In the recent US Go Congress, there were a lot of exciting half-point games. There was also some confusion over AGA rules and passed stones. On the top two boards of the US Open on the same day, for example, one game finished with black winning by a half-point while on the other, white won by half a point. How could this happen? Here’s an updated explanation of AGA rules, originally published back in 1992 when the rules were new.
In an even game with 7 and ½ komi, if White must make the third pass at the end of the game, that stone does change the score (from the traditional territory count) but does not (except rarely*) change the apparent result. The reason is a matter of parity.
Under AGA rules players alternately fill in any dame and both pass one stone to indicate the end of the game. That’s a design feature of AGA rules to avoid language problems and end game confusion and has no effect on the result.
If Black plays the last stone on the board, White – under AGA rules – also hands over a third pass stone. Why and what is the effect?
When Black plays last on the board, the number of stones played by both players (not including pass stones) must be odd. Since the board is odd (361), the territory after filling in prisoners will be even. (Odd minus odd equals even.) So any difference in the scores of the two players must also be even: 2, 4, 6, 8, etc. (e.g. 33 – 27 or 32 – 26).
If White is behind by 6 points (territory count) and gets 7 ½ komi, White wins by 1½ . The additional pass stone prisoner reduces the victory to ½ point, but White still wins. If White is behind by 8 and gets 7 ½ komi, White loses by ½ point. The additional pass means White is down 1 ½ points – just a bigger loss.
And if White plays last on the board, there is no third pass stone and no issue.
*Note, if there is a seki (or a combination of sekis) with an odd total number of shared liberties, the parity of points on the board changes and the added White pass stone can appear to change the result in a 1 point game. The combination happens very rarely – less than 1/1000. The Congress game between Matthew (Zi Yang) Hu 1p (w) vs Yuhan Zhang 7d (b) (U.S. Go Congress Recap/Preview: Wednesday, August 7 8/6 EJ; click here for the game) is the first reported example since AGA rules were introduced in 1991. But the “change” is an illusion. AGA rules are designed to produce the same result whether counted by territory or area. The last pass stone does that and the 7 1/2 point komi compensates White for Black’s last dame advantage. In addition, if you counted by traditional territory rules with a 6 1/2 point komi, this game would end the same: White loses by half a point.
– Terry Benson, with Dennis Wheeler and Phil Straus; photos of the Hu-Zhang game by Chris Garlock
