Difference between revisions of "A1 opening"
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(This does not mean that these are the worst possible opening moves. Compare with the diagrams on [http://www.cs.ualberta.ca/~queenbee/openings.html the openings page at the queenbee site]) | (This does not mean that these are the worst possible opening moves. Compare with the diagrams on [http://www.cs.ualberta.ca/~queenbee/openings.html the openings page at the queenbee site]) | ||
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| + | Like the proof that Hex is a win for the first player, the proof that A1 loses is non-constructive: Although we know that it exists, the winning strategy has not been found for regular sized Hex boards. | ||
Due to the [[Symmetries (board)|symmetry]] of the Hex board, the same is true of the [[opposite hex]]es, but they are not usually referred to explicitly because their [[Coordinates (board)|designation]] depends on the size of the board. | Due to the [[Symmetries (board)|symmetry]] of the Hex board, the same is true of the [[opposite hex]]es, but they are not usually referred to explicitly because their [[Coordinates (board)|designation]] depends on the size of the board. | ||
Revision as of 11:52, 5 February 2008
- The title given to this article is incorrect due to technical limitations. The correct title is a1 opening.
The a1 opening (in the acute corner) is one of only two openings known to be defeatable. The other is b1.
(This does not mean that these are the worst possible opening moves. Compare with the diagrams on the openings page at the queenbee site)
Like the proof that Hex is a win for the first player, the proof that A1 loses is non-constructive: Although we know that it exists, the winning strategy has not been found for regular sized Hex boards.
Due to the symmetry of the Hex board, the same is true of the opposite hexes, but they are not usually referred to explicitly because their designation depends on the size of the board.
Sketch for proof
a2 has been proved a losing answer
A sketch of the proof on kosmanor page
References
References for proofs can be found on the Hex Theory page.
