The Peace-Chess Challenge

[Henk]

I don't understand how you can create a good evaluation if you don't know much about a game.

[Evert]

Does it make sense to search release chains using some other search strategy? Like using proof-number search to solve tsume-problems in Shogi?

[Sven]

I don't understand how you can create a good evaluation if you don't know much about a game.

The challenge is to learn more about that game. That is exactly what HGM has started to do. I guess currently neither himself nor anyone else knows how to create a good evaluation for this game. You can start by writing a (more or less clever) search. Of course at some point you need an evaluation. One possible approach might be automatic tuning but you still need some minimal eval knowledge, and you also need some reference values. So basically you are right, in the beginning it will be hard to write an evaluation function.

But one thing is for sure: you will not solve it if you give up

My first approach for Paco Shako would be to write an evaluation only based on
- material (considering each possible piece combination in a pair as a different piece type),
- PST (piece-square table), and
- mobility.
(And possibly king tropism, see below.)

For material I think that single pieces of color C and type T should be worth more than pairs in which C has a "material advantage" corresponding to the value of T, e.g. a single white rook should be worth more than a pair consisting of a white queen and a black knight, because the placement of that queen is not fully under control of C.

For PST I think that basically similar methods like in standard chess could be applied, like centralization, pawn advancement, bishops on long diagonals, penalty for knights in corners, ...

Mobility is different for single pieces and for pairs. For single pieces it is probably (in a first approach) similar to standard chess. Pairs can only move to empty squares, or participate in a release chain. The latter is "something to learn more about it", see HGM's last posting. The former could be seen color-wise, i.e. the mobility of the white piece in a pair counts for white and vice versa.

Maybe king tropism is important as well so one could add it as a fourth component. I would not be surprised if someone would find out that a clever king tropism evaluation is already sufficient for a strong engine since I got the impression that this game is very tactical and attacking the king properly is the basic strategical element.

Whether tapered eval should be applied is unclear to me since I don't know whether there is really something like "endgames" in this game. Hugging a single enemy piece increases the number of pairs on the board by one, and when reaching 15 pairs the game is a draw, so the game phase might be determined by counting the remaining unpaired material. Also more pairs means more empty squares on the board. But even with 14 pairs you still have 18 occupied squares which is a lot more than in classical chess endgames, and I'm also not sure whether different eval weights for "close to opening" and "close to endgame" positions would even make sense - at least I think they wouldn't in case of king safety (I don't believe the lone king should walk to the center at any time in this game ...). My feeling is that tapered eval could be skipped in the beginning.

[hgm]

For material I think that single pieces of color C and type T should be worth more than pairs in which C has a "material advantage" corresponding to the value of T, e.g. a single white rook should be worth more than a pair consisting of a white queen and a black knight, because the placement of that queen is not fully under control of C.

That was my initial idea too. But I am slowly being converted to thinking exactly the opposite. Paired pieces are worth more than lone pieces, because they can be part of networks, which basically makes them Amazons, because anything could come out of the square they are on by traveling over the network. And they could come out at other stations of the network as well, rather than just on the squares they would attack if they were a single piece.

It is true that the current tactical value is less than that of a kown piece when only few pairs exist, and no networks can be formed. But the only way to get a big network is to start with a small one, and it will be a race to develop a powerful network. So the eval should encourage it to pair your pieces, preferably with weak opponent pieces, in particular with Pawns. Because by this your network will grow more than his.

It is a bit like having Rooks in orthodox Chess. You kow that in the early middle-game their tactical value is quite low compared to Bishops and Knights. But because you know that in the end-game they are much stronger than B and N, you put a high piece value on them even in the opening, to make sure they will be preserved for the end-game. Similarly you must invest in building a network in Paco Shako, because you know that there will come a time that there will be many pairs, where the paired pieces will get very strong.

[Sven]

For material I think that single pieces of color C and type T should be worth more than pairs in which C has a "material advantage" corresponding to the value of T, e.g. a single white rook should be worth more than a pair consisting of a white queen and a black knight, because the placement of that queen is not fully under control of C.

That was my initial idea too. But I am slowly being converted to thinking exactly the opposite. Paired pieces are worth more than lone pieces, because they can be part of networks, which basically makes them Amazons, because anything could come out of the square they are on by traveling over the network. And they could come out at other stations of the network as well, rather than just on the squares they would attack if they were a single piece.

It is true that the current tactical value is less than that of a kown piece when only few pairs exist, and no networks can be formed. But the only way to get a big network is to start with a small one, and it will be a race to develop a powerful network. So the eval should encourage it to pair your pieces, preferably with weak opponent pieces, in particular with Pawns. Because by this your network will grow more than his.

It is a bit like having Rooks in orthodox Chess. You kow that in the early middle-game their tactical value is quite low compared to Bishops and Knights. But because you know that in the end-game they are much stronger than B and N, you put a high piece value on them even in the opening, to make sure they will be preserved for the end-game. Similarly you must invest in building a network in Paco Shako, because you know that there will come a time that there will be many pairs, where the paired pieces will get very strong.

But with a decreasing number of unpaired pieces your ability to use that network decreases as well. If you pair all your seven non-pawn pieces then you only have unpaired pawns left, and who knows whether you can keep the ability to trigger your network only by using pawns? It is certainly true that each release chain can release a different piece at its very end so there are also some dynamic changes, but in general I think you have less flexibility if you mainly have pawns that are fully under your own control.

Also when pairing your queen with a rook or a minor piece you give the opponent a way to quickly move your queen away to some irrelevant place on the board. While when pairing a minor with an enemy queen it is you who could do so. And you would certainly want to avoid moving a pair of your minor and his queen to an active, important place since this would improve his network more than yours. So you would try to carry away his queen with your minor piece, just like you capture it in standard chess.

Your proposal of encouraging to hug minor enemy pieces with friendly major ones would also imply that hugging a major piece with a minor one should be discouraged (because the evaluation should be symmetric so that an advantage for one side is a disadvantage for the opponent). That sounds wrong to me.

[hgm]

Well, it certainly is counter-intuitive. But I am conviced now it is certainly true for Pawns: it is bad to hug the opponent's piece with your Pawn. It will never contribute to your own network because the Pawn moves irreversible, and it will contribute a Queen to the opponent's 'cloud'. And the Queen can easily position itself on a square where the Pawn cannot subvert its location, because that Pawn has no moves there.

For minors it is somewhat more dubious. But a Queen is much more likely to make a reciprocal attack with a Bishop or Rook (and thus form a network core) than a Knight. So it seems better to have a paired Queen than a paired Knight.

Having only Pawns as free pieces is probably bad. Although when some of the Pawns attack a pair they could liberate your piece in that, and possibly trigger a network action. I guess you should at least keep one lone piece more mobile as a Pawn.

That both players can move the same pair remains a source of worry for me: it seems that between good players this could easily lead to an impasse, where both keep pushing back and forth the same pair. I already discussed with the inventor what could be done against this (after he drew against my engine this way). My preferred solution would be to forbid moving a pair that the opponent just moved.