You may have noticed that towards the end of your game against the computer, there was a lot of pretty boring "cleaning up" to do. For example, the computer probably left a bunch of stones in places where you knew they couldn't live, and you had to go and kill them to make sure you got points for the eye they were in. In a game between two people, you usually don't bother to kill those stones - you just count them as dead when the game ends. For example, in this diagram, the greyed stone will be declared dead by the players at the end of the game:
Doing this doesn't change the score any, but it does keep the players from getting bored at the end of the game.
Think again of your game against the computer. You were given nine stones on the board at the start of the game. This is usually done when one player is a lot better than the other. It makes the game more even and more fun for both players. These stones are called "handicap stones." Games that use these are also called handicap games. A game with handicap zero is an even game; usually players don't go use more than a handicap of nine.
To give even finer control over the skill between players, one player may be given bonus points instead of (or in addition to) handicap stones. These bonus points are called "komi." In a game with a komi of 10 points, the weaker player will automatically get 10 bonus points at the end of the game. Often ½ point is added to the komi to make it impossible to have a tie game. Also, in truly even games, the player who moves first has an advantage, so the player who moves second (with the white stones) is usually given 6½ points of komi to balance out.
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