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Subject: New game, Oddical rss

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Nathan James
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Oddical

Material
- a square grid, empty at start
- sufficient pieces in two colors, one color for each player

Definitions
Group - Each piece in play belongs to exactly one group at any time. (A single piece is a group by itself.)
That group consists of the the piece itself and any orthogonally connected pieces of the same color. (Groups may be combined by placement of new pieces.)

A region is any orthogonally connected set of groups.

Rules
Players take turns placing a single piece of their own color in an empty space on the board.

A piece may not be placed adjacent to an opponent's piece, unless it is also adjacent to at least one of your own pieces.

Capture
Following each change in board state (move or capture), the board is assessed for captured groups. Captures are automatic.

Only the largest group in a region is eligible for capture. If two or more groups are tied for largest in a region, none are eligible for capture.

A capture only takes place if there is a smaller odd-sized group of the other color in the same region.

If a group is captured, all the pieces that form that group are removed from the board.

End of Game
The game ends when one player can not place a piece. The winner is the player with more pieces on the board.

---------

edited to add the additional check for capture.
further edited for clarity

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Luis Bolaños Mures
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Do captures take place automatically/everywhere/after a placement?
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Nathan James
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I look forward to any comments on the game.

So far, my play testing has been with a 4x4 board. While analysis of 2x2 and 3x3 is trivial, there is surprising depth on a 4x4 board.
 
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Nathan James
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Yes, captures are automatic.

Sometimes a series of captures may take place following only one placement.

....
XOOO
.XXX
...A


If X places at position A, his group of 4 pieces will be captured. Then, his opponent's group of three pieces will be the new largest group in the region and will also be captured.
 
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Luis Bolaños Mures
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I'm intrigued by this, although I think there will be cycles.
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Nathan James
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Cycles have so far not been observed.

I have seen blunders wipe out massive sections of the board. So clearly, cooperative cycling should be possible. I just don't know that it's feasible in a competitive game.
 
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Dieter Stein
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I like the "group of groups" idea.
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Nathan James
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Here is a sample game that may be of interest.

Black demonstrates an aggressive strategy, playing to the center early. White stays closer to the edges and gets the worse of the deal.

http://gc1.iggamecenter.com/gm.php?sid=705088&place=0&lang=e...
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Luis Bolaños Mures
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spielstein wrote:
I like the "group of groups" idea.

I once used that idea in a sort of Yodd variant where a player owns a group-of-groups by having the most (although I now prefer "least") groups of their color in it, and whoever owns the most groups-of-groups wins. Number of groups-of-groups and groups in a group-of-groups must be odd at the end of any given turn.

I called this game Hyper. Should be worth a try.
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Nathan James
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Quote:
I like the "group of groups" idea.


It seems as if I've seen exactly this comment in a thread introducing another game, but I can't remember what game.
 
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christian freeling
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NJames wrote:
Quote:
I like the "group of groups" idea.


It seems as if I've seen exactly this comment in a thread introducing another game, but I can't remember what game.

Google came up with this one, but it may not be the one you meant.
 
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Arnaud DUTARTRE
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Would be great to have a little program to test it against an AI or other human with bigger board size.
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Arnaud DUTARTRE
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A simple prototype is in development to validate the concept for different board size. Android version with simple IA.
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Nathan James
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Looks good, Arnaud!
 
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Nathan James
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A few words on cycling in Oddical

Cycles normally do not occur in a game of Oddical. This is despite the fact that the structure of the game permits them. From an empty board, it is easy for the players to cooperate to form a cycle. The players just need to play "suicidally." Here is an example.

1. b3, c4
2. c3x, c3
3. b2, c2x
4. b3, c4
5. b4x, c3

A few observations can be made about this cycle. The first situation to repeat is that of an empty board except for one stone, with the owner to play next. Each player in turn will find themselves in this position. Also, it is not one that can be arrived at without capture, namely where the player next to play already has more stones on the board than the other player. It is impossible to return the board to an empty state.

It is much more difficult to construct a cycle on a board with more than handful of pieces. This is because the presence of other stones not involved in the cycle exert a strong influence on the board. To easily construct a cycle, the cycling groups need to be isolated from stones of either player. The rules of placement and the definition of a group mean that it is impossible for either player to place next to an existing stone without extending an existing group.

In practice this tends to mean that players do not have the same degree of freedom in a given position. When a capture occurs it is often impossible to quickly reestablish the prior position. On the contrary, captures provide an opportunity for whichever player plays next to reapportion the space, normally to his own benefit.

Careful study has yet to reveal a position in which neither player is advantaged by breaking the cycle. Thus far, my study has suggested that if there is such a position, it likely exists at the beginning of the game, on boards whose dimensions dictate the game is a loss for the the first player unless he sacrifices. This will create cycles if the board is also a loss for the second player following the sacrifice, and if the second player is able to imitate the first by sacrificing in a similar way. A lot of ifs.

...

As a matter of design philosophy, a game intended for serious play should not be harmed by cycles provided they are both rare and the result of poor play. I suspect that this is true of Oddical, at least on certain boards.

For more casual play, we might expect players to blunder out of cycles much as they blunder into them. But we might also provide a "safety valve" for games that have drifted too far from good play to be enjoyable.

One possible mechanism that seems to serve well for both casual and serious play is to introduce another victory condition, namely the capture of a set number of the opponent's stones. Under this scheme sacrificed stones put you at a disadvantage and cycling will eventually end in a loss for the player who first gives up material.

This method of dealing with cycles is more suited to casual play than three-fold repetition or superko rules, since players need not identify cycles at all. It should not be any less suited to serious play than rules forbidding cycling. If my assumption that the game doesn't incentivize cycling is correct, then counting captured stones will not ultimately alter the character of the game, provided the number required is not too low.
 
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