Gothic Chess

Gothic Chess is a very interesting and exciting game. A decade or so ago I broadcasted engine-engine tourneys for 10x8 variants with the Capablanca pieces, Gothic Chess being one of the setups they had to start from. There existed many engines, some stronger than others, and the games were very interesting to watch. But then the interest amongst programmers subsided, and at some point there were no new engines or versions, and continuing the event ("Battle of the Goths") became pointless, as it would just repeat the games of the previous year.

I guess nowadays it would be pointless too, as Stockfish can now also play Gothic Chess, and would blow all other programs away.

As to the mentioned paper about piece values: I think this is a bit outdated. With the advent of strong computer programs, which can play many thousands of high-quality games in a few days, empirical values have become known for the Chancellor and Archbishop, and especially the latter turns out to be far more valuable than methods based on move counting suggested.

The unexpectedly high Archbishop value also undermines much of the criticism against Capablanca's setup; this analysis was based on the Chancellor being worth more than Archbishop + Pawn. But in reality The difference between C and A is only a quarted of a Pawn, while Queen minus Archbishop is about 75 centiPawn. (So that with Q vs A+P the Archbishop has the upper hand.)

HG, are those values true only for Gothic C. or for all knighted-family over a 10x8 board?

For all the 10x8 variants with the Capablanca pieces. I suppose this is by definition, as they all have the same material, and piece values are by definition averages over all positions. (Never mind how exactly that average should be taken.) In fact when I did the games to measure them, permuting the back-rank pieces in the initial setup was an important way to force game diversity in the computer self-play games. The values Q=9.5, C=9, A=8.75 are also approximately correct when they are playing as Queen replacements in a FIDE army on 8x8.

Piece values can depend on the total material that is present, and the underlying idea that the total strength of an army can be the sum of the values of the individual pieces in it is just an approximation. If the armies are sufficiently diverse, it is a reasonably good approximation. But it completely fails when you play (on 8x8) 7 Knights vs 3 Queens (in the presence of Pawns), where the Queens stand virtually no chance. (While the classical piece values predict an advantage of about 6 Pawns for them!) This is a consequence of the 'leveling effect', which diminishes the value of strong pieces in the presence of enemy weaker pieces.

In orthodox Chess the leveling effect is never very important, but in Gothic Chess (and similar 10x8 variants) it is very noticeable: in orthodox Chess a Queen is much better than Rook + Knight, and you would need between one and two Pawns of compensation. This is similar in Gothic Chess, when the Chancellor and Archbishop are already traded out of the game. But it is not true when C and A are still on the board. Then R+N is significantly stronger than Q. The reason is that R+N strongly hinder the remaining C and A, which have to avoid being traded for them. While the C and A that face a Queen can pretty much ignore the latter, as long as they stay protected.

The high Archbishop value is a bit of a mystery. The most obvious explanations for why the C-A difference deviates so much from the R-B difference can be falsified. E.g. breaking the color binding has very little effect on the value of a pair of pieces; a Bishop with an extra non-capture step backwards is worth a bit more than a plain Bishop, but the value increase is almost exactly the same as when a Knight gets such an extra step, and is thus purely tactical. Mating potential also contributes very little to piece value, as in most games enough Pawns remain to provide it.

My currently favored theory is that it is worth more to attack orthogonally adjacent squares than to attack isolated or diagonally adjacent squares. This could be the consequence of the Pawn move, by allowing the piece to attack both the Pawn and the square it could move to. (But for now this is just a conjecture; I have never measured piece values in a context with Berolina Pawns.) From watching games I got the impression that Archbishops are exceptionally adept at destroying enemy Pawn chains.

Anyway, by not just counting possible target squares, but adding a bonus for each orthogonally adjacent pair, we can explain why a Rook is significantly stronger than a Bishop even on a cylinder board (5 vs 4 Pawns), where they each always have the same number of moves. And when you add the Knight (or Bishop) moves to a Rook you create 8 new orthogonally adjacent pairs, while adding a Knight to a Bishop creates 16.

very interesting. Thank you

This is waaaaay over my head now.

To Musketeer:

I have not heard of Gemini Chess. Until just now

The movies are on the Gothic Chess site now displaying Trice's Chess as the new name. It's the one ending in ".info" and I don't know how to link to it from a post.

Fascinating analysis by HGMuller! Now I understand why the Archbishop seems much stronger than the 7 points I thought it was worth. If anyone wants to try Trice Chess you can find me at https://greenchess.net/rules.php?v=gothic

I can't find Janus or Gothic or anything on that green chess site. That layout sucks.

Value of 7.75 for archbishop make sense ?

I'm against any chess variant that require a different kind of board and number of pieces ,that's just stupid.

Yeah, well, take it up with Bird and Capablanca.  They had their reasons.

I think you have to sign up first, then things become clearer...  ;-)

In Janus I give it 7. It's not like your opponent is going to give you 0.25 pawns as change

Well you're doing an awesome job all by yourself.  There's only 8693 chess variants out there. Congratulations on your success.

Could you please elaborate why 🙂

That is a gross underestimation. (Even the 7.75 is.) The value in Janus Chess should be identical to that in Capablanca / Gothic. It should hardly matter whether the third super-piece is an Archbishop or a Chancellor. Playing by such a low value for the Janus you would make many losing trades, giving the Janus for material that is no match for it. E.g. in an end-game of a Janus versus Rook + Knight, and (say) 5 Pawns each, the Janus would nearly always win, and you would happily trade into that end-game if you think Janus = 7 and R+N = 8.

As to the quarter Pawn: you won't be able to trade it for a quarter Pawn, of course, but it just elss you that you won't be able to have exact balance in an unequal trade. (Assuming all other pieces would be an integer number of Pawns, which of course they aren't.) When a piece would be worth 5.25, and a Rook 5, it just means that trading it for a Rook put you at significant disadvantage (of the order of the initial-move advantage), while trading it for Rook + Pawn would be a good deal, and give you a 3 times larger advantage, in terms of winning statistics.

So you it would be wrong to trade such a piece for a Rook (and no major positional compensation) voluntarily. OTOH, the loss in such a trade is certainly survivable, so you should not try to avoid it too fearfully. That would limit what you can do with the piece too much, which also depresses its value. This is the leveling effect: if two pieces A and B are very close in value, the cost of trade avoiding by the intrinsically more powerful one can be higher than the difference, so that in practice, when playing against each other, they are best considered equal. Treating a piece as better makes it worse! You would only notice that A performs a bit better than B when they play against (the same) material that doesn't include A or B.

@HGMuller I'm only about 1800 FIDE and have only played about 40 games of Janus. In Janus, we have two of them, and no unusual "Janus for other stuff" trades come up that often. Usually it's Janus for Bishop pair plus or minus a pawn. Sometimes Janus for Rook and a bunch of pawns, but rarely. By then it already known who is going to win or lose. Janus players don't have a lot of source material. We have no "heroes" to follow. Nobody to show us the way. 

Bishop is closer to Rook on 10x8 than on 8x8; roughly we have N=3, B=3.5/4 R=5, J=8.75, Q=9.5. So trading a Rook for first Bishop (i.e. breaking the pair) + Pawn is already an equal trade. But this means BBP = 8.5, and that is quite close to an equal trade. I guess it depends a bit on how many Pawns are around, as Pawns are willing victims for a Janus, and difficult to protect by Bishops (which cannot protect each other). Giving J+P for the B-pair would be plain losing, after J for B-pair you will have to fight for a draw, other material being equal.

Janus for Rook + Pawns is pretty bad for that reason: for one you would need about 4 Pawns to break arithmically even. So that you must have a lot of Pawns, which the Janus then will handsomely exterminate in the end-game. Besides, Pawns cooperate very poorly, and should merely be considered 'change' when comparing other pieces. Trying to compensate a piece by just a huge number of Pawns (e.g. an end-game of Queen vs 10 Pawns, or Rook vs 5 Pawns) almost never works. The Pawns get toasted. If a material imbalance involves 3 or more Pawns, the Pawns become a liability rather than an asset, because the difference in piece material gets so large that you cannot effectively protect your Pawns from the opponent's superior attack force, and will simply lose them.

It makes sense to me that bishops benefit from the board being bigger, but shouldn't rooks and queens also benefit from that? Is the rook still only worth 5 points? Is the value of the bishop pair worth more or less on a 10x8 board compared to 8x8?