Help for the Game of Binar

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

binar challenge [-size=number] [-choose|-own] [-single|double] userid1 userid2

starts a new game for two players.

The -size parameter specifies the board size (default 5).
The -choose parameter specifies that players choose which parity to play each turn.
The -own parameter specifies that player must play their own parity each turn.
The -single parameter specifies that players need only form one line to end the game.
The -double parameter specifies that players must form two lines of the same parity.

Introduction

Binar is a simple logic game for people who think in binary.

Rules

The game is played on a square 5x5 grid which is initially empty. Two players, Even (0) and Odd (1), takes turns placing their number in an empty cell.

If a row or column is filled, then the sum of its numbers gives a parity (even or odd). If the row and column passing through a move are both filled and of the same parity, then the player of that parity wins. If the -single option is used then the game ends as soon any line (or pair of lines) is completed; if any completed line is of the opponent's parity then they win, otherwise the mover wins.

The following example shows a game won by Even:

```     a b c d e

5   . . 0 1 .   5 4   . 1 0 . .   4
3   0 1<1>0 0   3
2   . . 1 . .   2
1   . 1 0 . .   1

a b c d e   ```

Odd made the last move <1> at c3, however the row and column passing through c3 have both been filled and add up to even numbers (2 and 2) so Even wins.

The game is drawn if the board fills up before either player wins.

Notes

The game should be played on odd-sized boards. As Randall Bart points out: "The odd player is trying to get 1 or 3 of his pieces in a line, while the even player is trying to get 0, 2, or 4 of his pieces in a line. What is unusual is that the asymmetry goes away when the board size is odd. With size 5, each player wants an odd number of his own pieces (1, 3, or 5) and an even number of opponent pieces (0, 2, or 4) in a line."

Important Note: The game may be flawed as moves by 1 change parity but moves by 0 do not. This means that if 0 sets up a win, then 1 can play at the winning cell next turn to flip the parity and steal the win, however the reverse is not true (0 cannot flip the parity to steal a win off 1). This means that it may be impossible for 0 to win if 1 plays optimally. The -choose option was added to the game to address this problem.

Variants

If the -single option is used then the game ends as soon any line is completed (one or two lines may be completed per move). If any line completed on a move is of the opponent's parity then the opponent wins, otherwise the mover wins.

This variant was suggested by Paul van Wamelen as an attempt to fix the tendency towards draws using the original rules.

Syntax

The move syntax is:

binar move board# userid password d3

This command places the current player's number at position d3.

binar move board# userid password d3:1

This command places the number 1 at position d3.

History

Binar rules by Cameron Browne and copyright (c) Cyberite Ltd, March 2009.

Implementation and Help file by Cameron Browne, March 2009.