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# Variant pieces' values

• #1

Just wondering what people think in regards to the value of pieces from chess variants. http://www.pathguy.com/chess/ExoticCh.htm

There's a chessboard which you can change the size of and add weird pieces and then play on(some bugs though, probably). Now, I know you can't really fix values on these piece, but there are a few which I am wondering how people would rate in regards to others(for the whole game, on average).
For example, if you replace instead of a queen, a "marshall"(or whatever you want to call it, rook + knight, pawns promoting to whichever pieces they have on their side initially) for either colour, whose side would you prefer?(queen/marshall) Or a "pegasus" (bishop + knight) instead.
Also, I'm curious about the various types of pawns(in place of pawns...) and jumpers(in place of knights).

Just some of the ones I'm curious about -

Marshall/pegasus/queen(starting on queens square).

2,1 jumper(knight)/3,1 jumper/ 2,2 + 2,0 jumper (would the knight be valued over the other two due the fact that it could traverse across all the squares?)

Regular pawns/Berolina pawns(move diagonally forward and capture forwards)/"crab"(move diagonally and capture diagonally forwards)/Chinese pawns(move and capture forwards)  {all of which can promote}/Foot soldier(doesn't promote, moves straight back or forwards, captures diagonally back of forwards)

Now, I know I'm being very vague, but which would you value(on average in any given position) over one another.

• #2

In my opinion, a queen is worth more than a marshall.  ( In Seirawan chess the R+N is called Elephant and the B+N is called Hawk. )  Also, in my opinion a rook and a Hawk are almost equal.

I like your idea of replacing the Q with an Elephant or Hawk on the Queen's square.  I like that idea more than Seirawan's idea.

• #3

Marshals are generally given a higher ranking than a Queen, but just barely.

Berolina pawns are considered by most to be equal in value to Standard Chess (SC) pawns.

Chinese pawns promote faster than SC pawns, so again, probably similar value.  Chinese pawns also normally play in a board with much fewer pieces, increasing their value.  On a normal board, with normal promotion I'd estimate them to be valued at about 1/3 a normal pawn.

Foot Soldiers are actually valued higher than a pawn, at about 1.4.  Moving backwards is a big bonus for a pawn structure and promotion rarely happens.

• #4

The queen, marshall, and paladin are what I consider level two pieces as they are the combination of two pieces.

The queen has the most scope because of the movements of the rook and the bishop.  In open positions she would be stronger than the marshall.

The Marshall is the second most powerful piece because he has the movements of the rook and the knight.  In closed positions he would be stronger than the queen.

The paladin is the least powerful of the three pieces.  This piece has the movements of the knight and the bishop.

• #5

How would you value what you call a Paladin compared to a Rook?

• #6

In most analysis you find the M > Q > P, but I think it's actually M > P > Q... but that's my observation and may not jibe with other's views.

The comparison of Paladin to Rook is normally P=6-7 R=4-5

• #7

Now this is an old thread.

• #8

Indeed, but now that it surfaced it is important to put things straight. The value of Marshall-Chancellor-Elephant (RN) and Pegasus-Archbishop-Hawk (BN) has bee accurately measured in relation to the orthodox Chess pieces (by play-testing from materially imbalanced position), and on an 8x8 board is:

Q=950, RN=925, BN=875, R=500, B=N=325 (but B-pair = 700), P=100.

The (3,1) leaper (Camel) is next to worthless on 8x8: in the end-game it almost always is lost without compensation. The only value it has is that you can quickly try to trade it for B or N, while the board is still crowded, and it is difficult for the 4 minor pieces to dodge all Camel forks. That makes the opening value of the Camel about 250.

The (2,2) + (2,0) leaper was not tested, but should be worth very little, as it can only acces a quarter of the board.

• #9

@HGMuller

What method was used? I love seeing how people come up with way to measure pieces. I have a very bizarre method that no one uses, but that's my thing.

• #10

Computer self-play from materially imbalanced positions. E.g. if you replace the Queen of one player by a Chancellor, and play a few hundred games, the side with the Queen will score about 58%. If you then delete an extra Pawn for the Queen side, the Chancellor wins by ~58%. So Q is halfway between C and C+P. You repeat that with all kind of other combinations.

• #11
HGMuller wrote:

Computer self-play from materially imbalanced positions. E.g. if you replace the Queen of one player by a Chancellor, and play a few hundred games, the side with the Queen will score about 58%. If you then delete an extra Pawn for the Queen side, the Chancellor wins by ~58%. So Q is halfway between C and C+P. You repeat that with all kind of other combinations.

That is extremely clever design. I assume this is under end game condition or do you start with both sides fully set? Isn't it deterministic or are you using neural networks?

• #12

Actually you deserve part of the credit for this design. It all started when you posted a message here asking for a computer program to calculate mobility of an arbitrary fairy piece when added to a certain opening position of orthodox Chess. As I had a very simple, knowledgeless Chess program, (micro-Max) which could be very easily adapted to support extra piece types moving in different ways, it gave me the idea to actually do that, and evaluate the fairy pieces in entire games, rather than just a single position. This is how Fairy-Max was born.

I mostly do this under opening conditions: start from a FIDE setup, and replace or delete a few of the pieces, to get material balanced to within ~1.5 Pawns. If there is reason to suspect end-game values are very different (e.g. for hoppers like the Xiangqi Cannon), I sometimes also do it for end-game positons. (E.g. each side 6 Pawns, and then one side an Archbishop, and the other Rook + Knight.) The problem with end-game positions is that they often are already decided, so that scores are close to 100%, 50% or 0%, and not a continuous range that you could use to quantify the difference. From opening positions even an obviously worse position (e.g. being a Pawn behind) still can be won a fair fraction of the games.

The engine randomizes the first four moves, by adding a random score of about 0.5 Pawn to each move in the root. So it won't give away materal, but otherwise every move is eligibe. That already gives a very good game diversity. If I want to do really large numbers of games, I start from a number of different positions that permute the backrank pieces in a Chess960-like way. And of course I always average results with reversed colors, to eliminate any first-move advantage (or color bias of the engine). That also quadruples the number of start positions (because you can also make black start).

It is also good to test various materal combinations. E.g. if replacing a Queen by a Chancellor in the standard FIDE opening position makes the score drop to 42%, I also test how well a Queen does against 2 Rooks (i.e. replacing Q by R for one player, and delete a Rook for the other) or 3 minors, and how much the score then drops when I pit the Chancellor against 2 Rooks or 3 minors. To be consistent the score should always drop by ~8% when you replace Q by C in an opening position. (The latter being defined as al pieces being on the back rank, ad all Pawns on the rank in front of it.)

The engine is a normal alpha-beta searcher, with very basic evaluation: just piece values, a bonus for centralizing some of the pieces, a penalty for moving the King (but a bonus for castling), and a rudimentary Pawn evaluation that encourages pushing Pawns to promotion when the time is ripe for that. No neural networks. To get realistic play, you have to put in a approximately correct piece value, although this is not very critical. E.g. if you play the games with an engine that believes the Chancellor is worth more than a Queen, the Chancellor will still lose, probably by a differerence of even more than 8%. As long as the Q and C value is different, always one of the players will try to avoid their trading, no matter how misguided that may be, and you will learn how much damage they will do to other pieces. If my initial guess for the value is wrong, however, I just do a scond iteration of the experiment, with the value deduced from the result of the first. Of course if the values are very wrong, the results will be crap. E.g. if I will set the value of an Archbishop to below that of a Rook, it will never discover how strong an Archbishop really is, because it is strong enough to always force a trade for a Rook (which it will believe to be a gain), no matter how much the Rooks will try to avoid it.

• #13
HGMuller wrote:

Actually you deserve part of the credit for this design. It all started when you posted a message here asking for a computer program to calculate mobility of an arbitrary fairy piece when added to a certain opening position of orthodox Chess.

Whoa. I'm blown away and apparently I don't have to do the math on a spreadsheet anymore. That's awesome! Thank you for creating such a useful tool! Can the public use it or are you still working on it?

Again, amazing work and from the entire variant community "thank you!"

• #14

The Fairy-Max engine is available as part of the WinBoard binary package (for Windows,e.g. http://hgm.nubati.nl/WinBoard-AA.zip ), for Linux from the repositories as 'fairymax' (to be used i combination with the 'xboard' package), and as OSX App from the WinBoard forum ( http://www.open-aurec.fr/wbforum ). Configuring it for new variants / pieces (through the self-documenting fmax.ini file) is unfortunately not very user-friendly.

Note that there exist other configurable multi-variant engines that can work under WinBoard/XBoard, which could be used in a similar way (and slightly differ in what kind of pieces they can and cannot handle), such as Sjaak II or NebiyuAlien.

• #15

I'm on a Mac, so I'll look to see if I can get it to run here. If I improve the docs, I'll forward you a copy.

• #16

Sorry, I was wrong about the WinBoard forum link. It is not .fr but .com. The place where the OSX App can be downloaded is http://www.open-aurec.com/wbforum/viewtopic.php?f=19&t=53680 .

• #17
[COMMENT DELETED]
• #18

Our last two messages probably crossed.

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