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On an ordinary chess board (8x8) without any pieces on it as a starting position, two players will alternately place a pawn on any square (unoccupied) so that the first player that form a square (upright or tilted) with his 4 pieces on the board wins the game. This question mainly search for the best strategy to win as white or else black. Draw is possible when both players pieces can not form a square anymore. From the above position, what is the best move for black?

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  • $\begingroup$ This is similar to Teeko. $\endgroup$ – msh210 Jun 1 '20 at 6:37
  • $\begingroup$ Do tilted squares include only 45 degree tilts? Or would, say a Knight-move 1:2 square, e.g. d2, f3, e5, c4 be a valid square? Or 1:3, 2:3, 2:4, etc.? $\endgroup$ – Darrel Hoffman Jun 1 '20 at 16:12
  • $\begingroup$ Yes and one of the largest tilted square is a2,b8,h7,g1 $\endgroup$ – TSLF Jun 1 '20 at 17:10
  • $\begingroup$ Note: As stated from answer below: "if white goes first on an empty board then he can guarantee a win" .. and so to make it playable the "block" rule should be applied. If a player blocks the 4th corner of opponents winning square, that player do the next turn. (Block is not considered a turn). This would eventually make the OP much harder to determine. $\endgroup$ – TSLF Jun 1 '20 at 18:23
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If it is white's move then he can win like so:

  1. d4, forces d6
  2. c3

Now black has to stop white at both e3 and b4, which is impossible, so he loses. Note that white can win by doing the same starting with d6. So black has already lost this position. This also means that if white goes first on an empty board then he can guarantee a win, by forming two pawns in a straight line (like in the diagram).

If you remove tilted squares then the game becomes a lot more balanced in my opinion.

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    $\begingroup$ nice analysis.. so 1. e5..f3 means win for white! and maybe 1.e5 is the game solution for white? Considering the tilted square i see that "if white goes first on an empty board then he can guarantee a win" $\endgroup$ – TSLF Jun 1 '20 at 9:39
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    $\begingroup$ -This game may work with tilted and upright squares by adding "block" rule where a player is allowed the next turn if he placed a piece on the 4th corner of opponents winning square.. $\endgroup$ – TSLF Jun 1 '20 at 16:12
  • $\begingroup$ That's an interesting idea. If we remove tilted squares then I believe it will always be a draw. The black player always goes next to white move, blocking any pawns in a line being formed. $\endgroup$ – Dmitry Kamenetsky Jun 1 '20 at 22:54
  • $\begingroup$ I believe White would still win. $\endgroup$ – Daniel Mathias Jun 1 '20 at 23:01
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Suppose black passed. White could easily win in three moves: c3 forcing e3, then d4 threatening to create either of two squares. White could also use the same tactic starting with e3, c7 or e7.

If black doesn't pass, they can prevent this sequence starting c3 in three ways: play on one of the squares used for the sequence (c3 or d4), play on one of the final threat squares (d6 or b4), or make a play such that their forced next move will create a threat of their own (f4 or f2). Of these moves, only d4 or d6 will prevent all four sequences for white.

Suppose black plays d4. White can play c7 (forcing e7), then a5 (forcing a7), then b6, threatening to win on two squares; black never has a threat in this sequence. Similarly if black plays d6, white plays c3, a5 and b4. So black can only survive for a few more moves, and survives longest if their next move is d4 or d6.

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  • $\begingroup$ Just an additional note, for white, after c7 and a5, white wins with c3, no need to go to b6. $\endgroup$ – justhalf Jun 1 '20 at 10:35
  • $\begingroup$ @justhalf well spotted, thank you! In that case I guess the answer is, rather unsatisfactorily, that all moves for black are equally good (or bad), since it is trivial for black to avoid losing in two moves even if they pass now. $\endgroup$ – Especially Lime Jun 1 '20 at 11:28
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Applying the following rules with revision:

  1. Start with empty chessboard.
  2. White moves first (place a piece on any square).
  3. Black and white alternate take turns to move.
  4. Both players may "block" the 4th corner of opponents square.
  5. 1 block is allowed before the player's move turn.
  6. A player wins when 4 of his pieces form an upright or a tilted square.

Here is a line for continuing the above position.

1) e5..f3
2) c5..d5
enter image description here

3) white to d4.. black block 1-3-2 on d6'...then to e4!

4) white to c3 ?..two posible squares for pcs. no. 2-3-4 & 1-2-4

...black blocks 2-3-4 on b4'..then to e3 , turn block 1-2-4 w/ potential for 5-2-6 & 1-6-4

5) white make c2' to block 5-2-6 then to f4 , blocking 1-6-4..

enter image description here

6) ...black wins with d3!

7) if white blocks 1-4-7 on e2' and 1-7-2 on f5.. black wins on c4* (or blocks 7-3-8 on g3 and wins with g6*)

enter image description here

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