think this is now a nearly perfectly designed variant.

Chess is already a very complicated game in the sense of being able to "calculate" moves. Even normal chess cannot be perfectly calculated even if a modern engine had the support of supercomputers.

So in my opinion, it is never necessary to purposelly add rules simply for the sake of "adding complexity" (similar to Greg's comments). The complexity in chess is already inherent in the game itself. (For this same reason, I never add ice cubes to beer, and my coffee is not adulterated with extra flavorings).

This variant now has all the elements of a well-designed game: simple and clean graphics, good mix of traditional and new pieces, rooks placed traditionally at the corners, etc. The pawns also being allowed to make up to an initial quadruple-step, and knights a double-step is also good due to the large board.

Now just two more comments:

1) Nicolino says that pawns can't promote to Star Cat because that would be an overwhelming power increase. Using HGMuller's formula (value = 1.1*N*(30 +(5/8)*N), centipawns) the Star Cat should be worth about 12 points. I don't think that's too much, especially with the large board. But a reason to not allow it might be that the game already starts with 4 Cats and 4 Star-Cats, so promoting to queens or other pieces forces more variety on the board.

2) Also, with the rule clarifications/changes, I believe that Fairy-Max can be setup to play this game (please correct me if I'm wrong). Greg also said that after "play testing" this game in theory could be added to ChessV (a future possibility?) So for the sake of discussion could Fairy-Max be set-up to use one ChessV engine, or vice-versa? If so, an engine-vs-engine game (different codes) might be possible. That would be really interesting, especially for a game that is just barelly within the range of the engines that I'm aware of.

One final minor note: Rule#3 has a typo ("becuase" -> "because").

Good work on the game Nicolino!

How does the optional multi-capture work? Why make it optional? Do Knights also have multi-capture ability? And if so, what would count as intermediate spaces?

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.

@ V. Reinhart: I missed where H.G.'s formula was previously discussed, but I gather in case of your computation for the Star-Cat's value, "N" in the formula would be worth about 1/3 approximately. The value for the Star-Cat you gave (approximately 12 Pawns) doesn't seem too far off to me, if it weren't for the multi-capturing capability, as you noted in a later post. Based on some guesswork at a formula of my own, I'd only make the Star-Cat worth about a Pawn more on a 12x12 board with this variant's pieces in the setup position, due to it's multi-capturing ability.

A possible problem with this sort of value I'd note is that it's greater than what I'd put a queen at on a 12x12 board (say 10.5 Pawns approximately, which many might more or less agree with). A queen might not have too much trouble swapping itself off for a Star-Cat, or else delivering a series of checks or attacks, at least when there aren't many pieces left on the board, if nothing else. Fwiw, I had the same sort of vexing trouble when estimating the values of a couple of otherwise powerful pieces in the case of one of my own variants (i.e. Full house hexagonal chess, in case of the otherwise powerful Unicorn and Hydra pieces there, compared to the value I gave for a queen). Sometimes it's hard to come up with even approximate values that fully satisfy.

P.S.: Fwiw, by my crude & incomplete piece variant estimating methods, for a 12x12 board with this variant's pieces I would have put the Star-Cat at about 9.75 Pawns initially, then further added about a pawn's value (to take into account it's multi-capturing ability). The Cat I'd have initially estimated at about 5.75 Pawns on such a board, then further added about 1/2 a pawn's value.

Yikes! That's equal to or even stronger than an amazon, let alone a "mere" queen! The cat is worth about 7 Pawns, maybe 7.5-8 Pawns when you consider the multi-capture. That's roughly equal to an archbishop, and fit my predictions. A guard is only 3 pawns, oddly. I was expecting it to be closer to 4, given that a king is that strong. Because of all this, maybe I should have two queens and just one star cat per player, instead of the opposite. But wait! HGMuller says that the formula only works for pieces whose furthest move is no further than two king steps away, and the furthest star cat move is THREE king steps away! So maybe it's not as strong as we think.

I added a P.S. to my previous post, if it helps.

Okay, let's make a table.

Hmm, so the Kevin Pacey system and the Betza system both agree with each other and my own prediction on the value of the Star Cat. On the other hand, Betza system agrees with the HGMuller formula, for the Cat and Queen values, which also happened to match my own predictions. However, Betza's system is in complete agreement with my own predictions, which were just minor playtesting.

I'm not entirely confident of my own value for a guard (or king's fighting value, which is about the same IMHO) on a 12x12 board, which I put at only about 1.75 Pawns. This also affects my calculations for the value I gave for a Cat and Star-Cat, which would otherwise be higher. For an 8x8 board, I put a guard at worth 4, though H.G. has it considerably lower, at least for the opening phase of a game, I believe.

For a 12x12 board I put the value of a bishop at 3.75 and rook at 5.75, with queen = bishop + rook + pawn = 10.5. These arguably high values (for B, R and Q) are due to the increase in scope long-range pieces obtain on such a bigger board. Perhaps a counter-argument is that on bigger boards such pieces may reach a lower percentage of squares on the board in one move, on average, than on an 8x8 board, but this seems less important than scope.

On such a large board (12x12) this variant's special knight movement rule (initial double step) still might not make the knight in this game significantly stronger than a normal knight, I'd guess. In either case, I'd put it at worth 3 pawns. Sometimes a normal N is valued at less than 3 on a 10x10 board, even, though I think at least on that board size a N can still cope with 2 or 3 passed pawns quite often, if nothing else. Similarly, a pawn still = 1 in this variant, IMO.

P.S.: I don't know if H.G.'s formulae have ever included one for a multi-capture bonus, fwiw. If there is such a formula, it's likely different than the crude one I cooked up (and haven't disclosed).

I've edited my last post somewhat.

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.

Fwiw, here's how I so far have estimated the fighting value of a king (or the value of a guard) on many types of chess variant boards:

recall that a chess K has a fighting value of 4 (even though it cannot be exchanged); this value in my view might be rather oddly expressed (for lack of a known formula) as
chess K = 32 x (max. # cells chess K moves to [eight])
divided by
(# of cells on a chess board [sixty-four])
= 4

In similar fashion, for a Chess and a half K,
the fighting value of a Chess and a half K = 32 x (max. # cells Chess and a half K moves to [eight])
divided by
(# of cells in Chess and a half [one hundred and forty-four])
= approx. 1.77, or 1.75 (rounding to the nearest .25).

To V. Reinhart: I would be interested in the details of how you got your guard value.

Kevin Pacey, might I have your thoughts about the value of the king on a 144 square board. Is 1.77 a reasonable value for the king here? How does this contrast with the knight values on 64 and 144 square boards?

FYI, here's how I crudely estimated the value of the Cat:

Initial value (without multi-capture ability bonus estimate):

Just as Q=R+B+P in chess, similarly a Cat has a guard-movement component (worth 1.75 Pawns - see my previous post) plus more or less a knight-movement component, which is worth 3 Pawns IMO (max. 8 leaps that are 2 cells orthogonally or diagonally away, noting that though these all go to the same coloured cells, there's no concern about a Cat being colourbound since it moves as a Guard, too), plus a Pawn's value for being a compound piece like a queen, and so Cat's initial value =5.75.

Multi-capture bonus estimate (a really crude piece of guesswork here!):

First, estimate the Average value of an enemy piece at the start of a game, i.e. A=(Estimated Sum of Enemy Army's Piece Values [must be inexact since values of Cats, or Star-Cats, only initial ones, without multi-capture bonus]) divided by 24=approximately 3.5.

Next, estimate Limiting factor of a Cat's range, i.e. L=(max. number legal Cat moves) divided by 144=16/144=1/9 or 0.11.

Then, assume for now the chance of a Cat making a capturing move on any cell it can reach one or two cells away is 1/2 per cell (as if only in 1 direction). The value of zero captures available (x0) =1/4x0=0. The value of one capture available (x1)=1/2x1=1/2. The value of two captures available (x2) =1/4x2=1/2. The sum of these values is 0+1/2+1/2=1. We now take this sum and multiply it by A and by L to get our desired estimate:

Cat's multi-capture bonus estimate =1xAxL=approximately 0.39, or 0.5 Pawns (rounding to the nearest 0.25).

This estimate plus the Cat's initial value calculated gives final value of Cat=6.25 Pawns approx.

I used similar calculations to get the final approximate value of a Star-Cat as well.

Hi Joe

I'm not entirely confident of my formula for the estimated fighting value of a King (or Guard). The formula doesn't seem too bad when applied to 4D chess (e.g. 256 cells) where a King has many, many legal moves usually, fwiw.

On a 12x12 board I'm assuming if my formula makes for a good estimate (1.75 Pawns) it's because of such things as it taking a King many moves to cross from one edge of the board to the opposite one. On a 12x12 board a knight takes only two more moves to do so minimally than on an 8x8 board. Still, it might be quite reasonable to have a knight worth only, say, 2.5 on a 12x12 board. Big boards would seem to handicap short-range pieces. However, I recall the wikipedia entry for Grand Chess puts a knight in that variant at worth only 2.5 on its 10x10 board, which I don't agree with.

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.

Some general remarks on piece values:

@Ken: In the formula N is the number of moves. So for Cat N=8. The formula was obtained by fitting the empirical values of a large number of short-range leapers on 8x8 or 10x8 boards, in a way similar to what V.Reinhart describes below.

Effect of board size: I have never determined empirical piece values on larger boards; Fairy-Max can handle such boards only recently. Logic dictates that unlimited-range sliders would gain value compared to fixed-range leapers. Indeed on 10x8 a lone Bishop is already worth 0.5 Pawn more than a Knight, while on 8x8 these are equal. I don't expect the relative value of SR leapers to change much on board size. But when deciding on a scale, one it makes a difference whether one keeps Q=9 or N=3. Leaps of range > 2 should not be worth less than SR leaps on large boards. They have to be determined with care, because in the FIDE setup the backrank pieces are smothered, and range-3 leaps can attack them from outside Pawn range. Sometimes this makes an initial position non-quiet.

About the Commoner value: one can wonder if Fairy-Max' unawareness of mating potential could lead it to underestimate Commoner value. For this reason I experimented with an enhanced version of it (which I called 'Pair--o-Max), which could be made aware in the game definition of 4 things: pair bonuses, weak pieces with mating potential, minors unable to checkmate a bare King in pairs, and tough defenders. Pieces with value < 350 cP were assumed to be without mating potential if not explicitly marked. Stronger pieces were assumed to be without mating potential if their move pattern showed color binding. 'Tough defenders' are weak pieces that can draw against a Queen (like Commoner), which normally requires more than a Rook.

This information was then used to recognize certain matrial combinations as drawish, and strongly reduced any imagined advantage based on the piece values. This would avoid stupidities like trading the last Pawn for Knight in KBPKN, thinking that KBK is a +300 advantage,  and would make it prefer to trade B for N to get KPK. It also realized it takes about twice as much advantage to win without Pawns, and would recognize in the static evaluation when the last Pawn was in jeopardy, because the opponent could afford to sac a piece for it and still have a draw (such as in KRBPKRN, where N for P sac would leave you with KRBKR, which is a dead draw). This would give more realistic end-game play, and thus presumably more reliable empirical piece values when pitting minors (without mating potential) against Commoners (which do have that). Tested this way the Commoner value went up a little bit, from slightly below Knight to slightly above it. But a value of 4 is a gross estimation, and the Bishop pair usually crushes a pair of Commoners.

Some general remarks on piece values:

@Ken: In the formula N is the number of moves. So for Cat N=8. The formula was obtained by fitting the empirical values of a large number of short-range leapers on 8x8 or 10x8 boards, in a way similar to what V.Reinhardt describes below.

Sorry to be pedantic, but doesn't a knight have 8 moves, and a cat have 16, not 8? Do you know how I calculated the value of the cat?

I now understand how H.G.'s formula was applied by V.R. in the case of the Star-Cat, where N would be 24 (I overlooked that the final result is in terms of 1/100s units of a pawn - being sick, my problem-solving isn't at its best). In the case of the Cat, I too would understand N to be 16, not 8.

Unfortunately the diagram in your posting does not work, because you refer to betza.gif instead of betza.js in the line

<script type="text/javascript" src="../membergraphics/MSinteractive-diagrams/betza.gif"></script>

Newer browsers apparently do not accept a .gif file as a a source for JavaScript. Originally I had uploaded the script as .gif to the CVP site, because uploading of .js files was not supported in the submission script. By now there is a .js file for this available on the CVP site, though. Just change the extension.

I have adapted the Design Wizard in the Interactive Diagrams page to use betza.js in the diagram code it generates already some time ago, so I have no idea how you got stuck with the .gif extension.

Unfortually it is somewhat impossible to edit the HTML of posted comments here, with this new editor. Even when you switch it to 'source code' it completely f*cks up the original source. The easiest way I found to do this is click the 'View' link in the posting to get a page that only contains that posting and no others, then ask the browser to see the Page Source for that page, and then locate the submitted posting source near the bottom (behind an enormous amount of JavaScript to generate the CVP menus), copy that HTML search, and then finally paste that back into the comment editor in 'Source Code' mode. Then you can start editing.

Note that when you are not happy with the XBoard piece graphics, you could upload your own images for the various pieces to the CVP site, and tell the diagram to use those by setting the 'graphicsDir' to their location.

Also note that you can have the diagram implement the Cat -> Star Cat promotion, if you want. For that you have to embed a small JavaScript routine in your HTML. The betza.js code looks for such a routine, and uses it when present to handle exceptional promotion rules. This should do it:

<script>
function WeirdPromotion(x1, y1, x2, y2, promo) {
  var piece = board[y1][x1] & 2047;
  var promoRank = (piece & 1024 ? 0 : 11);
  if((piece & 512) == 3 && y2 == promoRank && y1 != promoRank) return piece + 3;
  return promo;
}
</script>

Oops, my mistake. Of course it is 16. Also sorry for the duplicate posting; I was posting from a tablet through a public network in a train, and have no idea why it did that.

BTW, I reformulated the formula a bit in order to make it more generally applicable:

value = 33*ELC + (33*ELC)*(33*ELC)/1584 (in centi-Pawn)

where ELC is the 'Equivalent Leap Count'. Through this formula you could assign an ELC to sliders of known value, e.g. 12 for Rook (on 8x8), and 8.5 for Bishop, based on values 495 and 330. The ELC would be additive, i.e. e Queen would have ELC = 12 + 8.5 = 20.5, which would result in a value of 965. Chancellor would have ELC = 20 (as Knight has ELC = 8), for a value of 935. So most of the time it seems to work pretty well, but it still cannot explain the high empirical Archbishop value (875). The predicted vanlue would be 732 (ELC = 16.5) Neither is there any explanation for why orthogonal slides seem worth so much more than diagonal slides. This suggests there is an ELC bonus involved with covering orthogonally adjacent squares. The Archbishop also has a lot of that. But it doesn't really show up in the value of Commoner or Woody Rook (WD). But those pieces might have some 'global defect' of their total move patter suppressing their value: they lack speed, and the number of squares they cover in 2 moves is much smaller than average for pieces with 8 moves. In addition, the formula was derived from SR leapers, many of which (especially those with many moves) do attack orthogonally adjacent squares, and thus contain the contribution of an average expected number of orthogonally adjacent squares for that ELC, explaining why Queen and Chancellor don't get any extra bonus despite the fact that they each have 8 extra orthogonal contacts between their move targets compared to their component R, B or N moves. Perhaps 8 extra such contacts is what you would expect when the ELC goes up from 12 to ~20. But the Archbishop has 16 such extra contacts.

Fwiw, the following link notes that in 1934 ex-world champion Lasker gave his opinion that in the endgame phase of a chess game, the fighting value of a king is about 4 pawns worth:

https://en.wikipedia.org/wiki/Chess_piece_relative_value#Standard_valuations

My own guess is that the value of a commoner in an endgame on an 8x8 board might be quite sensitive to the exact material balance or position. In some cases a commoner (aka guard) might outdo even a bishop on such a board, but two bishops might outdo two commoners in other cases - perhaps a bit like when 7 Kts outdo 3 Queens, with 8 pawns each, the formal 'point value' assigned to an army at times proves irrelevant.