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Subject: Non-transitivity in piece set-up rss

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Grant Fikes
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I forget what the turn order of the colors is, so for my convenience, let's replace the colors with 1, 2, and 3. The turn order is 1, 2, 3. Assume all pieces are rings in the extremely simple two-player set-up below:

1 . 1 . .
. . . . . .
. . 1 . . . .
. . . . . . . .
2 . 2 2 . . . . 2
. . . . . . . .
. . . . . . .
. . . . . .
3 . . . 3


As per the two-player rules, the player who didn't set up the board (player B) picks a color first, and then the original player (player A) picks one of the other two colors. I believe that player A has a winning strategy.

If player B picks 1, player A picks 3 and sacrifices either piece on his turn.
If player B picks 2, player A picks 1 and places a wall between the adjacent 2's (as per the strategy guide) and sacrifices two pieces on his next two turns.
If player B picks 3, player A picks 2 and moves the rightmost 2 as far left as possible.

Is such a non-transitive set-up possible with 60 pieces? I'm curious now.
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Néstor Romeral Andrés
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You might have missed this rule: purple starts.
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Grant Fikes
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n_r_a wrote:
You might have missed this rule: purple starts.


Okay, so 1 is purple, 2 is orange, and 3 is green. I don't see how that affects anything.

In a match-up between purple[1] and green[3], purple may have the initiative, but cannot do anything with it. He cannot unite his pieces in one move, nor block green from doing the same (either by placing a wall or by forcing green's winning sacrifice to create a larger united purple group). Green beats purple.

In a match-up between purple[1] and orange[2], purple's initiative suddenly becomes game-changing: he can block orange's one-move win with a wall between the adjacent oranges, buying enough time to unite his pieces to win. Purple beats orange.

In a match-up between orange[2] and green[3], of course, orange wins in one move, not even allowing green to play. Orange beats green.
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Néstor Romeral Andrés
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Yep. I wanted to make sure that you were not missing anything.

If such a full board non-transitive configuration exists, that would kill the setup phase of one of my favourite designs. But I can trade it for a nice puzzle!

 
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Grant Fikes
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n_r_a wrote:
Yep. I wanted to make sure that you were not missing anything.

If such a full board non-transitive configuration exists, that would kill the setup phase of one of my favourite designs. But I can trade it for a nice puzzle!



One possibility is to have player B select both players' colors, requiring player A to make a "fair" board, or make them pick randomly, or. . . I dunno, have both players participate in board set-up somehow.
 
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Russ Williams
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mathgrant wrote:
or. . . I dunno, have both players participate in board set-up somehow.

There is the DVONN and (one setup version of) TZAAR method for setting up such "arbitrary/jumbled setup" games, where the players alternate placing pieces.
 
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Néstor Romeral Andrés
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mathgrant wrote:
n_r_a wrote:
Yep. I wanted to make sure that you were not missing anything.

If such a full board non-transitive configuration exists, that would kill the setup phase of one of my favourite designs. But I can trade it for a nice puzzle!



One possibility is to have player B select both players' colors, requiring player A to make a "fair" board, or make them pick randomly, or. . . I dunno, have both players participate in board set-up somehow.


In fact the rules recommend leaving Green as neutral for a 2 player game. I can simply make it mandatory.

 
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Grant Fikes
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n_r_a wrote:
In fact the rules recommend leaving Green as neutral for a 2 player game. I can simply make it mandatory.


For some reason, I'm coming to like the idea of letting the second player choose to make the other player choose first if he believes there to be non-transitivity. It's the least drastic modification to the current rules (since I doubt that most randomly-generated boards will be non-transitive). . . .
 
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