Ratings & Comments

The main reason I gave the name "Decimal Chess" to this variant  because I did not find any Chess variant that went by that name. I  wanted to avoid stealing the name of another game and including any part of my name when naming the game. I wanted to give the game a name that referenced the size of the board, but I couldn't a good alternative. I will put a note on the page to avoid confusion until I decide on an alternative.

This is certianly an interesting idea.  The assignment of chip count to pieces though seems strange.  Why should a rook only be 3 chips?  It seems you'd immediately want to turn your bishops and knights into rook+pawns.

I'm sorry, but this game needs a different name.  "Decimal Chess" is existing terminology dating back at least a hundred years that refers generically to chess variants played on a 10x10 board.  It would not be appropriate at this point to use it as the proper name of a new variant.  Perhaps "DeWitt Decimal Chess"?

On /r/shogi today, someone asked where they could get BCMShogi, and the person who answered provided a link to the final version of BCMGames, which is later than the version I previously had here, and unlike that version, this one works. So, I added my Shogi graphics to it and made a new distribution. Since it also supports other games, I will look into adding graphics for other games. For now, this new distribution just adds the Shogi graphics I previously added to earlier distributions. I also updated the screen shots so that they say BCMGames instead of BCMShogi.

James Zuercher wrote on 2018-12-09 EST

Have the piece values on an 8x10 board been determined for the following variant pieces? Dragon Horse, Dragon King, Crowned Rook, or Gnu. If so what are these values and how were they determined?

In the better late than never spirit, now that there's a bit of a lull, I'll give you my own roughly estimated values calculated just now for such pieces, and how I reached them (noting first that a Crowned Rook is another name for a Dragon King, as is noted in CVP's Piececlopedia):

Dragon Horse (Bishop+Wazir compound piece) I estimate as =B+Wazir+P,

where largely based on the average number of squares a B can reach I guess [single] B roughly=3.75 (note I rate B=3.5 on 8x8, and prefer a B always worth less than 4 pawns),

Wazir = (Guard-P)/2 (note Guard=Ferz+Wazir compound, which I rate as =Ferz+Wazir+P, with Ferz approx.=Wazir); Guard's value on 8x10 computed by my home formula of 32x(max. number squares guard reaches)/(number of cells on board)=32x8/80=3.2 in this case (note this home formula doesn't seem to work too badly for a large range of board sizes, but there are limits). Thus Wazir=(3.2-1)/2=1.1 on 8x10.

Thus Dragon Horse on 8x10= 3.75+1.1+1=5.85 is my estimated value.

For Dragon King (Rook+Ferz compound piece) it's rated by me =R+Ferz+P where I estimate R=5.5 (unchanged from what I give it as on 8x8).

Thus Dragon King on 8x10= 5.5+1.1+1=7.6 is my estimated value.

For Gnu (Knight+Camel compound piece) it's rated by me =N+C+P where Camel is still assumed by me=2 on 8x10 (like it is commonly given by other people, and myself, as for camel on 8x8). I rate a Knight =3.5 on 8x8, but for board sizes other than that I'd apply a home formula which is rather complex, and doesn't work for every possible board size (similar to my Guard formula given earlier). If I've got it written down right, I estimated N=3.5-(0.25x{[no. rows]-8}/2+0.25x{[no. columns]-8}/2)+(Average number of squares N can move to on empty board-5)/8 for a given board size. For 8x10, I've thus worked out an estimated value of 3.38 for a N. Note that, like for the case of a B, on 8x10 a N has a considerable number of juicy squares in terms of influence, if it reaches any of them (which in the case of a N helps compensate somewhat for the greater board size than 8x8, IMHO).

Thus Gnu on 8x10=3.38+2+1=6.38 is my estimated value.

Now that you mention it, in the Champagne Chess preset's index page thread, I quietly gave, with edits to previous Comment(s) of mine, a number of mutator variant ideas I've since came up with, which perhaps didn't deserve their own pages (who knows, they may get tried out in actual play via unofficial presets created later on). I did a similar thing with a number of other edits to index/rules pages of mine. So far I have somthing like 8 mutators altogether that may get tried out some day. The use of the Bishop-Pawn piece type could be one way to help spawn further variants and/or mutators of such, depending how much I or someone else feels up for it at some point. Hopefully any such games could make for an artistic use of that piece type.

The Bishop-Pawn compound piece is, unlike a Dragon (i.e. Knight-Pawn), currently not listed in the CVP Piececlopedia, at least with a dedicated hyperlink (if given at all). It'd be slightly less powerful than a Dragon because the pawn component's available capturing moves would already be part of the bishop component's available diagonal movements, all assuming that like for the Dragon, the piece would not be allowed to promote. Depending on a given variant's setup, I'd assume that like for a Dragon, if it starts on the second rank, it can make a pawn's double step. Like for a Dragon, it would also be able to make en passant captures when possible. The piece figurine is also available in the Alfaerie: Many piece set, as .bp :

I just began play-testing and I like it a lot.  My thoughts so far:

There is a tiny bit of ambiguity as to whether the “same file rule” from Shogi is meant to apply to pawn drops (presumably it is not). I believe it can be played either way. I haven't tested it yet, but to try, the following condition could apply:

A pawn may not be dropped onto the same vertical diagonal of any other non-promoted pawn belonging to the same player.

Or an even stricter alternative:

A pawn may not be dropped onto the same rank or file of any other non-promoted pawn belonging to the same player.

In the illustrations for piece movement, notice how the rook travels through one edge and then through the opposite edge of each square in its path (even if the 'square' curves a right angle), while the bishop travels through one corner and then through the opposite corner of each square in its path, but seems to be prohibited from doing so on the curved squares (from the black bishop's position in the diagram). If this prohibition were lifted, that same black bishop's range of movement would include traveling from one curved edge square to the next and then back across the board horizontally, forming a loop back to it's original position.

Also, although it is not explicitly mentioned in the original rules, I think it's probably a good idea to declare that a rook or  a queen (or a bishop) may not land on the square from which they originated on that turn, even if a path to it exists unobstructed.

Finally, my thoughts about the pawn. The language and illustration of the original rules regarding pawn movement suggests that pawns capturing moves and non-capturing moves are executed in the same way (unlike conventional chess). Optionally, one could alter the rules for pawn movement so that it moves (but does not capture) exactly one square in either of the orthogonal directions that is away from its own side of the playing board or it can capture to the cell diagonally ahead of it (if there is an enemy piece occupying that square).

I just made my copy of the board yesterday, and have only had the opportunity to play-test the original rules.  But yeah, it was a lot of fun!  Thanks!

Once again I'm not sure how to argue with your most recent post, H.G. For that reason, and for the sake of not risking discussing too many points at once, which may in turn multiply (as it seems has been happening), I'll just mainly confine myself for now to answering your query of me, namely:

If I would make a new piece, by starting with a Bishop and replacing one of its Ferz moves by a Wazir move. Would you now argue that a normal Bishop is worth only half as much as this piece, because displacing that one move to a neigboring square made it color bound? Or would you argue that the piece is worth one Pawn more than a Bishop because it is the combination of 1/4 Wazir with a piece that was only handicapped so little compared to a normal Bishop by missing this Ferz move that it had no effect on the value?

The calculation I'd make for such a piece's value is a bit complex. First, I decide that such a piece is treatable as a compound piece of sorts, then I figure out the value of it's components in stages. However, first I need to assume a given board size, namely 8x8. That allows me to figure out what fraction of a bishop is left when a ferz move is taken away from it. A normal B on 8x8 has 10 moves on average on an empty 8x8 board (i.e. 7 minimum, 13 maximum), so taking away a ferz move gives 9 moves on average (just averaging the new minimum and maximum cases, maybe none too precise a thing to do). Thus I'd work out what 90% of a B is worth as the first component of the compound piece.

The second component of this compound piece would be 1/4 wazir (depending on if it was the forward step it would be 2/5 of a wazir, or if it was a sideways or backward step it would be 1/5 of a wazir, based on how I've implemented your previous discussions about the direction of a piece step, but you specified 1/4 wazir this time, perhaps to make things a little easier for me). In this case it does, because I can easily use the value of 1/8th of a guard instead of 1/4 of a wazir (more or less the same thing) which avoids what seems like a worse slight error I get if I used (wazir-P)/4 rather than using (guard-P)/8 - the latter produces the same value as wazir/4 (the only times fractions of pieces might IMHO clearly work out very 'nicely' for me as it were is when division of a piece by 2 is performed, such as a guard broken into its ferz and wazir components, each having values that I deem to be equal, with a Ps worth of co-operativity first subtracted).

Thus, First Component + Second Component + Pawn = value of the [compound] piece you enquired about, according to the way I'd do the calculation (for now, with my imperfect way of doing things). This becomes:

(B-P)x0.9 + (wazir-P)/4 + P = approx. value of compound piece, or (B-P)x0.9 + (guard-P)/8 + P, which becomes:

(3.5-1)x0.9 + (4-1)/8 + 1 = value of compound piece (note I rate B=3.5 and guard=4 on 8x8),

and thus value of [compound] piece that you asked about = 2.25 + 0.375 + 1 = 3.625 on 8x8, which I'd note is clearly far from twice the value of a B on an 8x8 board.

One of the other problems I have to cope with is that this sort of method wouldn't work (in any sort of fashion, at all) if e.g. a wazir's value was necessary to use in a calculation, and it was worth a pawn or less, since wazir-P would then be worth zero or a negative value. This is indeed the case for the value I give a wazir on 10x10, i.e. I put it at 0.75 on that size board (which you objected to, as well, and I'll more or less pass on that, except to note for now that a wazir crosses the board slower on 10x10 than 8x8, which I count as a tangible consideration all the same, though other considerations pro and con may be possible, especially depending on the armies deployed).

Anyway, for 10x10 figuring out the first component I'd do similarly as before, but for 1/4 of a wazir to be computed I'd now definitely first desire to compute the value of a guard, then hope to use the value of 1/8 of a guard (a similar thing as 1/4 of a wazir), i.e. hoping that a guard is worth more than a pawn on 10x10 (if not, I simply have to use wazir/4 rather than (wazir-P)x0.25, with any difference/error being rather small anyway). It just so happens my home formula for a guard's value puts it at approx. 2.5 on a 10x10 board, so I'd figure out 1/8 of a guard by using (guard-P)/8 = 0.1875 (happily the same as wazir/4, again, as it always would be), which in turn is what I'd use for the second component of the compound, if I were to compute its value for on 10x10. The first component I see as worth 12/13ths of a B, so now the compound's value that you asked about (if on 10x10) would be approx. (with having B=3.5 still, on 10x10):

(B-P)x12/13 + (wazir-P)x0.25 +P, or (3.5-1)x12/13 + (guard-P)/8 + P, or

value of [compound] piece you asked about (if on 10x10) = 2.308 approx. + 0.1875 + 1 = 3.496 approx., which I'd note is again nowhere near twice as much as a B's value on the given board size.

I'll have to admit again that my formulae and methods are not completely perfect, and seem unsound (in particular with fractions of pieces), but the values I get with them to date don't seem ever too far out of the ballpark, to me at least. One interesting thought experiment might be what to make of the value of some sort of 'half of an archbishop'. Doing things my way, (archbishop-p)/2 would be the answer, rather than archbishop/2 (or is half an A worth something different altogether?), and clearly A/2 would give a value greater than a B or N if one uses one, or even two, pawns worth of cooperativity between the bishop and knight components. For now, I still just assume one pawn's worth of cooperativity between those two components, so for me on 8x8 archbishop =N+B+P=3.5(approx.)+3.5+P=8 (noting Q=R+B+P=5.5+3.5+1=10), and thus (archbishop-p)/2=3.5 is the value I get for half an archbishop, i.e. about the value of a N or B. That's opposed to archbishop/2=4, or greater than the value of a minor piece. At any rate, there seems to be some sort of consistency with quite a few of the piece values I've come up with over time, in spite of the lack of perfection, at least it seems to me so far.

In a previous post in this thread I dealt at length with how I estimated the value of an alfil and a dabbabah, including how I factored in such things as my x0.5 binding penalties, plus counteracting bonuses for leaping ability and speediness, if you wish to see instances of how I've handled binding penalties in my personal calculations, when compound pieces are not deemed at issue. I've done calculations for the value of a knight in Alice Chess using a way to take into account the type of binding to it that happens on the two boards there, and I came up with a value for the N (and other pieces) close to what the rules page notes gave for piece values (maybe by ZoG?) in the case of that game, at least. The values are on my 4D Quasi-Alice Chess rules page, in the Notes section (note I used the initial chess base values N=B=3, R=5, Q=9 in that particular case, perhaps to try to match the chess base values I thought were probably initially used in the preliminary calculations made, for Alice Chess, by ZoG - I did all that work long ago).

I am in love with many Japanese toys such as kendama, go, shogi and Hanayamas

Regards from Spain

Well, that the Amazon value is just Queen + Knight is what I found when playing games where one player had one of its Knights removed, and an Amazon instead of a Queen. Neither player turned out to derive an advantage from this imbalance, in a match of a couple of hundred games. I was as surprised as you are. Perhaps at some point a piece is already so mobile that some kind of saturation sets in, and extra moves just don't provide that much extra. There also could be a risk penalty for 'putting so many eggs in one basket'.

My point was that your calculation is not self-consistent (and thus certainly wrong) if you use different methods for splitting pieces as for combining them, as split pieces can be recombined to give back the original piece, and that then should not suddenly have a different value.

But we were not really talking about splitting or combining here: you were comparing Knight and Camel, and calling the Camel the closest thing to a color-bound version of a Knight. (Indeed the Camel is the 'conjugated' piece of the Knight, i.e. it would be a normal Knight on the 45-degree rotated 'board' formed by the squares of one shade.) So we are talking of modifying moves to go one square instead of another. You applied a 50% penalty fot the resulting color binding, and that is totally off.

According to this estimation method, a Knight would initially not lose any value when I started to replace the (1,2) leaps one by one for the corresponding (1,3) leaps (as that would not cause color binding), until I replaced the very last move (after which it is color bound), after which it would suddenly halve. I don't think that would happen at all, but that the value decrease would be gradual. Yes, the Camel is significantly weaker thana Knight on 8x8. But IMO that is just because the (1,3) leaps are too large for the board. In games that pit Knight vs Camel I see that the Camels get usually lost in the end-game without compensation, because when they are chased away out of the center, a single move brings them so close to the edge that they hardly have any moves left (as their return to the center will remain barred). So that they are then trapped there. On a (much) larger board you would not have this problem at all, and a Camel might even be worth more than a Knight despite the color binding, because of its larger speed.

This is why I asked about the modified Bishop, (rather than an enhanced one), but I did not see an answer yet. So let me ask you again:

If I would make a new piece, by starting with a Bishop and replacing one of its Ferz moves by a Wazir move. Would you now argue that a normal Bishop is worth only half as much as this piece, because displacing that one move to a neigboring square made it color bound? Or would you argue that the piece is worth one Pawn more than a Bishop because it is the combination of 1/4 Wazir with a piece that was only handicapped so little compared to a normal Bishop by missing this Ferz move that it had no effect on the value?

P.S. It seems very wrong to rate a Wazir (4 captures, 4 non-captures, access to the full board) lower than a Pawn (2 captures, 1 non-capture, confined to the forward part of a single file until it captures, and even then confined to a triangle), on boards of any size. Promotion is surely worth something, but not that much, and it also gets more difficult on deeper boards. Even if you leave your Wazirs just sitting on the back rank as a sort of goal keeper, a Wazir must be able to trade itself for a passer that breaks through.

I had already put such a link in the single-piece version, but it was in an inconspicuous place at the end, usually out of view. I now moved it up to a more conspicuous place (just below the statistics table), where there was a large amount of white space anyway.

I think you are right: the general article logically belongs to the 'puzzles' section. I think the link in the per-piece page should be enough to catch the attention of anyone interested in this sort of thing.

The way it is linked to from the Archbishop page looks fine. One complication occurred to me, though: the statement whether a piece has mating potential can be dependent on board size. This is not the case for an Archbishop, but short-range leapers in general suffer from this. E.g. the fraction of won positions with white to move for King + Gold General vs. King drops from 92.1% on 10x10 to 10.8% on 11x11. We should think a bit of how to handle that. Perhaps by adding a static table in the Notes section of the few Piececlopedia pieces to which it applies.

The one thing I've done so far is to treat a super-bishop (aka promoted bishop in shogi) as a compound piece where I add a B's value plus a wazir's value plus a pawn, on 10x10 (for my Sac Chess variant). On 10x10 I rate a B worth 3.5 (as opposed to a N being just set=3 there, unlike on 8x8), and I rate a wazir as worth 0.75 there (half of what I rate it as on 8x8). So Super-bishop=B+wazir+P=3.5+0.75+1=5.25 on 10x10, which feels about right to me, especially as most people seem to value it as about worth a rook on 8x8. Note I'd similarly rate a super-B as worth 6 on 8x8, slightly more than R (I set to 5.5), in line with Greg's post about the super-B compared to the R a while back in another thread, i.e. re: (8x8) Pocket Mutation Chess (both are put in the same piece type class in terms of value by that game's inventor).

Observe also that colour-binding is built into a B's known value, and having a B as a component of a compound piece still includes that built in binding penalty (whatever it is) for the B; the masking of the colour-binding by the addition of another component (in this case, a wazir) is taken into account by (in addition to adding a wazir's value) adding a pawn's value (only), much as Q=R+B+P in chess. So, there is no sudden doubling of the Bs value as it were, in the case of a super-B (or a Q) compound piece, the way I do this particular calculation (i.e. as a sum).

At the risk of repetition, that (not always perfectly applicable) Q=R+B+P analogy, when used for estimating the value of compound pieces, often seems (to me at least) to produce results that aren't too badly off, when I've run with it in order to make many of my estimates. The case of valuing an archbishop on 8x8 being one quite possible exception, however, though on 10x10 at least, I wonder if that piece might be nearly as potent as on 8x8 - I sense this when I play 10x10 Sac Chess, though I do sense a certain potency of an Archbishop when I play 10x8 Capablanca Chess. My guess is that the N component of the archbishop suffers from less influence on 10x10, the largest size of these three sizes. It's also quite possible a B enjoys a 10x8 board even more than a 10x10 one (indeed I rate a B as 3.75 on 10x8), so that may explain why an archbishop seems extra strong to me on 10x8, in spite of a slightly less influential N component (than if it were on 8x8).

One thing that still makes no sense to me, btw, is if Amazon at best =Q+N in value (as I recall the wiki for that piece implies), then why zero co-operativity between the Q and N components? That's why I feel still more comfortable with Amazon set=Q+N+P at the moment. There also may be a similar problem for Guard set=3.2 on 8x8, if ferz and wazir are each approx. 1.5 (as I vaguely recall the wiki for each more or less gave), as the co-operativity seems all but shockingly low between ferz and wazir, if so.

Note I still rate a rook as worth 5.5 on 10x10 (as I would for any number of board sizes), since for one thing I don't believe a B's value should ever be 4 or greater (since it can't often restrain 4 pawns in an endgame - though a problem for me may be that if I set Guard=4 [incidentally =ferz+wazir+P, perhaps] on 8x8, as some chess authorities have done similarly for a K's fighting value, the same reasoning, about not restraining 4 pawns in an endgame, might be argued), and a rook should pretty well be worth about a B and 2 pawns on any board size, at least for square or rectangular boards.

There are, I imagine, many things I have yet to try to take into account when tentatively evaluating piece values, such as what Betza has written about pieces with negative values.

Note a colourbound penalty of e.g. x0.5 can be just one part of an estimating process, possibly. There can be offsetting bonuses, such as a x2 bonus for a leaper. There can also be a x0.5 penalty for non-capturing movements that make up part of how a piece moves, too (then there's forward as opposed to sideways or backward movements by a piece, and how to reckon with the valuation of that). At the moment my repertoire of formulae and methods is limited, but, again, I try to keep my life simple when possible, and I hope to compare my estimates with existing ones, if any, to get a feeling for if I am in the right ballpark before giving an estimate of my own.

In the case of the (colourbound, but 8-target leaper) camel, its value of 2 is still close to N/2 on 8x8 (especially if N set to =3.5 is used, which is even close to Guard, if that's set to =4), coincidence or not, which gives me some encouragement. Incidently, I assume a leaper bonus is not used for pieces (or components of them) that take just a one cell step, which is why I see a N in a way more different from a ferfil than a N is from a camel, in spite of a ferfil being closer to a N in value (on 8x8, in all cases).

Aside from all that, I hope you (and everyone else) are enjoying the holiday season, H.G.

(Further comments, made during the creation of this tool, can be found in this Subject thread.)

The BN piececlopedia page now has a blurb (in the Notes section) as suggested by H.G., passing the appropriate information to the limited EGT page.  If it looks and works fine, I will try to include similar links in the other Piececlopedia pages.

I currently have this page set as a Piececlopedia page, but that seems somehow unsatisfactory.  It strikes me as best categorized as Reference or Problem/puzzle/1-player, but those are not highly publicized.  Maybe the link from the minimal tool (from Piececlopedia pages) is enough?  Or perhaps a direct link from Topic Index is warranted?

Re: earlier points, see the applet's page.

On the other note:

While doing this it turned out the form for editing a submission has a pretty bad bug: in the first draft I had forgotten to adapt some links, and it included a header that turned out redundant. But when I try to edit, the edit window initializes each time with the first version I submitted, reverting all the changes I made in previous edit sessions, I then have to redo all these, and not forget a single one, or I would be back to square a1...

I played around with this for a little bit, and I think it's your browser caching the old submission data.  Refreshing the page fixed the problem for me.  (We could add a dummy variable to the end of the url as Fergus did for the Random Game menu link, but that might cause worse issues for using the browser's back button when submission fails e.g. because of being logged out?)

Thanks HG!

Well, a 50% penalty for simple color binding (i.e. access to 50% of the board) is really a luducrous over-estimate. More reasonable would be 10%, and then only for the case that you do not have the pair. You cannot really believe that adding a single non-capture backward step to a Bishop (which would lift the color binding) would double its value?

What do you think a piece would be worth that can do all moves a Bishop could do to non-adjacent squares (i.e. the Tamerlane Picket), plus all Wazir moves (to make up for the lost Ferz moves)?

In WinBoard I use the Unicorn image as the Royal Knight in Knightmate, so I was probably thinking of that. The Camel-Zebra compound is usually referred to as Bison, but the lame multi-path version of it is George Duke's Falcon, and in WinBoard I use the letter V for the Falcon symbol. (Because F was already taken by Ferz, and Dutch for Falcon is 'Valk'.) Not sure why I gave S the same move. Anyway, the main idea of the piecedef.ini file was that people could put their own piece definitions in there.

Note that the basic version of the generator assumes total symmetry and an 8x8 board. If you undefine the symbol DIAGSYM in the source code and recompile it would only assume 4-fold symmetry. This is not only needed for doing less symmetric pieces, but also for non-square boards. The way diagonal symmetry is implemented is leaning very much on the board size being 8x8, because it extracts the X and Y coordinates of the pieces by masking out groups of 3 bits from the index (through the RANKS and FILES masks) to be able to swap those. Even without diagonal symmetry it would not be so easy to adapt to other board sized; e.g. the tables bcode[] and deltaVec[] assume '0x88' square numbering, and would have to be changed.

FairyGen doesn't use any bitboard techniques, so the fact that the word length of a computer is only 64 bits in principle should not pose any limitation. It is just that everything having to do with square numbering and index calculation would have to be changed.