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?
If it is white's move then he can win like so:
- d4, forces d6
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.
Suppose black passed. White could easily win in three moves:
d4 threatening to create either of two squares. White could also use the same tactic starting with
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 (
d4), play on one of the final threat squares (
b4), or make a play such that their forced next move will create a threat of their own (
f2). Of these moves, only
d6 will prevent all four sequences for white.
Suppose black plays
d4. White can play
b6, threatening to win on two squares; black never has a threat in this sequence. Similarly if black plays
d6, white plays
b4. So black can only survive for a few more moves, and survives longest if their next move is
Applying the following rules with revision:
- Start with empty chessboard.
- White moves first (place a piece on any square).
- Black and white alternate take turns to move.
- Both players may "block" the 4th corner of opponents square.
- 1 block is allowed before the player's move turn.
- A player wins when 4 of his pieces form an upright or a tilted square.
Here is a line for continuing the above position.
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..
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*)