TAU (2011)

TAU is a simple 2 player abstract strategy game that can be played with a marker and a piece of paper.

It is played on a rectangular grid of n x m squared cells (n can be equal to m). Both players must agree on the grid size before the game starts.

There are 2 phases on the game:

1- Negotiation phase

A random player starts by telling a number. Then the other player must tell a higher one or pass. The process is repeated until one of the players passes.

The player that 'passed' is called 'LOW', and the other player is called 'HIGH'. Write down the last number reached during the negotiation. This number is the called 'LIMIT'.

Example:

A: 70
B: 120
A: 143
B: Passes

A is 'HIGH', B is 'LOW' and LIMIT = 143

2- Playing phase

The game is played in turns. Each game lasts a number of turns equal to (m+n)/3 rounded up. A turn is considered a player's move (not 2 players).

Starting with 'HIGH' players take alternate turns removing an entire row or column of cells from the grid, by drawing a line on it. The line must go through at least one square which doesn't already have a line. It is forbidden to draw a line so that it leaves the board with no 'unremoved' cells remaining.

When all the turns have been played, the game ends.

Scoring

Several rectangular groups of 'unremoved' cells have been created. Multiply the size of all the groups to calculate the score.

Example:

The following groups have been created: 1,1,2,2,3,6. Score= 1 x 1 x 2 x 2 x 3 x 6 = 72

If the final score is higher than LIMIT, the 'HIGH' player wins. Otherwise, 'LOW' wins.

Designer notes

TAU was evolved from OMEGA while teaching my students how to multiply in binary base. It uses Linkage's fewer/more idea. I recommend starting with boards of m+n = 20..30. Trivial sizes might be interesting only from a mathematical point of view. I recommend the shortest side to be at least 1/3rd of the longest one. Squared boards are particularly interesting.

Thank you, Russ Williams and Nathan Morse for the corrections.

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