Comments/Ratings for a Single Item

VARIANT CHESS Volume 4, Issue 29 - Autumn 1998

On page 10 Paul V. Byway writes: "Once again it is seen that a bishop gains most from the wider board." He was discussing a drawn ending K+R+P against K+B in Modern Courier Chess (12x8 board). I had previously assumed that the Bishop would not improve much on a 12x8 board, being still limited to a maximum move of seven squares. But Byway's detailed analysis is more convincing than my own guesswork.

I still believe that the WA, FA and WDA are each worth three-quarters of a Pawn more than the original estimates given here. For this game: Knight = 3 = Work Elephant, Lead Elephant = 3.25 and Bishop = 3.75 The WA is a solid piece that continues to impress me. The FA is used in many chess variants - where it seems close to a Knight in value, perhaps a quarter-pawn less. The Lead Elephant may not attack any more squares than the FA, but the increase in mobility (also no longer colorbound) should be worth another half-pawn. Time will tell.

The Interactive Diagram estimates the sWAAF stronger than a Bishop. I suppose this has to do with blocking of the slider move. The Bishop might appear to have many more moves as an Alfilrider, but the extra moves are all very distant moves. The larger the board, the more distant they are. And on a board that isn't empty, but 25% filled (as the Interactive Diagram uses for value estimation), those very distant moves will almost always be blocked. So it is much better to have the unblockable sWF steps of the sWAAF.

That doesn't explain the good performance in the mentioned end-game, though. The board there is so empty that the Bishop only rarely finds two pieces on its diagonal, so that blocking hardly occurs.

H.G. wrote: "The color binding does not make much difference. If I give the Bishop an extra backward non-capture (BbmW) to break the color binding, the sWAAF still wins almost all games from the given position."

That's interesting. Without recalling how I used to do such calculations exactly, I'd roughly estimate those two piece types as worth about 5 pawns and 5.66 pawns in value (for middlegame at least), on that board size, respectively. The huge winning score of the latter piece type may have something to do with the latter piece type being way more effective in (most?) endgames.

The color binding does not make much difference. If I give the Bishop an extra backward non-capture (BbmW) to break the color binding, the sWAAF still wins almost all games from the given position.

Yes, well a N is about the same in value as a B on 8x8, in spite of the N having less mobility on average. There is the colourboundness of the B to compensate/consider.

I was wondering what is it that makes a Kraken so powerful, then.

That it attacks more squares than any other piece on the same board?

BTW, I now tried a few end-games with sWAAF vs B from this position:

where the unorthodox piece represents the sWAAF. The Bishop almost always loses. The only game I have seen it win was where black was so stupid to trade sWAAF for B + Pawn when it was several Pawns ahead already, leaving an unstoppable passer for the opponent that promoted first (to Queen). Because I was playing at fast TC, and it did not have the search depth to see the promotion. I suppose these kind of mishaps could be prevented by programming such a high value for the sWAAF that it would never consider trading it.

So it seems that despite its smaller average mobility the sWAAF is much stronger!

H.G. wrote: "The percentage of the board that a piece covers is not relevant for the relative values. Absolute values are meaningless."

I was wondering what is it that makes a Kraken so powerful, then.

The percentage of the board that a piece covers is not relevant for the relative values. Absolute values are meaningless.

It is true that sliders gain in value compared to leapers on larger boards. There is another effect as well: sliders that can 'stop and destroy' an isolated Pawn (like a Rook, Queen or Dragon Horse) gain strength compared to sliders that cannot (like Bishop or Nightrider). On large boards one is typically left with a scattered isolated Pawns, some of those passers. A Rook just seeks those out one by one, and then captures them. A Bishop, however, can at best stop their advance, but thenmust remain dedicated to doing so. It can then no longer effectively act against other passers. I noticed that on 12x12 boards it was very difficult to balance an end-game of R vs B with extra Pawns on the side of the Bishop. (As long as there were some Pawns on both sides, as pure R vs B gets even more drawish on large boards as it already is on 8x8.) The Rook just seemed to keep winning, no matter how many Pawns I added on the other side.

[Edit] This suggests (average) mobility might not be the dominant factor on large boards. I did some experiments with an interesting piece: AAFsW. It turns out this piece can always force mate even on a 16x16 board (in maximally 96 moves). But the average mobility of AA on 16x16 is 8.75 (same as B on 8x8!), while B on 16x16 has on average 19.7 moves. So even with the maximally 6 moves of the FsW added, AAFsW has poorer mobility than B. Yet I expect it to easily beat a Bishop in an end-game with otherwise only Pawns, because it has a 'seek-and-destroy' capablity for Pawns. When I have time I will try some such end-games on 14x14 with Fairy-Max.

Hi David

In assessing the values of Qs on rectangular or square boards, I didn't like the idea that the Qs value could grow enormously if it were simply valued more on bigger boards. So, I set some limits on R and B (R+B+P=Q). For a R I took it as a standard candle - equal 5.5 on almost any size board (except very small, like 2x2). That's Euwe's value for the R on 8x8 (chess).

For a single B, I did not want it to be worth 4 pawns or more on most any size board, as in an endgame a B almost never can restrain 4 passed pawns. So, 3.99 maximum, e.g. for extremely large boards.

For Kts, being short range pieces, smaller boards are better, so N=3.5 on 8x8, N=3 on 10x10 and I worked out N=3.38 on 10x8 - the average number of squares a N can reach on 10x8 affecting the value; notice there are proportionally (compared to number of board cells) many high mobility cells for minor pieces on rectangular boards, both for N and B, thus boosting their value (Bs also hit more of the enemy P-line on rectangular 8 rank boards than say 10x10). That's why I have B=3.75 on 10x8 or 12x8 (I found having a formula for B's 'exact' value difficult). On 10x10 square board I was content to have B=3.5 still (as on 8x8), making it more valuable than N, yet Q still about 10 (exactly in fact).

Notice too that on very large boards, the value of sliders is in a way decreased by the fact that the proportion of the number of cells that a slider hits is decreased compared to board size being large (e.g. high percentage for Q on 8x8, not so much on 12x12).

1. h3 g5 2. Kh2 Ll6 3.Ki3 Qj4 is a very foolish mate. If the type font is confusing, Black's second move is "ell-ell-six".

While the stated NBRQ values are suitable for a 10x10 board, the Bishop simply cannot attack as many squares on a 12x8 board. Bishop = 3.50 and Queen = 10 seem more appropriate for this game. I reserve judgement on the Elephants for the time being - currently working on a new game with "Wafflephants" on 12 columns.

Anthony Viens wrote on 2020-04-14 UTC "I quite like the simple approach you have to this variant.

However, both the working elephant and the lead elephant are fairly similar pieces. They are both very good pieces, but I would think in a game with standard chess pieces +2, that the 2 additional pieces would be better off more divergent.

Just a thought...."

I'd wondered about how to compare 'divergency' of piece types in some sort of objective way. In case of comparing a Q to a R, a Q is a compound of a full R and a full B. In case of a lead elephant (lieutenant from Spartan Chess), it is a compound of a large chunk of a work elephant with a ferz (i.e. the lead elephant is almost clearly a stronger piece than a work elephant (phoenix), and seems so on average I'd guess).

The work elephant has 8 capturing moves and 8 non-capturing moves. The lead elephant has 4 of the former, and 6 of the latter, when comparing it just to the work elephant's; thus you might say a lead elephant is a compound of 10/16th of a work elephant, plus the full ferz piece type (a whole new different piece type), which has 4 capturing moves and 4 non-capturing moves. So, 10/18 ways same as a working elephant, 8/18 ways different.

Maybe a lead elephant is not at all that striking in appearance and/or effectiveness compared to the Q (a compound of R and B), as a ferz is a less fearsome piece than a B, and on the graphics of CVP the ferz is often just denoted by the modest 'x'; also, the lead elephant has to keep the alfil symbol on CVP graphics, whereas the Q gets a whole new symbol (rather than a R somehow crossed with a B).

Note that if you compare a FAD to a WAD (aka Champion), the WAD is 16/24 ways the same and only 8/24 ways different. At least a Champion gets its own distinct symbol sometimes on CVP site, with no elephant or D symbols showing for it, unlike for the FAD.

I quite like the simple approach you have to this variant.

However, both the working elephant and the lead elephant  are fairly similar pieces. They are both very good pieces, but I would think in a game with standard chess pieces +2, that the 2 additional pieces would be better off more divergent.

Just a thought....

Here's a (10x8) variant I stumbled onto that has castling rules somewhat similar to that of Wide Chess, in that a king may pass over squares under attack (though not finishing on such a square, nor is castling legal if the K is initially in check). So, a sort of precedent for (part of) the special fast castling rules used in Wide Chess (and subsequently in a number of other CVs I've invented since):

https://www.chessvariants.com/large.dir/21st-century-chess.html

Here's another sort of precedent, perhaps, in that in the following (12x12) CV, a king, if not in check, may (with its initial move only) leap to an unoccupied (& unattacked) square on its back two ranks (including possibly 'over' any attacked square)- though this does not include a change of position by a rook or any other piece, as part of the special leap process:

https://www.chessvariants.com/large.dir/quinquereme.html

I've added (to the Notes Section of this game's page) a paragraph about the mutator variant possibility of substituting champions (also known as WADs) for the waffle pieces used in this variant, in case anyone ever wishes to experiment. I've also made a note that a WAD+K can force mate against a lone K on a 12x8 board, as Dr. Muller once related.

[edit: Note that another mutator variant idea of mine (Wide Frog Chess) would be Wide Chess to be played with Frogs in place of the Lieutenants in the setup. Frogs move like threeleapers (leap 3 cells by rank or by file) or move like ferz' (stepping one cell diagonally). On 12x8 I'd put a frog at 3.33(or 3.5 approx.).]

No matter, it is not importan, I do remember thinking it is a good idea but not much besides that :)!

Hi Aurelian

I was going by H.G.'s comment suggesting the lieutentant to me on the 13th November in the Diagram Testing Thread. You subsequently asked if he was correct on the Betza notation he gave for that piece (you mentioned the captain piece type in Spartan Chess in your question , but I assumed you meant the lieutenant). I cannot seem to find other discussion about the lieutenant piece type, except for when I subsequently named that piece myself at other times.

Are you sure it is not I who has suggested the Spartan lieutenant? I remember at least reinforcing the idea. But please don't change the article for such small minutia :)!