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Infinite Chess. Chess on on infinite board.
V. Reinhart wrote on 2017-12-24 UTC

Considering Ji's rule #3 that pieces are stranded if there is no "8x8 square which includes at least one piece of the opponent" then there may be positions where many pieces are lost in one move. For example, if White's pieces (quantity "n-1") are in a legal position because they are within 8 squares of a Black bishop, and if the bishop flees to a legal position by "1" White piece, then White loses all except the "1" piece. I'm not sure if such a position would be reached in a well-played game, but it is interesting that multiple pieces can be lost in a single move. Has anyone played this, or thought it out in more detail?

George Duke wrote on 2017-02-08 UTC

The most featured Angel Problems are situated on infinite chessboard: https://en.wikipedia.org/wiki/Angel_problem.

V. Reinhart wrote on 2017-02-08 UTC
I'm now experimenting with a version of chess which uses a board of infinite size. I call it "Chess on an Infinite Plane".

I didn't worry about any rules requiring pieces to not move to remote areas. I don't think this has to be worried about, because moving too far away would be poor play. It's self-regulating and therefore does not need to be in the rules. Pieces that move far away would lose their targets (and ability to create forks). I did add some other pieces and pawns so that each player has more attacking power, and help ensure there is enough material in the endgame for the winning side to create checkmate.

I'm currently in three games (playing about one move per day).

And, I also have a second version: "Chess on an Infinite Plane - Huygens Option". It adds the huygens, which is a piece which can jump a prime number of squares. It helps to protect some pieces in their starting positions. (As a side-effect it also makes it more difficult for computers to "solve" this game, because the set of prime numbers itself is unknown, and not easy to calculate).

Some discussion about the game is here:
https://www.chess.com/forum/view/chess960-chess-variants/chess-on-an-infinite-plane
If anyone would like to play either of these games, let me know.:)

Larry Smith wrote on 2007-05-30 UTC
I like the option of instant capture by stranding. This would actually keep the game area tight, and the endgame could be a bloodbath.

Jianying Ji wrote on 2007-05-28 UTC
```Re:Larry,

There are two solutions:

1. Capture by stranding, where after every move, any opponent pieces that are stranded are considered captured.

2. Stranded disapear, after every move, any friendly stranded pieced are removed.

Larry, your idea most align with the second choice. I think both are viable, the first being simpler to understand, but the second give the player a 'second chance' of a sort.```

Larry Smith wrote on 2007-05-28 UTCExcellent ★★★★★
```Since each piece 'must' exist within an 8x8 area of an opposing piece, what happens when a piece is stranded? Is the player forced to move that piece back into an appropriate position? And if unable, what then occurs with that piece?

I advocate that a player must immediately correct any inappropriate position, or forfeit the offending piece(s). If multiple pieces are 'stranded', a player would only be able to recover one. If in a checking position, the player could be forced to abandon such to avoid capture of their King. And a King in such a position would be considered in check.

As the number of pieces are reduced during play, the potential size of the playing field would likewise reduce. It still may be quite difficult to promote until well into the end-game.

All in all, a great idea. Definite a brain-squeezer.```

Jianying Ji wrote on 2007-05-27 UTC
```David:
'shifting patches of sunlight scattered across a limitless dark plain'

I never imagined when I first submitted my rules that such a poetic description as David's existed. It is such an appropo description! It seems almost the essense of the game. There's certainly untapped depth to this game.

Thanks so much to Joe and David's interest and conversation. It adds so much to the mystic of this game for me.```

David Paulowich wrote on 2007-05-26 UTC

My statement should be rephrased to read: the smallest rectangular board containing all of the pieces may increase beyond any limit. This can be demonstrated by two pairs of (opposite color) Rooks moving off, one pair in a vertical direction and one pair in a horizontal direction.

Joe Joyce's statement should be rephrased to read: any White move takes place in a playing area consisting of no more than 32 square areas (15x15) centered on the Black pieces. Black's reply must take place in a playing area consisting of no more than 32 square areas (15x15) centered on the White pieces. These 15x15 areas will overlap the previous areas centered on the White pieces.

So the game may be regarded as taking place in (no more than) 32 shifting patches of sunlight scattered across a limitless dark plain. Note that a piece may move thousands of squares in a single move, provided it starts and ends its move within the required distance from an opponent's piece.

Joe Joyce wrote on 2007-05-26 UTC
```I would respectfully disagree that the board is infinite. By the rules, there can be at most 16 pairs of pieces, each in its own 8x8 playing area. If I'm doing the numbers right, that's 1024 squares maximum that can be used, although it is true that these 16 areas can be totally disconnected.

Well, that seems reasonable, but let's re-think this. Assume the pair of pieces are diagonally separated by 6 empty squares. The opponent piece can move anywhere up to 7 squares away from the friendly one, giving a 15x15 square centered around the friendly piece. That gives 15x15 squares x16 pairs, or 3600 squares max potential board squares. If we don't know who's turn it is, that 15x15 square is duplicated over every piece, friendly and enemy. Doubling 3600 gives 7200, but there's overlap - 64 squares per pair, if I understand this correctly - subtracting 1024 squares from the total, leaving 6176 squares as the maximum potential size of the 'infinite' board. I think the 'actual' maximum size would be 3200, given that we know who moves next. That would occupy about a third of a 100x100 board.

This of course ignores any concept of chess strategy.```

David Paulowich wrote on 2007-05-26 UTC
`'For each piece there must exist a 8x8 square which includes at least one piece of the opponent.' ==> which allows a White Rook and a Black Rook to take turns moving away from the main body of pieces, causing the play-area to increase without limit.`

Anonymous wrote on 2005-12-01 UTC
There is too! 256 by 256 is 'big enough'

Anonymous wrote on 2004-05-25 UTC
If the player's co-operate, there is <strong>no</strong> definition of 'big enough'