Pasang

Objective

Pasang Emas is based on a traditional board game of Brunei. In this game, two players take turn accumulating points by capturing tokens while avoiding getting stuck. The game ends when either

• all tokens have been captured, in which case the player with the higher score wins,
• or a player gets stuck and automatically loses.

Game Set

The game set consists of the following:

• A board that is marked with 11 horizontal and 11 vertical lines forming a grid, except in the middle where the lines are broken.
•  60 white and 60 black tokens. A white token is worth 2 points; a black token 1 point.

A kas (mobile piece) for each player, conventionally one black pawn and one white pawn.

Board Arrangement

Before a game starts, the black and the white tokens are arranged on the board, each covering a line junction, forming a pattern. Before play begins, both players must agree upon the pattern of the board. There is a catalogue of over 30 different patterns to choose from. Here are some examples :

 

1

 

2

 

3

Passage Creation

The first move for each player is to create a passage by capturing a column of 5 tokens. The  first  player may capture any column on his side of the board.

The second player must capture a column from the diagonally opposite quadrant

Kas Selection

After passages are created, each player takes turn promoting a token to a kas, the mobile piece that will be used to capture more tokens. The token to be promoted must be chosen from the two-column bands on either sides of the player's passage, as illustrated in the figure below.

The chosen token is moved horizontally (possibly jumping over another token) into the passage, immediately capturing an odd number of tokens. There are two ways to play this move : "Sliding Play" and "Jumping play".

• Sliding Play : in the sliding play, the player to move selects a token from either bank of his passage, and slides it horizontally into the passage. The token becomes a kas, immediately capturing an odd number of tokens.
• Jumping Play : in the jumping play, the token is chosen from the column adjacent to either bank. The token jumps horizontally into the passage. The token become a kas, immediately capturing an odd number of tokens.

Odd Capture Rules

Each move in Pasang Emas, including kas selection, is a capture move.
The kas must be moved to form a line with an odd number (1, 3, 5, 7, 9) of tokens of the same colour. The line may pass through empty junctions.

However, the line must not be broken by a token of a different colour or by the opponent's kas. The tokens forming the line are immediately captured.

If more than one such line are formed, the player may capture any one (and only one) of them.
The figure below shows how the game might proceed after the two players have created their respective passages. Player 1 is promoting a token. The back layer of the figure shows the newly promoted kas being moved, forming a line with 3 black tokens. The front layer of the figure shows the arising position after these tokens have been captured.

The figure below shows how Player 2 might continue the game. The back layer of the figure shows his kas selection. With this move he might capture either 1 black token, or 3 black tokens, or 3 white tokens. The front layer of the figure shows the arising position after he has resolved his capture.

Kas Movement

The rest of the game is spent taking turns moving the kas. A kas can move either vertically or horizontally, sliding over any number of empty junctions.

There is a further imposition over the odd-capture rule: if a kas moves horizontally, it must capture vertically, and vice versa.

The figure below shows a position with red to move. His possible moves are indicated on the back layer of the figure. Should he choose the move indicated on the front layer of the figure, he might capture either 1 black token or 3 white ones. The 5 white tokens horizontally aligned with the kas cannot be captured with this move.

Game over

The game ends when no more tokens are left on the board, in which case the player with the higher score wins. The game also ends when the player to move cannot make any capture, a situation called “suntuk”.  The player who gets himself into suntuk forfeits all his tokens to the opponent and loses the game. In the figure below, it is red's turn to move. He loses due to suntuk.

Complexity of Pasang
(source : http://pasang-emas.blogspot.com/)

• In the opening stage, exactly 11 possible moves are available for the first player and 10 for the second.
• In the kas selection stage, an average of 31 possible moves are available. The number will be less if we "merge" different moves that result in identical situations. Theoretically, the maximum branching factor during this stage is 50.
• In the rest of the game, a player has an average of 6 possible moves to choose from at each turn. This is very much less than the theoretical maximum of 40.
• Overall, the average branching factor is 7.
• Game length : Since there are 118 pieces to capture, and each move is a capture move, the game obviously cannot exceed 118 plies. The longest game seen was 94 plies. On average, a game takes 56 plies.