ko

An abbreviation for Knock Out, as in when one person has brutally maimed another into a state of unconsciousness.

Often encountered in fighting games where KO is the objective, rather than to brutally murder your opponent, ala Mortal Kombat. A Fatality is NOT a KO! If you can't remember this, just use this little rhyme:

If they have no head, they are DEAD!

A Japanase word for eternity.

In the game of go, a ko occurs when one player could immediately recapture a stone that was just captured, and the opposing player could immediately recapture that stone, and so on, forever.

Like this:

+++OX+++++
++OX*X++++
+++OX+++++

There is a rule in place to prevent this: No player may make a move that would result in a board position which has already occurred. This means that in a ko situation, the player whose piece was captured must play elsewhere before they can recapture. So, in the above picture, white (the "O's") must play elsewhere. If white's move is important enough, black may choose to respond to that move, rather than playing in the * position to "fill in." Often a ko will move back and forth over the course of a game this way.

At least in the sport of Boxing, KO does not necessarily have anything to do with unconsciousness. A KO, or "knockout" is scored when a boxer is counted as being down by the referee and this leads to the end of the fight.

Traditionally, this means the boxer is knocked on his butt and doesn't get up before the referee counts to ten. Very often though the entire count is not given, or the ref will stop the bout immediately after the knockdown. This is done so that the ringside doctors can quickly enter the ring and make sure the fighter is ok. Knockouts in modern boxing rarely involve the boxer becoming completely unconscious, or truly "knocked out".

On the other hand, KO is also used in boxing statistics to represent the number of stoppages a boxer has won. See my WU on TKO for a discussion of what counts as a Technical KO and a real KO. So, in this sense, "KO" represents a situation where a boxer did not even get knocked to the floor.

"Ko rules" prevent games of Go from degenerating into "non-advancing" situations. Without any ko rules, a single ko is sufficient to lock the game into an infinite loop.

The "simple ko" rule above (artfuldodger's writeup) is sufficient to prevent a game from looping due to a single ko, but insufficient for the general case.

Suppose we have 3 kos:

.............
..xo.........
.xo3o....xo..
..xo....x2xo.
.........xo..
..ox.........
.ox1x........
..ox.........

(The numbered places are blank places, marked for use in the sequel)
Call the two kos where white (o) may play (1) and (2), and call the ko where black (x) may play (3). Assuming it's white's turn to move, the following may ensue:

1. White plays in (2). Now black could play in (2) or (3).
2. Forbidden by the "simple ko" rule immediately to respond in (2), black plays (3). Now white could play in (3) or (1).
3. Forbidden by "simple ko" immediately to play (3), white plays (1)
4. Forbidden by "simple ko" immediately to play (1), black plays (2)

And the situation repeats: "simple ko" can only prevent one move on the entire board (retaking the last ko), so at every ply, the player has two open kos and can play the ko not blocked by the rule.

A cycle ensues, regardless. And for more kos on the board, the sequence can become even more complicated!

There are several solutions to the problem. Japanese go relies on a referee (who decides based on precedent) to rule for each case; in practice the correct solution is almost always "obvious", but there are some known holes.

Western go players (and, I think, Chinese players of Wei Qi) usually use a more sophisticated ko rule. Call a "position" the state of the goban (board) along with the side whose turn it is to move (the number of stones taken is not part of the position!). Then it is forbidden to make a move that causes a position to repeat. Simple ko is a direct result. But any situation where moves are made with no "progress", such as the sequence above, is (eventually) forbidden.

This is not an empty obsession with unreasonable positions; multiple kos arise in many real games!