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Who wins Balanced Double-Move Hex?
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Alice Abusmus
Apr 11, 2018, 6:09:14 PM4/11/18
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AKA Hex with 12* mutator. Standard NxN Hex board. First player places one stone, thereafter, each player places two stones per turn without placement restrictions.
As in standard Hex, draws are not possible. But, unlike Hex:
It's trivial to see that on a 1x1 board, it's first player win.
On a 2x2 it's a 2nd player win.
Then on a 3x3, it's a 1st player win again.
4x4 is a 2nd player win, 5x5 1st player, 6x6 2nd player ...
So, does this pattern continue? It's easy to analyze these smaller boards as it's all tactics and no strategy. I assume that on larger boards, tactics will become less and less overwhelming.
So, the question is, is Balanced Double-Move Hex a theoretical win for Player ONE on ODD order boards and for Player TWO on EVEN order boards?
As in standard Hex, draws are not possible. But, unlike Hex:
It's trivial to see that on a 1x1 board, it's first player win.
On a 2x2 it's a 2nd player win.
Then on a 3x3, it's a 1st player win again.
4x4 is a 2nd player win, 5x5 1st player, 6x6 2nd player ...
So, does this pattern continue? It's easy to analyze these smaller boards as it's all tactics and no strategy. I assume that on larger boards, tactics will become less and less overwhelming.
So, the question is, is Balanced Double-Move Hex a theoretical win for Player ONE on ODD order boards and for Player TWO on EVEN order boards?
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