Equivalence Scoring

Equivalence scoring provides a way for the players to count territory, even though they are using area scoring. It is used by AGA rules and French rules. It makes use of pass stones: When a player passes, they give one stone as a prisoner to the opponent. In addition, White must make the last pass. With the addition of these two rules, the players can count territory (including territory in seki) plus prisoners and get the same result as if they counted area (territory plus living stones). The pass stones and White's playing last ensure that the winner and the difference in scores will be exactly the same with either counting method.

Having to pass last may seem detrimental to White, but since prisoners don't count under Area scoring, it doesn't change the outcome at all.^[1] The only effect of White's last pass stone is to help ensure that the score using territory counting is the same as it would be under area counting.

In handicap games, when using area scoring, AGA rules also require that Black gives White one point of compensation for each handicap stone except the first under area scoring. This is a separate question from equivalence scoring.

Bill: Equivalence scoring in the AGA rules may be traced to an article I wrote for the AGA Journal in the 1970's. (Equivalence counting would be a better term. It's area scoring.) I have removed references to Japanese and Chinese counting, because they seem to have caused some confusion. (Witness the discussion below.) In even games, pass stones are used to ensure that the score is the same regardless of the counting method. Because each player has the same number of stones on the board for counting (when the prisoners have been placed inside the opponent's territory), the players may ignore the stones and simply count territory, instead of counting area (territory plus stones).

As for handicaps, the AGA decided not to count a point for each handicap stone past the first one. With area counting Black gives one point in compensation for each of those stones to White. With territory counting White is compensated by not having to give Black a pass stone for each of those stones.

Pledger: I think the previous statement about handing over a prisoner for each additional handicap stone in equivalence scoring may be incorrect. This is only for area counting. If using territory counting in equivalence scoring, giving White extra prisoners will not make the area and territory scores equivalent. There don't need to be any extra points given to White at all. If I'm mistaken about this, someone please correct me.

Rubyflame: Actually, it is White who would need to give prisoners to Black.

Pledger: If white were to give black extra prisoners, blacks advantage would almost double. I was somewhat confused by this at first, but after mulling over it for a few days it suddenly became clear. Equivalence scoring is a way to determine the area "score" using either area "counting" or territory "counting," both giving the exact same result. If using area counting in a handicap game, black gives white an extra point for each n-1 handicap stones. If using territory counting, no extra points or stones need to be exchanged, and both results should be the same, provided of course that the basic rules of equivalence scoring are followed (pass stones, white passes last). I counted several handicap games both ways until I proved this to myself. But as I said, if I'm wrong, someone please set me straight.

blubb: In my view, it would be far more elegant to simply treat handicap beyond one as white passes, naturally involving pass stones. Alas, that`s not the AGA way, supposedly because handicap compensation is still used in China, too. Provided komi remained untouched, the black advantage would slightly (!) increase without (nowhere near double though). So, at worst, the ranks could spread a little wider.

Pledger: Looking back at this discussion, I realize that Blubb is right and that black's advantage would certainly not double with the extra points; however, allowing black those points would still exaggerate the difference between area scoring and territory scoring under a given handicap.

Pledger: Hmm...looking back yet again and having learned a bit, I see the whole issue of handicap somewhat differently now. Whether or not white recieves compensation for black's handicap stones just depends on what we think the value of a handicap stone should be, which could be arbitrary. I see where blubb is coming from. White giving a prisoner for each n-1 handicap stones in equivalence scoring would allow no thought at all about extra compensation when using an area counting technique. The value of handicap would then be as it is in New Zealand scoring if I am correct. I suppose the AGA chose their particular handicap rules to conform to general practice.

Above it is stated that "Equivalence Scoring" leads to the same difference in score regardless if Chinese or Japanese Counting is used. This doesn't seem to be correct in all situations: If there is a seki with a white eye with 2 empty points inside it, and Black has no eye, chinese counting should give 2 points more to White than japanese counting, correct ? (By the way: It seems that the descripions of Japanese and Chinese counting simply don't cover Seki.)

SAS: Yes, although it depends what exactly is meant by "Japanese counting". Under AGA rules (and presumably under French rules too), eyes in seki count as territory. You can use Japanese counting, it's just that what you have to treat as territory during the counting process may not be the same as it would be under Japanese rules.

[1] xela: I'm confused by this statement. Imagine a final position where, by "Japanese scoring" (without using pass stones) White wins by 0.5, and where Black has the last move (including dame). Then, if I understand correctly, with "Chinese scoring", Black would win by 0.5; and if "equivalence scoring" (with pass stones) is used, then White's final pass stone also means that Black wins by 0.5. So it may or may not make a difference, depending on which scoring system you would otherwise have used.

Pledger: Equivalence scoring is the same as area scoring. The only difference is the counting method used to determine the score. It is not Japanese scoring at all and should not always equal the Japanese score. Equivalence scoring is just a neat trick for determining the area "score" using territory "counting."

jfc Exactly! Equivalence scoring is just a different procedure for determining the area scoring result.

TRIVIA: It is also possible to go the other way, to use area scoring and make it equivalent to territory scoring: If white passes first then 1/2 point is deducted from black's score and added to white's score ( [ext]

Ikeda's Rule). NOTE: This makes area counting equivalent to territory counting in which seki territory is counted. I don't know of any trick to make area scoring give the same result as territory counting that does not count territory in seki.

P.S. is there a SL page that shows examples of sekis that are counted differently under Japanese (no territory in seki) and area counting?

/WME