Why a mill is a removal, not a picture

Published

This is one subject: three counters in a straight marked line are a mill only because they let you take an opposing counter off the board. The board has twenty-four points. Lines do not run on the diagonals. This is not a list of famous mill problems.

1. Placement is nine counters each

You place one counter on an empty point. Ivory places first. When your placement closes a mill, you remove one opposing counter. If the opponent has a counter that is not in a mill, you must take one of those. You may take from a mill only when every opposing counter is already in a mill.

2. After that, move along a line

Once both sides have placed all nine, a turn is a slide along a marked line to an empty neighbouring point. Closing a mill by that slide is still a removal. Opening a mill and closing it again on a later turn removes again. There is no diagonal step.

3. Three counters may fly, and some games draw

A side that has exactly three counters left may move to any empty point, not only a neighbour. A side with fewer than three counters loses. A side that cannot move also loses. The same position three times is a draw, and so is one hundred plies with no capture.

Examples on this board

  1. Closing a line while placing. Your ninth point, or any earlier one, completes three counters on one marked line. You then take an onyx counter that is sitting outside a mill. The line by itself does not score. The removal is the result.
  2. Every opposing counter is already in a mill. You still remove one. The protection only applies while a non-mill counter exists. It is not a permanent shield.
  3. Open, then close. In the movement phase you slide one counter out of a mill, along a line, to an empty neighbour. On a later turn you slide it back and close the same line. Each closing removes another counter, if the removal rule still has a legal target.
  4. Flying. Onyx is down to three counters. Onyx can leave a corner of the board and appear on an empty point across the board in one turn. Ivory, still with four or more, cannot do that and must follow the lines.
  5. A draw, or an empty queue. You repeat a position for the third time, or a hundred plies pass with nobody captured. The game draws rather than playing on. If instead you were waiting in the public queue and no person joined, about ten seconds later the page starts a computer game and says so. That computer game uses these same mill rules.

Why it matters

A mill that you cannot open is one removal. A mill you can open and close is a series of removals, and the opponent’s counters disappear until flying, or a loss, or a draw, arrives. Players who build one pretty line and then ignore the neighbouring points find they cannot move when the board fills, which loses even if they still have all nine counters.

The date is the day this was written for the live twenty-four point board, including flying at exactly three and the about-ten-second computer game.

Closing

Place until a marked line closes, remove a counter that is not sheltered in a mill, and later slide only along the lines unless you are down to three. Remember the two draws. An empty public queue becomes the computer after about ten seconds. The about page and the privacy page are the site notes, not extra rules.