Pah Tum

Pah Tum is a two-player abstract strategy board game, played on a 7x7 square board. An odd number of squares are randomly closed off for play. These squares are called "black holes". Players alternate turns placing their pieces on the remaining squares attempting to create as many lines horizontally or vertically. The lines must be at least 3 squares long to score any points. The longer the line, the more points are scored for that line. The winner is the player with the most points.
Pah Tum is an alignment game distantly related to Go Moku and Dara. Pah Tum may be considered a game isolate.
Goal
The player who has the most points after scoring all their lines is the winner. If both players have an equal number of points, then the game is a draw.
Equipment
A 7x7 square board is used. Each player has 24 pieces. One plays the black pieces, and the other plays the white pieces. Not all 24 pieces may be used by each player during the game.
Gameplay and rules
1. An odd number of squares on the board are to be randomly closed off for play. No pieces can be placed on these black holes. Players decide the number of black holes, and then decide randomly which of the squares on the board will be the black holes. Usually, the number of black holes will be either 3, 5, 7, 9, 11, or 13. Marking a big "X" to denote the black hole squares on the board will suffice. The other remaining squares are available for play.
2. Players decide who will play the black pieces, and who will play the white pieces. They also decide who will move first.
3. Players alternate their turns.
4. On a player's turn, one piece may be placed on any vacant available square on the board. Players attempt to form (straight) lines (horizontal or vertical) with their pieces according to the following scoring system:
* 1 piece = 0 points
* 2 pieces = 0 points
* 3 pieces = 3 points
* 4 pieces = 10 points
* 5 pieces = 25 points
* 6 pieces = 56 points
* 7 pieces = 119 points
Therefore, a line must be at least 3 pieces long to score any points. The lines must contain only pieces of the same color and no black holes.
Note that a piece can be part of a horizontal line and a vertical line at the same time, and therefore, be counted twice when scoring.

5. When all the available squares have been filled, the game ends. Players tally up the points from the lines they formed. The winner is the one with more points. If both players have an equal number of points, the game is a draw.
6. Pie Rule (Optional): The first player may have an advantage in this game. Therefore an optional "Pie Rule" is applied. The rule states that if the first player's first move is too strong or advantageous, then the second player can decide to swap sides. This prevent the first player from performing a strong first move, and opt instead for a move that is fair for both players.
Analysis
An odd number of black holes are needed in order to ensure an even number of available squares for play, which means that each player will be able to place an equal number of their own pieces on the board which makes it a fair game.
The formula for the scoring system can be described as the following:
* score(1) = 0
* score(2) = 0
* score(3) = 3
* score(n) = 2 * score(n-1) + n
Related games
Go Moku, Dara, Tic-tac-toe,

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