Help for the Game of Pyloff

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**  NOTE: The Pyloff rules do not work very well as they currently stand.   **
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**        Please try the subsequent game of Margo which is far superior.    **
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Introduction

Welcome to the network Pyloff server. The challenge command is described here. Other commands are the same as for all pbmserv games.

  pyloff challenge [-size=number] [-all_freedoms] [-cut_down] userid1 userid2 [.. userid4]

starts a new game for between two and four players.

The -size parameter sets the size of the board (default is 6).

The -all_freedoms parameter specifies that freedoms may exist on any level, not just the board level.

The -cut_down parameter specifies that the game is to be played according to the "cut down" rules (described below).

Introduction

Pyloff is similar to Go, except that it's played with marbles which may stack up to form piles. A special capture rule is used to resolve potential problems with retrieving buried pieces after capture; captured pieces with any piece(s) resting directly upon them are not removed.

Rules

Players take turns placing a piece (marble) of their colour at any valid empty point. A point is valid if it is: 1) a board point, or 2) supported flatly by four existing pieces.

Connection: Two pieces of the same colour are connected if they are squarely adjacent to each other, or one rests directly upon the other. A group is a visibly connected set of pieces which may visit multiple levels.

Freedom: A piece has freedom if it is adjacent to at least one valid empty point on the board level. A group has freedom if at least one of its member pieces has freedom.

Surround capture: After playing a piece, all enemy groups without freedom are captured and removed from the board, except for pieces that support one or more higher-level enemy pieces either directly or indirectly. Such pieces are not removed and remain alive in the game.

No suicide rule: It is not permitted to place a piece without freedom, unless that move captures neighbours to create its own freedom.

Ko rule: It is not permitted to repeat a previous board position (this has not been implemented so is up to the players' discretion).

Over/under rule: A connection passing over an enemy connection cuts it. Buried pieces (those with a piece directly above them) do not count in any connections; groups must be visibly connected.

Players may not voluntarily pass, but are forced to pass if there is no legal move.

The game ends when neither player can make any further move. The player with the most pieces in play wins.

Multiplayer: Multiplayer Pyloff is played using exactly the same rules as the two-player version.

Examples

   An X piece at 'a' captures the O group, which has no remaining freedoms.


   |    .       .       .       .       |    .       .       .       .
   |                                    |                                 
| _____ | _____ _____
| / \ | / \ / \
| a | x x | . . || x x | x x | . .
| | x x | || x x | x x |
| _____ \_____/ _____ | \_____/ \_____/ _____
| / \ / \ / \ | / \
|| o o | o o | x x | . | . . | x x | .
|| o o | o o | x x | | | x x |
| \_____/ \_____/ \_____/ | \_____/
| / \ / \ / \ | / \
|| o o | o o | x x | . | . . | x x | .
|| o o | o o | x x | | | x x |
| \_____/ \_____/ \_____/ | \_____/
| / \ / \ / \ | / \
|| o o | o o | x x | . | . . | x x | .
|| o o | o o | x x | | | x x |
| \_____/ \_____/ \_____/ | \_____/
+----------------------------- +----------------------------- An X piece at 'b' does not capture the O group, as it still has two freedoms after the move (marked '*'). | . . . . | . . * .
| |
| _____ _____ | _____ _____ _____
| / \ / \ | / \ / \ / \
| b | x x__|__o o | . || x x | x x__|__o o | *
| | x / \ o | || x x | x / \ o |
| _____ \__| o o |__/ | \_____/ \__| o o |__/
| / \ / | o o | \ | / \ / | o o | \
|| o o | o \_____/ x | . || o o | o \_____/ x | .
|| o o | o o | x x | || o o | o o | x x |
| \_____/ \_____/ \_____/ | \_____/ \_____/ \_____/
| / \ / \ / \ | / \ / \ / \
|| o o | o o | x x | . || o o | o o | x x | .
|| o o | o o | x x | || o o | o o | x x |
| \_____/ \_____/ \_____/ | \_____/ \_____/ \_____/
| / \ / \ / \ | / \ / \ / \
|| o o | o o | x x | . || o o | o o | x x | .
|| o o | o o | x x | || o o | o o | x x |
| \_____/ \_____/ \_____/ | \_____/ \_____/ \_____/
+----------------------------- +----------------------------- An X piece at 'c' captures the O group. Note that captured pieces which support higher-level enemy pieces are not removed. | . . . . | . . . .
| |
| _____ | _____ _____
| / \ | / \ / \
| c | x x | . . || x x | x x | . .
| | x x | || x x | x x |
| _____ \_____/ _____ | \_____/ \_____/ _____
| / \ / \ / \ | / \ / \
|| o o | o o__|__x x | . | . | o o__|__x x | .
|| o o | o / \ x | | | o / \ x |
| \_____/ \__| x x |__/ | \__| x x |__/
| / \ / | x x | \ | / | x x | \
|| o o__|__o \_____/ x | . | . | o \_____/ x | .
|| o / \ / \ x | | | o o | x x |
| \__| o o | o o |__/ | \_____/ \_____/
| / | o o | o o | \ | / \
|| o \_____/ \_____/ x | . | . . | x x | .
|| o o | o o | x x | | | x x |
| \_____/ \_____/ \_____/ | \_____/
+----------------------------- +----------------------------- The O overpass cuts the following two X pieces (over/under rule). _____ _____
/ \ / \
. | o o__|__o o | .
| o / \ o |
\__| o o |__/
/ | o o | \
. | x \_____/ x | .
| x / \ x |
\__| o o |__/
/ | o o | \
. | o \_____/ o | .
| o o | o o |
\_____/ \_____/
. . . .

All Freedoms Version

In the "all freedoms" version, freedoms may exist on any level, not just the board level. This means that an X piece at 'e' does not capture the O group, as it still has two level 1 freedoms after the move (marked '*').

   |    .       .       .       .       |    .       .       .       .    
| |
| _____ | _____ _____
| / \ | / \ / \
| e | x x | . . || x x | x x | . .
| | x x | || x x | x x |
| _____ \_____/ _____ | \_____/ \_____/ _____
| / \ / \ / \ | / \ / \ / \
|| o o | o o | x x | . || o o | o o | x x | .
|| o o | o o | x x | || o o | o o | x x |
| \_____/ \_____/ \_____/ | \_____/ \_____/*\_____/
| / \ / \ / \ | / \ / \ / \
|| o o | o o__|__x x | . || o o | o o__|__x x | .
|| o o | o / \ x | || o o | o / \ x |
| \_____/ \__| o o |__/ | \_____/*\__| o o |__/
| / \ / | o o | \ | / \ / | o o | \
|| o o | o \_____/ x | . || o o | o \_____/ x | .
|| o o | o o | x x | || o o | o o | x x |
| \_____/ \_____/ \_____/ | \_____/ \_____/ \_____/
+----------------------------- +-----------------------------

This makes higher level plays much stronger and encourages a higher stacking of pieces, but unfortunately makes groups all but impossible to capture. This results in a rather cold game in which the board tends to fill up without capture, until an unlucky player is forced to make a negative move and lose.


Cut Down Version

The "cut down" version is played according to the above rules, with the following changes:

  1) Connections do no propagate downards. This means that pieces cannot rely on freedoms below
        them, and it is possible to capture higher-level subgroups rather than entire groups.

  2) Freedoms are valid as long as they are legal board points; they need not be supported by four existing pieces.

Rule change 1) makes it easier to capture pieces, while rule change 2) makes it easier to place higher-level pieces.

The cut down version was suggested by Phil Bordelon as a way to reddress the cold nature of the "all freedoms" game.

Notes

Higher level plays are strong, as the lower-level pieces that support them remain fixed and cannot be removed from the board (unless the higher level pieces are themselves captured and removed).

Multiple groups may be joined by higher-level pieces to create safe supergroups with multiple eyes. However, the fact that players cannot pass means that they may eventually be forced to fill in their own eyes and render groups unsafe.

Adjacent friendly pieces on the outermost row or column of any level cannot be cut, as it's not possible to bury them or separate them with an overpass. Edge moves can therefore be quite strong (especially if they support higher-level pieces) despite the fact that the edge removes a potential freedom. Edge play becomes increasingly predominant as the levels build up and the ratio of edge points to interior points increases.

Removing buried pieces from connection calculations means that players do not have to remember the colour of hidden pieces, except when it comes to counting the score at the end of the game.

The board, when fully stacked, forms a pyramidal or cannonball stacking. The maximum number of pieces that may be played on a board of size n is given by the pyramidal number Pn = n (n + 1) (2n + 1) / 6.

    Board size      Max pieces
        3x3             14
        4x4             30
        5x5             55
        6x6             91
        7x7            140
        8x8            204
        9x9            285
       10x10           385
       11x11           506
       12x12           650
       13x13           819
        ...            ...
       19x19         2,470 

A game of Pyloff will therefore take several times as long as a game of Go on the same sized board. For example, a 10x10 Go board has room for 100 pieces whereas a 10x10 Pyloff board has room for 385 pieces (although these limits will never actually be reached).

Each ball in a cannonball stacking has up to twelve connected neighbours, however only the four squarely adjacent neighbours on the same level count as freedoms in Pyloff (as in Go), not diagonally adjacent neighbours on the next level up/down. This is for two main reasons:
1) It makes groups easier to surround (otherwise captures would rarely occur); and
2) It means that some members of surrounded groups may remain uncovered (otherwise only singleton captures would remove pieces from the board).

Some multiplayer Go variants relax the connection definition so that enemy groups may consist of stones of any colour except the current player's. Pyloff maintains the stricter definition - that any group may only consist of one colour - to encourage captures.

Translating Pyloff to the hexagonal grid is complicated by phase problems; for any packed level there are two ways to pack the level above, both of which are valid but incompatible. The square grid is better suited to ball-stacking games of this type.

Syntax

The move syntax is:

  pyloff move board# userid password a7       (place a piece at A7)   
  pyloff move board# userid password swap
  (swap sides - second move only)

History

Pyloff rules copyright (c) Cameron Browne, February 2006.

The name Pyloff derives from the fact that pieces form piles and are taken off the board following capture. This is in contrast to the related game Pylon, in which captures result in pieces being added to the board.

Implementation and Help file by Cameron Browne, February 2006.