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Infinito
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epicu...@gmail.com
May 16, 2013, 9:03:52 AM5/16/13
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It is for two years that I sometimes dream about an uncomputable game. How should this game be? Is such a thing even possible? I think from a theoretical point of view it is possible, but, how?
This is my holy grail. (I have another holy grail other than this one, but another thread on it... )
How... I decided to not consider Gödel, so I pick the other, and simpler, way: a game with a game-tree of infinite width. A game with an unlimited number of moves per turn, but with a finite number of turns.
I don't think this kind of game is uncomputable, but it is the closest as I could get.
Of course it is not enough to have an unlimited number of moves in principle, it should be interesting and valuable to have this potential infinity at disposal. So the game needs intense playtesting to check the actual infinitude.
The game is Infinito and the rules are inspired by Nick's Heatseekers.
INFINITO
Infinito is a two-player game, played on a square board. One player owns the black stones, the other player owns the white stones. Grey neutral stones are needed.
Each player has an infinite number of stones with an unique natural number printed on them: 0, 1, 2, 3, and so on...
(For practical use, you can have blank stones and write numbers on them.)
Players move alternately, starting with the player controlling the white stones. Each turn consists of two actions, performed in this order:
1. OPTIONAL MOVE: you can move a stone exactly as a Queen’s moves in Chess, i.e. any number of cells horizontally, vertically or diagonally.
If your stone ends its move (orthogonally and diagonally) next to one enemy stone whose value is less than your stone, and your stone wasn’t (orthogonally and diagonally) next to that enemy stone to start its move, replace any friendly stone – but the stone just moved – on the board with a neutral grey stone with “∞” printed on it. In one move you can end up close to more enemy stones whose value are less than your stone, in that case you replace your stones with neutral stones for each of those stones.
When you remove your stones from the board, those stones will be available for future placements.
2. COMPULSORY PLACEMENT: you must place a stone onto any empty space.
THE END. The game ends when the board is full, whoever has the least sum of his values wins.
VARIANT: Players can place duplicate stones.
This is my holy grail. (I have another holy grail other than this one, but another thread on it... )
How... I decided to not consider Gödel, so I pick the other, and simpler, way: a game with a game-tree of infinite width. A game with an unlimited number of moves per turn, but with a finite number of turns.
I don't think this kind of game is uncomputable, but it is the closest as I could get.
Of course it is not enough to have an unlimited number of moves in principle, it should be interesting and valuable to have this potential infinity at disposal. So the game needs intense playtesting to check the actual infinitude.
The game is Infinito and the rules are inspired by Nick's Heatseekers.
INFINITO
Infinito is a two-player game, played on a square board. One player owns the black stones, the other player owns the white stones. Grey neutral stones are needed.
Each player has an infinite number of stones with an unique natural number printed on them: 0, 1, 2, 3, and so on...
(For practical use, you can have blank stones and write numbers on them.)
Players move alternately, starting with the player controlling the white stones. Each turn consists of two actions, performed in this order:
1. OPTIONAL MOVE: you can move a stone exactly as a Queen’s moves in Chess, i.e. any number of cells horizontally, vertically or diagonally.
If your stone ends its move (orthogonally and diagonally) next to one enemy stone whose value is less than your stone, and your stone wasn’t (orthogonally and diagonally) next to that enemy stone to start its move, replace any friendly stone – but the stone just moved – on the board with a neutral grey stone with “∞” printed on it. In one move you can end up close to more enemy stones whose value are less than your stone, in that case you replace your stones with neutral stones for each of those stones.
When you remove your stones from the board, those stones will be available for future placements.
2. COMPULSORY PLACEMENT: you must place a stone onto any empty space.
THE END. The game ends when the board is full, whoever has the least sum of his values wins.
VARIANT: Players can place duplicate stones.
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