Castellum Chess, unequal armies game

Hi,

Proud to announce the release of our Game of Chess with unequal armies: Castellum Chess

Take a look at it here:

http://musketeerchess.net/games/castellum/

It does not seem to load.

I believe it is a browser issue. With the Internet Explorer it does not work with me, but with Firefox it works well.

Hi Zied

I have tested it again:
With the iPad it works with Safari easily.
On my PC (Windows 7) it works with Firefox and also with Chrome.
But with the Internetexplorer 11 it does not work with me on the PC.

Very nice 3d graphics.

The game, however, is totally unbalanced. In self-play Fairy-Max scores about 87% for white (bullet games, 40 moves/min). [In this test I goofed and gave black the exotic pieces, and white the FIDE army, and black won by 87%. So that is despite the white advantage, which normally is some 53%. Giving white the exotic pieces should make it win even more.)

This makes sense from the individual piece values: when you would replace Q + 2B by 3R it is about even (9 + 2x3 = 3x5). But the black replacements for Q and B are all very much stronger than Rook, as are the Rook replacements.

Taurus is a regular 8-leaper, similar in value to Knight. But the Flying Rook is obviously stronger than a Rook; it does everything a Rook does, has 4 extra moves, and can jump to 2 squares where the Rook has to slide (and thus can be blocked). Rook plus 4 extra moves is typically worth 700 cP (like the Crowned Rook, R+K). So a good guestimate for Flying Rook would be 750 cP.

Pieces with 12 direct leaps are typically worth as much as a Rook. So 16-leapers, which have 4 moves extra, are also worth ~700 cP. The Hawk is a 16-leaper. It lacks the steps to adjacent squares that are very important for manoeuvrability, though, and the range-3 leaps often fall off-board on 8x8. But it should be worth at least 650 cP. The Duke also has 16 move targets, but four of those are blockable. But these should at least count as half, making it effectively a 14-leaper. Which should be about 600 cP.

So the Duke is worth 350cP less than Queen, But the Flying Rook alone already more than compensate for that, giving 500 cP extra compaired to two normal Rooks. Two Bishops are worth 700 (3x325 + 50 pair bonus), so barely more than a single Hawk. Two Hawks give you an advantage of 600 cP.

So white effectively has an advantage of 750cP, i.e. more than two minors. Not really fair...

I've tried a bit with White and Black. With White I clearly win, with black I have big problems. But probably that's logical because I'm (still) not sufficiently familiar with Taurus, Flying Rook, Hawk and Duke. And with black I really miss the bishoph, diagonal attacks are possible with the Hawk only partially.

One of the reasons orthodox Chess is such an interesting game is the good distribution of piece values. Each higher class of pieces has about twice the value and half the number of pieces (1 Queen, 2 Rooks, 4 minors). This provides good 2-for-1 trading opportunities, and thus maximum variation in material.

The Castellum army seems much less interesting in this respect: 2 Knight-class pieces, and 5 pieces intermediate between R and Q, pretty close together in value. Most armies in Ralph Betza's 'Chess with Different Armies' are much more balanced in this respect. The exotic armies are objectively all stronger than FIDE, however, as Fairy-Max self-play has shown. (Not so extreme as the Castellum army, though, just 1 to 1.5 Pawn. Betza was pretty good in estimating piece values.) It seems that humans have more difficulty handling an army with unfamiliar pieces, than defending against it.

I am using firefox on my computer (A windows) but it doesn't load.

Who designed the engine for Castellum chess? (at the website when playing human vs engine)?

If this game is unbalanced (white advantage), but if the engine is not very good, then it might be fun to play from Black. The engine has the advantage in material, but human has the advantage in that the engine is newly designed and maybe not so good. Like in the "old days" of playing chess against a machine.

Beware that a lot of work has already been done in this respect. Ralph Betza's original Chess with Different Armies had 3 armies beside 'Fabulous FIDE: Colorbounmd Clobberers, Nutty Knights and Remarkable Rookies. That made for 16 combinations (including orthodox Chess: FIDE vs. FIDE), 9 of which not including the FIDE army. Since then many people have devised their own armies. I once even designed an army with mostly 'chiral' pieces (i.e. unequal to their mirror image, so that the K-side and Q-side piecese would be each other's mirror images).

And then of course there is Spartan Chess, which puts the FIDE 'Persian') army against the very special Spartan army, which even has different Pawns, and a pair of Kings.

This works on Chrome!

Yay!!

I haven't tried it with Fairy-Max yet, but it is pretty obvious that the Marsupial army is enormously stronger than FIDE. The Archbshop has been extensively tested, and is worth only about a Pawn less than a Queen. The value of the other pieces can be guestimated from their move counts. The Buffalo and Antelope have 12 direct (unblockable) leaps, making them equivalent to a Rook. The four orthogonal leaps on the Flying Bishop should already make it stronger than a Rook, when operating in pairs to neutralize the color-binding. (A well-tested augmented Bishop that does single orthogonal steps is worth 525 centi-Pawn.) But in addition it has 8 more extra moves. These are blockable on the diagonally adjacent squares, but that still should make them count at least half. (The Horse from Chinese Chess, which has a similar blocking pattern for its Knight moves, is worth exactly half a FIDE Knight.) In fact I would think the blockability hurts less here because the blocking squares are attacked by the piece itself, so that blocking cannot be done with impunity. So the Flying Bishop should be worth about 750 cP.

So the Marsupials gain (compared to FIDE) 2*250 = 500cP by the Rook->Flying Bishop substitution, 2*175 = 350cP by the Knight->Antilope substitution, 2*150 = 300cP by the Bishop->Buffalo substitution, and lose 75cP by the Queen->Archbishop substitution. That totals to an advantage of 1075 cP, more than Queen + Pawn. Black should not stand any chance at all, here.

It is not clear why you call this army 'Marsupials'. The Antilope and Buffalo are both placentals. And so is a Bishop (human), while to my knowledge flying marsupials do not exist.

Color binding usually does not cause noticeable weakening of a pair of pieces on opposite colors. It is only noticeable when a single copy of the piece is present, or all copies of the piece are on the same color.

It is true that color-bound pieces can never have mating potential, no matter how strong they are. (This also holds for color-alternators, BTW, and pieces covering squares of both colors can also lack mating potential.) It cannot be excluded that when too many strong pieces lack mating potential, the total strength of the army suffers a bit. Mating potential doesn't seem to contribute much to the value of pieces in general, though, as long as Pawns can promote to a strong piece with mating potential. Virtually all chess games that last into an end-game are decided in end-games where multiple Pawns are present. The value of the piece is mostly determined by how well it can support Pawns to promotion, or prevent enemy Pawns to promote. Not by whether it can checkmate itself.

A good example is Betza's "Colorbound Clobberers" army. This has two pairs of Rook-class color-bound pieces. It significantly beats FIDE, with a score similar to Pawn odds (~68% in Fairy-Max 40moves/min games). This is not as much as you would expect on the base of the individual piece values, as a pair of Rooks is about 300 cP stronger than a pair of Bishops, and only 75 cP of that is compensated by substituting Archbishop for Queen. (And perhaps another 25cP by the "Fibnifs" being slightly weaker than Knights.) So it seems there is a penalty of about 100 cP. Not really significant compared to the more than 1000cP advantage based on adding piece values of the Marsupials.

It seems you don't have the right idea about how Fairy-Max 'evaluates pieces'. Your remark about "nearest squares" is meaningless to me, I haven't a clue what you could possibly mean by that. To determine piece values with the aid of Fairy-Max, I just have it use the pieces in play, to see how they perform. If substituting the Rooks of one player by piece X (e.g. a Bishop that also can leap to the second orthogonal square), and the side with the Rooks then loses, I know X to be stronger than a Rook. By testing against other material combinations until you find one where the score is about even, (possibly interpolating) you will eventually get a precise piece value. E.g. if R+R+P beats X+X as much as X+X beats R+R, the difference between X+X and R+R must be half a Pawn (which without pair bonuses would imply X is 25cP stronger than R, i.e. worth 525cP).

I would never trust any piece value that was derived solely by arguing; I have seen too many examples where any kind of reasonbly sounding argument proved dead wrong. (The Archbishop is a good example.) So yes, doing a guestimate like I did for the Marsupials can be wrong. But it can never be so wrong as to erase a difference of more than a Queen.

Ah OK. That could be Sjaak II; I believe it has a built-in algorithm for determining the value of pieces that are not explicitly given in the game definition. Zillions of Games also has that, but there theexact algorithm is a company secret. It seems to have to do with the number of moves the piece has, though: people programming games for Zillions tell they can tweek the values by adding duplicates of moves to the piece, in order to fool Zillions into thinking the piece is stronger. (This probably makes the search less efficient.)

For Fairy-Max the user has to provide a piece value. The self-play results are highly independent of the value given, though, if it is not very far off. Ideally one should do a 'self-cosistent' test, where the value deduced from the score is very close to the value given in the game definition.

Just from looking at the rules I would say the jumpers are some 4-5 Pawns weaker than FIDE (so that it is somewhat like facing Rook odds). The Vicar and Carvi should be as strong as Knight and Bishop, as they are 50-50 mixtures of those, and the Vicar is a minor (no mating potential). So indeed not a suitable Rook replacement. The Rhino (Betza's 'Fibnif' in the Nutters army) is about Knight strength. The Vixen might also be somewhat weaker than Queen.

In case you want to make a tightly balanced game rather than one that wildly favors one of the players: it is quite easy to play-test such setups with configurable variant engines like Fairy-Max or Sjaak II. You are only using 'regular' chess pieces (i.e. without any peculiar side effects on squares other than they move between), and in fact only elementary slider-leaper compounds, and it should be quite easy to configure the engines for that. Then you can just have the engine play a couple of hundred games to see who has the advantage.