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Subject: New game: Whirlwind rss

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Luis Bolaños Mures
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WHIRLWIND

Introduction

Whirlwind is a drawless connection game for two players: Black and White. It's played on the intersections (points) of an even-sized square board. The recommended sizes are between 12x12 and 20x20. The top and bottom edges of the board are colored black; the left and right edges are colored white.

At the start of the game, some black and white stones are arranged on the board in an interspersed pattern, as shown in the picture:



Play

Black plays first, then turns alternate. On his turn, a player must place one one or two stones of his color on empty points of the board. On his first turn, Black can only place one stone. Passing is not allowed.

At the end of a turn, any two like-colored, diagonally adjacent stones must share at least one orthogonally adjacent, like-colored neighbor.

Objective

The game is won by the player who completes a chain of orthogonally adjacent stones of his color touching the two opposite board edges of his color. Draws are not possible.

Acknowledgements

The restriction on diagonal connections as a means to prevent deadlocks was first used in Corey Clark's Slither.
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Russ Williams
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Looks interesting!

Rule question:

For a given board size, there seem to be multiple ways to place the interspersed pattern onto the board, and unless I'm missing something, the setup is not uniquely defined.

E.g. the illustration is 14x14; if we wanted to play a game on 12x12, would we remove the outside edges from all 4 sides (I'm guessing this is the intent), or remove the 2 northern edges and 2 eastern edges, or impose the pattern however we like by mutual consent (so that multiple setups are possible), or what?
 
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christian freeling
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Congrats, I already suspected you hadn't emptied that cup completely.

I guess the setup could be by mutual consent. It would seem hard to argue one or the other would be better. The game seems to complex to determine any difference in actual play, at the moment.

This is a hot game, so why would a player choose to place only one stone if and when he has the right to place two?

P.S. Barring a complete connection at the first placement of a turn of course.
 
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Luis Bolaños Mures
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russ wrote:
Looks interesting!

Rule question:

For a given board size, there seem to be multiple ways to place the interspersed pattern onto the board, and unless I'm missing something, the setup is not uniquely defined.

E.g. the illustration is 14x14; if we wanted to play a game on 12x12, would we remove the outside edges from all 4 sides (I'm guessing this is the intent), or remove the 2 northern edges and 2 eastern edges, or impose the pattern however we like by mutual consent (so that multiple setups are possible), or what?


Good catch. I intended to let the players choose, but I forgot that this would allow asymmetrical set-ups, which even have different numbers of black and white stones.

So, answering your question, only symmetrical set-ups are allowed. For every board size, two different symmetrical set-ups exist. Reversing the colors in one yields the other. Both of them are equally valid.

To get a valid set-up, it's best to start by arranging the central 4x4 area and then proceed outwards.
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christianF wrote:
Congrats, I already suspected you hadn't emptied that cup completely.

Thanks for the confidence. I'm actually surprised myself.

christianF wrote:
This is a hot game, so why would a player choose to place only one stone if and when he has the right to place two?

Forcing players to always place two stones would only complicate matters because of the existence of illegal placements.

First off, illegal placements mean that the game isn't completely hot, so there can be situations where it's not in the interest of the player to make a second placement.

Also, if you forced players to always place two stones, you would also have to specify whether a player is allowed to choose a first placement which leaves him with no legal second placements available, or if he is forced instead to choose a first placement which will allow him to make a second placement whenever there is any such first placement available.
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christian freeling
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luigi87 wrote:
christianF wrote:
This is a hot game, so why would a player choose to place only one stone if and when he has the right to place two?

Forcing players to always place two stones would only complicate matters because of the existence of illegal placements.

That sounds a bit like "forcing players to move would only complicate matters because of the existence of illegal moves".

luigi87 wrote:
First off, illegal placements mean that the game isn't completely hot, so there can be situations where it's not in the interest of the player to make a second placement.

Also, if you forced players to always place two stones, you would also have to specify whether a player is allowed to choose a first placement which leaves him with no legal second placements available, or if he is forced instead to choose a first placement which will allow him to make a second placement whenever there is any such first placement available.

So there are positions in which a player cannot legally make a second placement (an example would be appreciated). This leads me to the assumption that there must be positions where a player cannot legally make his first placement. Then what?
 
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Russ Williams
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FWIW I believe here's a kind of minimalist contrived 3x3 position where players (B & w) can place neither 1 stone nor 2 stones without violating the diagonal rule:

w . B
B . w
w . B

Finding whether it is adaptable to be a real position which can arise from a proper Whirlwind setup position is left as an exercise for the reader.
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christianF wrote:
So there are positions in which a player cannot legally make a second placement (an example would be appreciated).

Imagine a position with no other empty points than those included in:

a) One or more instances of the following pattern:


b) Exactly one instance of the following pattern:


If the first placement is at a point of type b, a second placement can't be made.

christianF wrote:
This leads me to the assumption that there must be positions where a player cannot legally make his first placement. Then what?

There aren't any such positions. The proof rests on two easy-to-check facts:

a) In a legal position, it's impossible to make a (legal or illegal) first placement that creates two different diagonal connections unremovable by a single second placement.

b) If a first placement at 1 would create a diagonal connection and playing at 2 to resolve it would create another diagonal connection, then there will always be an empty point (3) orthogonally adjacent to 2 such that a first placement there either creates no diagonal connections (and is therefore a legal move in itself) or creates one or two diagonal connections that are removable by a second placement.

Of course, this also proves that the game is drawless.

(EDITED)
 
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Russ Williams
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luigi87 wrote:
a) In a legal position, it's impossible to make a (legal or illegal) first placement that creates two different diagonal connections.

I must be misunderstanding what you mean by that, because it seems to me that you can certainly make a first placement which creates 2 different diagonal connections, e.g. after a few turns the upper left corner of the sample setup position in the original post could look like this:
. w w . . .
. . w B . .
B . . . w w
. . w . . .

and then w plays the first placement on their next turn to make 2 different diagonal connections:

. w w . . .
. . w B . .
B . . w w w
. . w . . .


which of course can be made legally connected with the second placement :

. w w . . .
. . w B . .
B . w w w w
. . w . . .

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russ wrote:
luigi87 wrote:
a) In a legal position, it's impossible to make a (legal or illegal) first placement that creates two different diagonal connections.

I must be misunderstanding what you mean by that, because it seems to me that you can certainly make a first placement which creates 2 different diagonal connections, e.g. after a few turns the upper left corner of the sample setup position in the original post could look like this:
. w w . . .
. . w B . .
B . . . w w
. . w . . .

and then w plays the first placement on their next turn to make 2 different diagonal connections:

. w w . . .
. . w B . .
B . . w w w
. . w . . .


which of course can be made legally connected with the second placement :

. w w . . .
. . w B . .
B . w w w w
. . w . . .


True. I think my mind just went past that (an excuse as bad as any other) because that pattern is obviously not problematic. You can even make the second placement as the first and omit the other.

Anyway, I guess I should rephrase my original statement as follows:

In a legal position, it's impossible to make a (legal or illegal) first placement that creates two different diagonal connections such that a single second placement can't remove both.

EDIT: Done.
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russ wrote:
FWIW I believe here's a kind of minimalist contrived 3x3 position where players (B & w) can place neither 1 stone nor 2 stones without violating the diagonal rule:

w . B
B . w
w . B

Finding whether it is adaptable to be a real position which can arise from a proper Whirlwind setup position is left as an exercise for the reader.

There's yet another such position. Those that complete Russ' exercise can proceed with this one for bonus points.

[EDIT: Answering someone's request for clarification: I mean there is another position that could be the subject of a similar "riddle", the solution of which is the same as in Russ' position.]
 
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George Leach
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Wait... clearly Russ' position breaks your proof about the drawlessness, what am I missing that means this is not a possible position?

Edit: Ah ok, that's not possible because of the setup... At least that's obvious to me in open space but perhaps there's a problem at the edges or corners?
 
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Jugular wrote:
Wait... clearly Russ' position breaks your proof about the drawlessness, what am I missing that means this is not a possible position?

Edit: Ah ok, that's not possible because of the setup...

That's right. The other problematic position made impossible by the set-up is this one:


In my game Vimbre, these two situations are taken care of by a flipping rule instead.

Jugular wrote:
At least that's obvious to me in open space but perhaps there's a problem at the edges or corners?

Well, if anything, I think the edges are less problematic because there are fewer possible diagonal connections to worry about there.

However, reflecting about this has made me realize that the following statement of mine is both false and irrelevant:

luigi87 wrote:
In a legal position, it's impossible to make a (legal or illegal) first placement that creates two different diagonal connections unremovable by a single second placement.


It's false because playing at a in the picture above would create two such diagonal connections, but it's irrelevant because, in that case, either b or c will necessarily be legal for White, after which a play at a creates only one diagonal connection. (It's also irrelevant because it's not really related to the second part of my "proof".)
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Whirlwind is now in the database.

The release date is taken from my first public mention of the game, which took place in a Little Golem thread a couple of months ago.
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