| Position 1 | Position 2 | Position 3 |
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 White prisoners: |
A stone's liberty, also called its freedom, is any empty intersection horizontally or vertically (not diagonally) adjacent to this stone. For example, in Position 1 of Fig 1-1, the stone by 'a' has 4 liberties, the stone by 'b' has 3 liberties, and the stone by 'c' has 2 liberties. This illustrates the fact that the most liberties are in the center of the board and the least in the corner.
| Position 1 | Position 2 | Position 3 |
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White prisoners: |
A stone is killed (or taken prisoner) when all his liberties are taken away by enemy stones! This distinction is important because a stone which is connected to friendly stones might allow itself to have all its liberties taken away and still survive - but more about this later. For now, Position 2 of Fig 1-1 demonstrates some Black stones which are totally surrounded by Whites - these Black stones are killed because all their liberties are taken away by enemy stones. These Black stones are removed from the board and kept aside for final scoring of the game. Each of such prisoners counts as one point towards opponent's final score.
The resulting position after the Black stones from Position 2 are removed from the board is showed in Position 3.
Atari means that a stone (or a group of stones) has only one liberty left, thus it is prone to be killed by the opponent on the next move. An atari-move is a move which takes the second-last liberty of an opponent's stone - it is said that such move puts the opponent's stone(s) "in atari". An example can be seen in Position 1 of Fig 2-1 - here the White move at '1' puts the Black triangled stone in atari. Black can save his stone (prevent it from being killed) by extending to 'a' next. If he fails to do so, White will be able to play at 'a' himself and kill the Black stone.
| Position 1 | Position 2 | Position 3 |
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Position 2 of Fig 2-1 shows a possible continuation from Position 1 when Black decides to abandon his triangled stone (which was in atari) and so White is able to kill it with '3'. Position 3 shows two more examples of atari moves on single stones - White moves at '1' put the respective black stones in atari.
Stones which are adjacent horizontally and/or vertically (but not diagonally) are said to be connected. Such stones count as a group and they cannot be separated by the opponent. An example of connected stones is given in Position 1 of Fig 3-1. The four Black stones in this position are connected together to form a single group. Each of the White stones, however, is by itself - none of them is connected to any of the others. Notice again that diagonal relationship like between the White triangled stones is not a connection!
| Position 1 | Position 2 |
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Connected stones (or groups) have to be dealt with as a single unit - they cannot be considered separately for the purposes of life and death. They live together, or they die together. They cannot be separated.
More about connecting stones here.
The important thing which needs to be mentioned here is that fact that everything that was said in previous chapters about single stones still apply to whole groups. So the liberties of a group are the combined liberties of the stones which form this group (without double-counting liberties of course). For example, the Black group in Position 1 of Fig 3-1 has 9 liberties. To kill this groups, White would have to make 9 moves to take all the liberties away.
Position 2 of Fig 3-1 shows how White can put a whole group of Black stones in atari - by playing at '1'. If Black does not defend (by playing at 'a'), White can next play at 'a' and kill the 3 Black stones. White move at '1' was an atari move.