Comments by Ben Reiniger

I would play some 3+ dimensional variants.  As Joe might be able to confirm
by now, my chess playing skills might be a bit lacking, but I think I can
hold my own at design discussions.

Dan Troyka includes an impressive history on high dimensional variants in
his 6D chess download.

I have proposed an (countably)infinite-dimensional chess game before, but
the complete lack of visual ability dampens hope for ever actually playing.
 :P

Unless anyone minds, I might collect and edit some ideas from here into the
wikidot.  It would be nice to have a relatively central source for these
things.

Daniil:
I'm not certain, but I don't believe there's a nice tiling of 3-space which is hexagonal in all (reasonable) directions.  Maybe you can manage it, but only by thinking of the cells as points to occupy rather than regular, spacial objects.

Daniil, are you suggesting a different game?  In this game it seems that compound pieces (including the two variant pieces) never promote, and only demote upon capturing.  Any noncapturing move they make leaves them as they are.

It is interesting that a queen can never demote then promote back to a queen, whereas the variant pieces can demote then promote back to themselves.

I really like this concept, though I haven't played it before.  Concerning the sample 'Case II', it is worth noting that even if U captures R--freeing B--W can immediately recapture B by the same move suggested.  (It might be worthwhile to capture B now (as in the suggestion) just to threaten U's current square (if R is ever captured at his starting square, that is).

Rooks do have the devastating ability to win the game in four moves (after two moves getting into position) by sweeping through the opponent's home row if they can avoid being captured first.  While bishops enjoy greater mobility, their range is only half the board, so I think the pieces are relatively well balanced.

So this is really (locally) a hexagonal game, since each 'square' has six neighbors; is it different (globally) from a standard hex setup?

EDIT: Ah, I missed this discussion a couple years back.  I think perhaps the original comment by Gilman answers my question most fully: it's not a 'standard' hex setup.  It seems too that the piece movement is not standard for hex games, but I don't see anything that forces us to use the pentagonal layout for ease of visualization.  It is neat though how the pentagons have been laid out.

When playing on borders, how do you define an adjacent location?  Is it a
border that shares an endpoint with the current one?  I suspect a lot of
these ideas will wrap around onto one another (for instance, the duality
between triangular and hexagonal boards, the self-duality of rectangular
boards, etc.)  I think also that when you pass between these viewpoints,
some of the pieces may be defined differently from their standard.  (That
is, if you define what you think pieces should do in a hex corner game,
perhaps they will move differently than what their counterparts in
triangular chess usually do.)  This may or may not be a good thing.  I
generally like it, but it's nice too if they work out to be consistent.

Another way to get triangular is by playing on the corners of a hex grid, so you could use the rectahex board in the same fashion; you just have to be able to remember that the intersections of a vertical edge with what appears to be a square's edge is actually another corner (since the apparent edge of the square is in fact two separate edges in the rectahex sense).

Looking a bit more closely though, this won't work if the board is turned around in the 'proper' orientation.  Notice that the corner of the hexes d4,d5,e4 should be adjacent to the corner of the hexes d5,e4,e5; but on the usual orientation these are the same corner!  You could get around this I suppose, but it would be ugly.

I think everyone should keep in mind the line below the game:
'These are simple illustrations rather than strong opponents.'

The beauty of this applet is Ed's extension of it to so many variants.

George, I don't understand your calculation.  Each non-king piece starts with 7C, so there are at least 30*7=210 non-king moves that can be made.  And each capture increases this number, right?

Also, the wording is a bit ambiguous regarding captures: the captor recieves 'Calories equal to its traditional value'.  I read that as the value of the captured piece, is that correct?  [E.g. if a pawn with 4C captures a knight with 5C, then the pawn now has
4 - 1(movement) + 5(knight's Cals) + 3(bonus) = 11C ?]

Also, I presume that a pawn retains its Calories upon promotion?

I have to largely agree with the direction of that article.  It should give
some overview of the idea behind 3D chess, and list some few noteworthy
examples.  Then, I think the link to this site is sufficient as an external
link for other variants.  I would emphasize the multitude of other existing
games in the article and reference the external link, but I think listing
too many examples directly in the wiki article may be too much.

I think your image of the contraction capture is off...also I'm not sure I understand the Drop rule.  Can you get the queen before placing the remaining four pawns?  Are captured pieces droppable?

The Big Crunch idea seems to already be in place in terms of the contraction of the board.  An interesting implementation of the Big Rip idea would be to have the board disappear from the inside out rather than contracting:  say the outer edge of the board is determined by the number of pieces placed throughout the game, and the inner edge is determined by the number of captured pieces.  (This assumes captured pieces are dead for good, not switching sides and dropped.  Also, this probably isn't very close to the actual idea of the Big Rip.)

Not to spark another debate on what constitutes a chess variant, but I imagine this fails the criteria for most people.  Gameplay is nothing like chess, but uses chess equipment.  (This is not to say it doesn't belong here, I think CV.org should be fairly all-inclusive of anything chess related.)

As to MP's proposed alternate puzzle solution, it assumes that the ball may be kicked 'past' an allied piece.  This seems to be disallowed by the rules, but not specifically.  If we think of chess, such a move should be disallowed; if we think of soccer it should be allowed.  Also, the rules disallow passing to an unmoved piece which doesn't follow soccer very closely.  (I would propose each piece be allowed a null move, that would include the possibility of passing to a friendly piece provided it makes the next (null) move and kick.)

Note too the applets
/play/erf/SoccerC1.html
/play/erf/SoccerC2.html
(interestingly, Ed doesn't have a link on his personal page to SoccerC2; finding it here was my first clue to its existence!)