Anyone for Chmess?

[njas...@gmail.com]

In a review of the book "I've been thinking" by the (late)  philosopher Charles Bennet I saw a mention of a variant of chess called Chmess.  I created A366476 for the number of positions after n half-moves, but since the review did not make the rules very clear, I only gave three terms.  This entry needs work!

This reminds me that there was long-standing story at Bell Labs that Ken Thompson wrote Unix so that he could write a chess-playing program.  And did both in one weekend.  The program was called "Belle", and after it started competing, but before it won the world computer chess championship, I went up two flights of stairs to the Unix room, and asked him if he could work out the number of possible chess positions after n plies.  The result was A006494 and A007545 (the latter still needs work, by the way).

Neil Sloane

[Hans Havermann]

"Chmess is an imaginary game very similar to chess, with the exception that the king can move two squares in any direction instead of just one. To get a(1) = 25 I am assuming the king can jump over an occupied square, but is not allowed to move out and back (which would give a(1) = 26)."

I feel it's important to go back to how chess moves are described to beginners. The King, Rook, Bishop, and Queen are generally noted as moving one or more squares horizontally, vertically, or diagonally. The Knight jumps in an L shape, two squares in one direction and one square perpendicular. When Daniel Dennett allows the King to move two squares in any direction, surely he means to tell the beginner "horizontally, vertically, or diagonally". If we don't allow a Knight direction for the Queen, why would we allow it for the King without making a note of it? I'm arguing that a(1) = 23.

I've done some searching for an actual board position and/or some moves of Chmess and have come to the conclusion that Chmess may be the only chess variant ever, never to have been played.

[Sean A. Irvine]

> I've done some searching for an actual board position and/or some moves of Chmess and have come to the conclusion that Chmess may be the only chess variant ever, never to have been played.

In which case "mess" is entirely appropriate.

[Arthur O'Dwyer]

This thread is apparently related to OEIS sequence A366476, "Number of possible chmess games at the end of the n-th ply." The quote above ("To get a(1) = 25 I am assuming...") is from Neil Sloane, 2023.

Chmess itself was invented by Daniel Dennett as an example of something that is intrinsically just as fruitful a field of inquiry as chess itself (after all they're almost exactly the same game), and yet, somehow, chmess is obviously a waste of everyone's time.

...And yet, here we are.

This is certainly (as Dennett actually says in his essay) a prime example of Hebb's Rule: "Research [or OEIS entries] that aren't worth doing, aren't worth doing well."

Anyway, I count the following possible chmess moves from the opening state:

a2, a3, b2, b3, c2, c3, d2, d3, e2, e3, f2, f3, g2, g3, h2, h3

Na3, Nc3, Nf3, Nh3

Kc3, Ke3, Kg3 (assuming that the king can, knightlike, jump over pieces)

for a total of a(1) = 23.

Or, if we assume that the king, bishoprookqueenlike, can't jump over pieces, then we should subtract all three of those for a(1) = 20, the same as normal chess (A048987).

Actually, I would fairly strongly advocate for the latter. The chess knight is special in that it can jump over pieces, but the chess king is not special in that way, and Dennett didn't say he was making the chmess king special in that way, so I don't think the chmess king is special in that way. It's totally blocked in at the start of the game, and it's not until the third ply that a corrected A366476 would actually diverge from A048987.

Uselessly,

–Arthur

[njas...@gmail.com]

I'm glad to see the first Conversation in the new group has attracted some attention.  As I said, I was unable to find the official rules for Chmess, so I made a guess, which led to A366476. I felt  that a king should be more powerful than a knight, which led to my version.

By all means create sequences for other versions, especially if you can get more than three terms.

I'm going to add a link to the present Conversation from A366476, with a remark that other possible rules are discussed here.

[Marc LeBrun]

=Arthur O'Dwyer:

[...] and yet, somehow, chmess is obviously a waste of everyone's time.

...And yet, here we are.

...breathless before the vast new vistas of Chmess versions of the Bongcloud!

Carlsen - Nakamura, 2021

1. e4 e5

2. Ke2 Ke7

...

[M. F. Hasler]

Hello SeFans,

my 2 cents on this, in spite of the following point 0:

0) If I understand well, the whole point of Dennett's "invention" of Chmess was to give an example of something NOT worth being studied or discussed... [I think Arthur also pointed that out.]

1) My first reaction when I saw Neil's message/comment on oeis.org/A366476 was the same as Hans'  in that I do not think that "can move 2 squares" should imply that the King can jump over other pieces.

(OK, that just means that we actually have 2 variants in one, Chmess and (maybe) Jmess (for "jumping mess") ...)

Which would only change the number of moves at ply 2 (White's 2nd move, where the K now has several more possibilities in case they played the d-, e- of f-pawn on the first move. [and Arthur's 

2) In either variant, it wouldn't really change that much for the Bongcloud opening,

because essentially here the main idea is that the king blocks the queen & bishop, and not the inverse,

effectively losing a move. If the king moves 2 squares on the second move, it will rather block less than more.

But yes, in case of "Jmess", one would have openings where the King moves *first*, thus blocking one of the pawns, which might be even worse for development.

3) I could compute a few more terms with PARI code I have ready or using Python's chess library where it would be very easy to implement this a variant.

But again, there is point 0 ...

Oh, and I'll have to stop here, because I'm awaited for some chess (1.0) now... :-)

- Maximilian

[Marc LeBrun]

...it wouldn't really change that much for the Bongcloud opening,

I was thinking it might create more interesting divergences later in those lines where the king staggers further afield, seeking a post over on the rook file etc...

For some value of "interesting".

========

Gratuitous Fairy Chess Aside:

This caused me to wonder about a different variant chess, where to the standard rules you just add

   If your king has any legal moves, you must make one of them.

Kind of like treating the king as "touched".

This would have the effect (among others) of forcing any 1. e4 into a Bongcloud...

[Arthur O'Dwyer]

On Fri, Oct 18, 2024 at 6:42 PM M. F. Hasler <prof....@gmail.com> wrote:

Hello SeFans,

[...]

2) In either variant, it wouldn't really change that much for the Bongcloud opening,

because essentially here the main idea is that the king blocks the queen & bishop, and not the inverse,

effectively losing a move. If the king moves 2 squares on the second move, it will rather block less than more.

But yes, in case of "Jmess", one would have openings where the King moves *first*, thus blocking one of the pawns, which might be even worse for development.

Worse? you mean better, of course...

1. e4 Kc6!

immediately threatens to control the center with 2. ...Kxe4. Alternatively — if White foolishly attempts to set up a belated defense for that lone pawn — Black's King remains only one ply away from an admirably daring forward command post at a4. During this blitzkrieg advance, the absolute minimum of pawn movement by definition signifies the absolute maximum of beneficial piece development, while also preserving the utmost flexibility in pawn structure.

*taps temple smugly* Can't incur a backward pawn if you never move any pawns.

;)

–Arthur

[M F Hasler]

Dear chess^H^H^H seqFans,

One more (last?) remark on this, esp. sequence oeis.org/?q=chmess,

in spite of being aware that we are victims of the trap Dennett explicitly wanted us to avoid according to the abstract of his paper.

Even if we admit that the king could hop over other pieces, I think that the last part in

"[the king] is not allowed to move out and back (which would give a(1) = 26)."

should be deleted, because even if it could go somewhere and back, that could only be possible if there wasn't an own piece on that "somewhere" square. 

So the idea of "moving somewhere and back" (or elsewhere)  appears "mutually exclusive" to the "leaper" concept, allowing it to hop over other pieces.

But as Hans and others I also think Dennett's formulation "the king can move two squares in any direction instead of just one"

indicates that we should consider it as a "slider" rather than a "leaper", and only queen-like directions should be allowed.

Anyways,

* if we accept the (IMHO improbable) "leaper" idea, we can (or not) allow the king to make also knight moves in addition to {0, +-2} x {0, +-2},
   but I think "zigzag" moves (one up, one left) that would end on a direct neighbor square of the departure square
   should be excluded in this "leaper" scenario.

* if we allow the king to make two usual king's moves (as if the opponent would have to pass their turn), then it must be impossible to walk over own pieces. But capture of opponent's pieces on the intermediate square should logically be possible, and going back to the departure square should be possible in that case, too. [Also, walking over an attacked square should be possible given that opponent doesn't have the right to move.]

* if we adopt the "slider" scenario, then there is the question whether "can" means "must" or "possibly can" (move 2 squares instead of just 1).

* I just realize that the "can vs must" question also applies in the "two usual moves" case.

- Maximilian

[Arthur O'Dwyer]

On Fri, Oct 25, 2024 at 11:08 AM M F Hasler <mha...@dsi972.fr> wrote:

Dear chess^H^H^H seqFans,

One more (last?) remark on this, esp. sequence oeis.org/?q=chmess,

in spite of being aware that we are victims of the trap Dennett explicitly wanted us to avoid according to the abstract of his paper.

Even if we admit that the king could hop over other pieces, I think that the last part in

"[the king] is not allowed to move out and back (which would give a(1) = 26)."

should be deleted, because even if it could go somewhere and back, that could only be possible if there wasn't an own piece on that "somewhere" square. 

So the idea of "moving somewhere and back" (or elsewhere)  appears "mutually exclusive" to the "leaper" concept, allowing it to hop over other pieces.

But as Hans and others I also think Dennett's formulation "the king can move two squares in any direction instead of just one"

indicates that we should consider it as a "slider" rather than a "leaper", and only queen-like directions should be allowed.

FWIW I agree with that interpretation too, although I also think that leaping is funnier. ;)

 

Anyways,

* if we accept the (IMHO improbable) "leaper" idea, we can (or not) allow the king to make also knight moves in addition to {0, +-2} x {0, +-2},
   but I think "zigzag" moves (one up, one left) that would end on a direct neighbor square of the departure square
   should be excluded in this "leaper" scenario.

* if we allow the king to make two usual king's moves (as if the opponent would have to pass their turn), then it must be impossible to walk over own pieces. But capture of opponent's pieces on the intermediate square should logically be possible, and going back to the departure square should be possible in that case, too. [Also, walking over an attacked square should be possible given that opponent doesn't have the right to move.]

* if we adopt the "slider" scenario, then there is the question whether "can" means "must" or "possibly can" (move 2 squares instead of just 1).

* I just realize that the "can vs must" question also applies in the "two usual moves" case.

I think I unconsciously assumed that "the king can move two squares [...] instead of just one" meant "can, not must." Good point that it's ambiguous, though.

Finally, here's another variable you didn't mention, which you inspired me to think of with your thoughts on "walking over an attacked square." In ordinary chess, whenever the king moves >1 space in a single turn (i.e. during castling), the king is specifically forbidden to move through check. So I would actually assume that chmess also forbids the king to move through check. E.g. if f1 is under attack by Black, then the White king isn't allowed to move from e1 to g1, regardless of whether that's a castling move or an ordinary two-square move.

Maybe the most appropriate OEIS sequence would be "how many unique interpretations of Dennett's rules are possible to distinguish by the k'th ply." ;)  (Kidding! Don't add this sequence!)

a(0) = 1

a(1) = 4 (slider; leaper queenwise; leaper knightwise; leaper out-and-back)

[...]

–Arthur

[Ruud H.G. van Tol]

On 2024-10-25 17:56, Arthur O'Dwyer wrote:
> [...]

> FWIW I agree with that interpretation too, although I also think that
> leaping is funnier. ;)

To me, the King always was slow, and not fit to leap.

> whenever the king moves >1 space in a single turn (i.e. during

> castling), the king is specifically /forbidden/ to move through check.

Yes please.

And the rook also doesn't leap, as nothing leaps a King, so it uses a
secret path.

Next rule: let black start.

-- Ruud