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New orthogonal connection game. Is it finite?
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Luis Bolaños Mures
Aug 1, 2023, 12:08:03 PM8/1/23
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On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of a crosscut. As a result, the swapped friendly stone must not be part of a crosscut any more. If the swapped enemy stone is still part of a crosscut, remove the other enemy stone in that crosscut.
You win if, at the start of your turn, there is a chain of orthogonally connected pieces of your color touching the two opposite board edges of your color.
Note that, at the end of your turn, there will be no crosscuts on the board, so deadlocks are not possible. Cycles might be possible. You never remove more than one stone on a single turn, so a cycle requires removing a stone on every turn.
You win if, at the start of your turn, there is a chain of orthogonally connected pieces of your color touching the two opposite board edges of your color.
Note that, at the end of your turn, there will be no crosscuts on the board, so deadlocks are not possible. Cycles might be possible. You never remove more than one stone on a single turn, so a cycle requires removing a stone on every turn.
Luis Bolaños Mures
Aug 1, 2023, 10:17:44 PM8/1/23
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> You win if, at the start of your turn, there is a chain of orthogonally connected pieces of your color touching the two opposite board edges of your color.
Small update:
You win if, after a full move by either player, there is a chain of orthogonally connected stones of your color touching the two opposite board edges of your color.
As usual, the top and bottom edges of the board are colored black, and the left and right edges are colored white. The board is initially empty. The players are Black and White, and Black plays first.
This game will be called Reneo (Latin for "I unravel").
Luis Bolaños Mures
Aug 1, 2023, 10:52:05 PM8/1/23
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Variant with fewer swaps: Black may only swap vertically, and White may only swap horizontally.
Luis Bolaños Mures
Aug 2, 2023, 2:29:25 AM8/2/23
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Variant with more movement:
On your turn, place a stone of your color on an empty point or on a point occupied by an enemy stone. In the latter case, move the enemy stone to an orthogonally adjacent empty point before placing your stone. Your stone must not be part of any crosscuts, and the enemy stone must not be part of more than one crosscut. If the enemy stone is part of a crosscut, remove the other enemy stone in the crosscut.
This variant is more likely to have cycles, but here's hoping it won't.
On your turn, place a stone of your color on an empty point or on a point occupied by an enemy stone. In the latter case, move the enemy stone to an orthogonally adjacent empty point before placing your stone. Your stone must not be part of any crosscuts, and the enemy stone must not be part of more than one crosscut. If the enemy stone is part of a crosscut, remove the other enemy stone in the crosscut.
This variant is more likely to have cycles, but here's hoping it won't.
Luis Bolaños Mures
Aug 3, 2023, 8:45:56 PM8/3/23
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These are all the variants I'm currently considering:
V1: On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of a crosscut. As a result, the swapped friendly stone must not be part of a crosscut any more. If the swapped enemy stone is still part of a crosscut, remove the other enemy stone in that crosscut.
V2: On your turn, place a stone of your color on an empty point or on a point occupied by an enemy stone. In the latter case, move the enemy stone to an orthogonally adjacent empty point before placing your stone. Your stone must not be part of any crosscuts, and the enemy stone must not be part of more than one crosscut. If the enemy stone is part of a crosscut, remove the other enemy stone in the crosscut.
V3: On your turn, place a stone of your color on an empty point or on a point occupied by an enemy stone. In the latter case, move the enemy stone to an orthogonally adjacent empty point before placing your stone. Your stone must not be part of any crosscuts. If the enemy stone is part of one or more crosscuts, remove the other enemy stones in those crosscuts.
V4: On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of a crosscut. As a result, the swapped friendly stone must not be part of a crosscut any more. If the swapped enemy stone is still part of a crosscut, remove that stone.
V5: On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of a crosscut, so that your swapped stone is not part of a crosscut any more. If this is not possible, your placement is illegal. If this swap creates another crosscut, swap two opposite-colored stones in the crosscut so that your stone in the pair is not part of a crosscut any more, and keep doing so until no crosscuts remain. Note that, after any swap, you will always have a legal sequence of swaps available that ends with no crosscuts on the board.
In all versions, passing is not allowed, but, if you have no legal moves available, your turn is skipped. V5 is cycle- and deadlock-free. The others are deadlock-free, but I don't know if they are finite.
V1: On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of a crosscut. As a result, the swapped friendly stone must not be part of a crosscut any more. If the swapped enemy stone is still part of a crosscut, remove the other enemy stone in that crosscut.
V2: On your turn, place a stone of your color on an empty point or on a point occupied by an enemy stone. In the latter case, move the enemy stone to an orthogonally adjacent empty point before placing your stone. Your stone must not be part of any crosscuts, and the enemy stone must not be part of more than one crosscut. If the enemy stone is part of a crosscut, remove the other enemy stone in the crosscut.
V3: On your turn, place a stone of your color on an empty point or on a point occupied by an enemy stone. In the latter case, move the enemy stone to an orthogonally adjacent empty point before placing your stone. Your stone must not be part of any crosscuts. If the enemy stone is part of one or more crosscuts, remove the other enemy stones in those crosscuts.
V4: On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of a crosscut. As a result, the swapped friendly stone must not be part of a crosscut any more. If the swapped enemy stone is still part of a crosscut, remove that stone.
V5: On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of a crosscut, so that your swapped stone is not part of a crosscut any more. If this is not possible, your placement is illegal. If this swap creates another crosscut, swap two opposite-colored stones in the crosscut so that your stone in the pair is not part of a crosscut any more, and keep doing so until no crosscuts remain. Note that, after any swap, you will always have a legal sequence of swaps available that ends with no crosscuts on the board.
In all versions, passing is not allowed, but, if you have no legal moves available, your turn is skipped. V5 is cycle- and deadlock-free. The others are deadlock-free, but I don't know if they are finite.
Luis Bolaños Mures
Aug 3, 2023, 9:01:12 PM8/3/23
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Also, in V5, you never need to swap more than three pairs of stones on a single turn.
Luis Bolaños Mures
Aug 12, 2023, 6:23:34 PM8/12/23
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