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Ko-Fight

The Ko rule (Basic rule 8) prohibits to make a move that results in a repetition of position (stone allocation) on the entire board.  This rule serves to prevent the possibility of endless recaptures that might otherwise tie the game.

  • Black has just captured a white stone at the point X with move 1.  White is prohibited by the Ko rule (Basic rule 8) from recapturing black stone by making his next move to the point X (recapture would lead to the repetition of stone position on the board).  White has to play elsewhere on the board (or pass a move, which is always permitted by Basic rule 9).
  • If Black wants to save his stone 1, he has to connect at the point X.  If Black will play elsewhere on the board, White can now recapture black stone 1 by playing into point X (position on the entire board has changed due to white and black stones played elsewhere).
  • After White recapture of the black stone the situation gets reversed, and it is now Black who has to play elsewhere before trying to recapture White.

It is important to note that what's prohibited by the Ko rule (Basic rule 8) is a repetition of position on the entire board, not just stone recapture at the point of the original capture.  The following sequence is a legitimate one (though senseless such positions are normally left as-is until game ends White is "dead" unconditionally here).

                 

Thus the Ko rule permits Black in fact to make two successive moves in the local position (capture and connection).  This is a great advantage considering that the fate of large groups of stones might depend on the ability to make two successive moves within or at the borders of these groups.  The disadvantage is that the opponent also gets the opportunity to make two successive moves in some other local position.  So if opponent wants to prevent the player from taking an advantage of two moves in a row in one local position, he looks all over the board for another local position where he can create a threat of making two successive moves, and causing the damage that overweights the advantage the first player might get in the first local position (a Ko-threat).

These opportunities of playing two moves in a row locally lead to so-called Ko-fights in Go, which can change dramatically the balance of the entire game, turning the lost game into a victory with only several moves, and visa versa.

White group seems to be "alive" in the left position below, considering White's threat to cut and capture black stone by making a move to the point X.  This threat calls Black to protect his weak point X, which gives White an opportunity to play at point Z and "live" unconditionally.  Exchange of Black 1 and White 2 is one possibility of such peaceful development.

         

Let's suppose, however, that in some other locality Black has a group of an unconditionally "dead" stones shown in the left position below.  There are only two ways make a "live" group with two "eyes" out of this position.  Both ways require that Black will be able to make two successive moves in this locality without White's resistance.  Hope that White won't notice Black's first approaching move is quite naive.  However, the the Ko-fight initiated elsewhere might prevent White from answering to Black's approaching move in this position for the possibility of a bigger loss in another local position.

           

Left position above is Black's Ko-threat that Black can utilize at the right time in order to win a Ko-fight elsewhere on the board.

  • Backed-up by this Ko-threat, Black starts a Ko-fight with the move 1
  • White has no other choice but to counter with the move 2 (otherwise White will loose unconditionally).
  • Black plays Atari by 3 and "life" and "death" of six white stones depends now entirely on the outcome of the Ko-fight in this corner.

  • White has to capture black stone 3 by making a move at 4 in order to have any chance for survival.
  • White stone 4 is in Atari, but Black can't recapture it immediately because of the Ko rule (Basic rule 8).

Instead Black can make move 5 in another part of the board threatening to save his four stones in another corner by making a group with two "eyes".

     

     

White can now connect all stones with 6 thus making an unconditionally "alive" group and finishing the Ko-fight in this corner.


Black in this case will place next stone at 7 making a group with two "eyes".  Ko-fight permitted Black to make two moves in a row in this local position and to save a group that otherwise would be unconditionally "dead".  Black's gain in this corner is 14 points:

  • 4 black potentially "prisoner" stones are saved.
  • 8 points of territory which White might have gained (after removing 4 black "prisoner" stones).
  • 2 points of black territory gained.

     

Black's gain of 14 points is definitely more than the potential black gain from connecting at point X in initial position (which leads also to loosing the chance to save black group in another corner).  Black's gain from destroying white group in initial position might be even more, but before trying to do this Black must find at least one Ko-threat big enough to prevent White from connecting with move 6.  Evaluation of subsequent potential Ko-threats on both sides is also important for a prolonged Ko-fight in order to be reasonably sure that one can win it.

If Black will try to make two "eyes" in the corner without initiating a Ko-fight first, just hoping that White won't pay due attention to Black's approaching move, Black most likely will be stopped by White and will loose both the Ko-threat and potential opportunity to save his group.  Such a play, though not prohibited by Go rules, shows not only a disrespect of the opponent, but also a lack of understanding of the possibilities of Ko-fight.

Similar to the threats of occupying own "critical" points in an attempt to save otherwise "dead" group are the threats of occupying "critical" points within opponent's otherwise "live" group.  What matters most in Ko-fight is the balance between loss and gain, i.e., finding the adequate Ko-threats just enough to force the opponent to make certain move in certain local position.  It hardly makes any sense to use a large threat in the situation when the smaller threat will give the same result the habit to assess potential Ko-threats, sorting them according to potential gain or loss, might prove to be very helpful in the cause of the game.

Certainly White might choose not to connect the Ko, but to destroy Black's group by playing 6.

     

  • In this case Black can use its next move 7 to recapture white stone 4 at the point X.
  • White can't recapture black stone immediately because of the Ko rule (Basic rule 8).
  • So it's now White's turn to look for a Ko-threat large enough to prevent Black from from connecting at the point X.
  • If White won't be able to find an adequate Ko-threat, all White's stones in this corner will be "dead".

Since potential White loss of their stones in the corner is obviously greater than their loss due to letting Black live in another corner, the most likely outcome of the presented position is White connecting and saving his stones.  In exchange for that opportunity White has to permit Black to make two moves in a row in another corner making a "live" group with two "eyes".

Situations discussed above are intentionally simplistic in order to make the idea of Ko-fight as clear as possible.  The real Ko-fight usually goes all over the board often with several local positions involved where it is difficult to evaluate on the fly the gain-and-loss balance for each position.  It makes sense to take a good note of all potential Ko-threats and never waste them.  A plenty of Ko-threats permits a player to be invulnerable in the Ko-fight, or to be able to launch one himself.  In a well-balanced game the outcome of a Ko-fight can easily determine the result of the entire game.


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