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Chess board as a function of the number of players:

  • 2 players - 8x8 square board
  • 3 players - a special hexagonal board
  • 4+ players - theoretically a (players * 2) gonal board.

First Question: Does this gonal board exist? Is it playable (talking about practical needs, e.g. size of a field)? How would the desk look like?

Second question: Would a 2+ players 3D-chess room be possible to create?

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    Comment and body do not match: three-player chess may exist (see answer), but four-player is just a thought-experiment.
    – Tim Lymington
    Commented Sep 11, 2019 at 20:42
  • what is GONAL? google only finds Follicle-stimulating hormone
    – Cohensius
    Commented Sep 12, 2019 at 7:52
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    Please try to narrow your question. Your two questions aren't really that related, and there are too many aspects of your questions to address.
    – ryanyuyu
    Commented Sep 12, 2019 at 18:11
  • There was a middle-ages chess variant for 4 players, known as 4-seasons chess. It was played on an 8x8 board. Each player had 4 pawns, 1K, 1B, 1Kt, & 1R formed as an angle in a corner of the board. Sets were often red, green, white, and black. I have played this a few times, years ago. There may be other 4-player varsions
    – David Siegel
    Commented Sep 13, 2019 at 21:44
  • Also, a '(players+2)gonal board' is a mathematical nonsense. A board can have triangles, squares or hexagons (equivalent to squares with alternate rows offset). Nothing else tesselates properly.
    – Tim Lymington
    Commented Sep 21, 2019 at 11:57

4 Answers 4

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Yes, chessboards for 3 players exists. I have a similar to the following at home:

https://www.chesshouse.com/products/3-player-medium-wood-chess-set

It is playable and it is fun, however don't expect a really deep chess game. The main tactic is to be not the one who gets ganged upon. The better chess player won't win. The player who can manipulate the best will win (by making the other one vulnerable to attacks or just by talking).

It is almost impossible to defend against two opponents. For example one captures a piece and the second player captures another piece that was defending the first piece. Another situation is as one attacks your king ('check') and the other one attacks your queen. There are also some funny checkmates, like Scholar's mate where one person uses the bishop and the other uses the queen.

Be prepared for these situations, otherwise it feels very unfair. By times very funny, but also very unfair :)

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  • I've got the same board and reached the same conclusions - in our games we actually ended up playing in silence or at least disallowing any conversation related to the game, because it was just too easy otherwise for two players to gang up, even inadvertently. It's an ingenious board though.
    – Phueal
    Commented Sep 23, 2019 at 4:07
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The question is a bit vague. But there already is a 4 player chess. It would be possible to expand that to more players, but it's not sure if that is playable.

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To answer the first question as posed: no, the n-gonal chessboard doesn't exist for n>6 (assuming Euclidean geometry).

You can't tile the plane with octagons -- you end up with small empty square spaces at every other side, so the symmetry is lost. Regular tilings (using regular polygons) are possible only with 3-gons (triangles), 4-gons (squares) and hexagons.

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