1997-5-3 last update, 1997-2-4 first day, Robert Jasiek

Commentary on Tromp-Taylor Rules

These very simple and logical go rules are known as Tromp-Taylor rules.

The game is played on a square grid by two players called black and white.

square grid

• This grid has 9x9 grid points.
• Paths of grid lines are between any two grid points.
• This is the outset.
• The game is played by two players. Each player has a color: black respectively white.

Each grid point may be black, white, or empty.

grid points with colors black, white, or empty

• Two players compete using black respectively white color.
• Grid points without black or white have empty color.

If a path along the grid lines leaves a grid point A, passing only grid points of A's color, to end at a grid point of color C, then A is said to reach C.

grid point A reaches white

• A path along grid lines leaves the grid point A, passes the squared grid points, and ends at the triangled grid point.
• The grid points A and squared all have the empty color of A.
• The triangled grid point has white color.
• The grid point A reaches white.

A, B, C reach white

• Each of the grid points A, B, and C reaches white.
• The grid point D does not reach white.
• All four grid points reach empty.
• B, C, and D also reach black.
• A does not reach black.

A reaches black

• The grid point A reaches black using a short path.
• A also reaches empty.

Clearing a color is the process of emptying all grid points of that color that do not reach empty.

clearing black

• The black grid point near to white grid points does not reach empty. Thus it is to be cleared.
• After clearing the grid point is empty.

clearing black

• Several black grid points do not reach empty. They all become cleared.
• After clearing the grid points are empty.

The players alternate turns, starting with black.

black starts, then both players alternate

A turn gives a player the right to move by coloring an empty grid point with his color, then clearing the opponent's color, then clearing his color.

white's turn is a move at 1

• Most turns are used for a move.
• White uses his right to move by coloring the empty grid point 1 white.
• Black needs no clearing then.
• White needs no clearing then, either.
• Often no clearing at all occurs.

white's turn is a move at 1

• White moves at 1, making the empty grid point white.
• Then black is cleared: One black grid point becomes empty.
• Then white needs no clearing.
• A move can include clearing of one color only.

white's turn is a move at 1

• White moves at 1, making the empty grid point white.
• Then black is cleared: Several black grid points become empty.
• Then white needs no clearing.

black's turn is a move at 1

• Black moves at 1, making the empty grid point black.
• Then white needs no clearing.
• Then black is cleared: Three black grid points become empty.
• Such suicidal clearing rarely occurs.

No move may repeat an earlier grid coloring.

2 repeats an earlier grid coloring and is not allowed

• If black played at 2 after white's 1, then the grid coloring before 1 would be repeated.
• Black may not play at 2 right now. He is required to use his turn differently.
• Black might get a chance to play at the grid point 2 later.

A turn may be a pass. Two consecutive passes end the game.

white's turn 1 is a pass - black moves at 2 - white's turn 3 is a pass - black's turn 4 is a pass

• White has the turn but no useful move. Therefore white uses his turn 1 to pass.
• Black still has a useful move: he moves at 2.
• Black 2 is the last move coloring a grid point.
• Black 2 prepares the grid for scoring by clearing white.
• After 2 no player can increase the number of empty grid points that do not reach the opponent's color.
• The turns 3 and 4 are both passes. They are played consecutively and thus end the game.

At the game end a player's score is the number of grid points of his color plus the number of empty grid points not reaching the opponent's color. The higher score wins.

black score - white score

• The black score consists of the black grid points and the empty grid points not reaching white.
• Black's score is 40.
• The white score consists of the white grid points and the empty grid points not reaching black.
• White's score is 41.
• White has the higher score and wins the game.

black score - white score

• Black's score is 44.
• White's score is 35.
• Black has the higher score winning the game.
• The two empty grid points reaching black and white score for neither player.