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Vying Games : Pah-Tum

Pah-Tum, sometimes written as POTM, is an ancient game. Several boards were found in Mesopotamia and Assyria dating back to 1800 BC. Its game play is similar to other n-in-a-row games, but different enough to be interesting.

How to Play

Pah-Tum is played on a 7x7 board with an odd number of randomly positioned blocks (or unplayable positions). We were unable to find a definitive source for the proper number of blocks, so we've opted for 5, 7, 9, 11, or 13 blocks (the number of blocks is determined randomly).

The goal of the game is to score more points than your opponent. The players, Black and White, take turns placing black and white stones, respectively, on the board's intersections until the entire board is completely filled.

Scoring

Points are scored for getting 3 or more stones of your color in a row horizontally or vertically, but not diagonally. The number of points scored is:

3-in-a-row: 3 points
4-in-a-row: 10 points
5-in-a-row: 25 points
6-in-a-row: 56 points
7-in-a-row: 119 points

This scoring system already includes points for any embedded n-in-a-rows. If you're curious, this is the scoring formula:

score(1) = 0
score(2) = 0
score(n) = 2 * score(n-1) + n

Why an odd number of blocks?

The board is 7x7, so there are 49 possible places to put a stone, and thus moves. With an odd number of blocks, the number of places to play is reduced to an even number. For example, 49 places - 5 blocks = 44 places. If there are an even number of moves, each player is guaranteed an opportunity to place an equal number of stones. If the number of blocks were even the first player would get to place one more stone than the second player, which just wouldn't be fair.

Pie Rule

The random blocks help reduce the first player advantage, but it is still strong on some boards. To further balance the game, the pie rule is used. With the pie rule, the second player has the option of swapping sides after the first move. So, if the first player makes too strong a move, he or she can expect the second player to swap sides. This should provide incentive for the first player to find a fair move.