Ok I think I understand the misunderstanding. AGA is not territory. AGA is area which has been adjusted in such a way that you can also use territory counting method to get the same answer. In this way, the statement is preserved that “for area scoring, score differences will always be odd, and thus only odd komi will change the result”
I think you can come to this conclusion quite naturally when you think of AGA as area scoring with added features to make territory method work, rather than thinking of it as an implementation of territory scoring, which then leads to questioning whether 6.5 komi works (like all area scoring, 6.5 komi in AGA will give the same result as 5.5 komi, for the same reasons as all area scoring)
In fact, I had worded it better earlier than I did in my last post - my first question was specifically whether under area scoring (AGA or Chinese or New Zealand or otherwise) a 6 komi was equal to 5 komi or 7 komi. The explanation I got was that any komi greater than 5 (whether it be 5.5 or 6 or 6.99) would work as a tiebreaker for white, which makes sense to me.
My follow-up question had been whether that meant that under territory scoring, a komi of 5.5 was equal to 4.5 - but that was the one post in which I didn’t qualify that I was assuming a pass stone provision, and really, I should have just asked whether a komi of 5.5 was equal to 4.5 under area scoring
So let’s see one more time if I got this right, because the following situation is the reason I started wondering about this issue in this thread in the first place:
Let’s assume I think a komi of 7 (under NZ rules) would be fair for a 13 x 13 board as well as a 15 x 15 board. If I wanted to compensate white for black’s first move by the same amount and still enable ties on a 14 x 14 board, would the komi have to be 6 or 8? I think the answer is 6…?
komi across board sizes cannot be directly compared.
If you took the fair komi values for 3x3 and 5x5, and expected to be able to extrapolate the fair komi for 4x4 from that you would be WAY off.
Completely abandon the idea that komi on different board sizes, no matter how similar they may appear, have anything to do with each other. ESPECIALLY when jumping between even board lengths (no tengen point symmetry) and odd board lengths (tengen point symmetry).
No. In the same way that any number between 5.01 and 6.99 is a tie breaker for 5 komi in area scoring, anything between 3.01 and 4.99 is a tie breaker for 3 komi in area scoring.
All of those are special cases since they are solved games. We know the forced win sequences. For (even slightly) larger boards, there likely are no forced win sequences, and even if there were, we’re not likely to find them (at least within, let’s say, our lifetimes).
Now I grant that tengen-less boards behave differently than uneven boards, but I disagree that komi across different board sizes has nothing to do with each other. The most common komi values used for 9 x 9 and 13 x 13 differ only by 2 points (or 1, under Japanese rules ) from 19 x 19 komi. I don’t think it’s vastly unreasonable to assume that the komi for, let’s say, 14 x 14 would be within 1 point from the komi used for 13 x 13. However, I also grant that it might not be possible to infer from my line of questioning whether a komi of 6 or 8 would be closer to the desired goal…
Right, but under non-NZ rules, every komi includes a tie breaker for white (by means of adding 0.5 to the integer). My question, rephrased once again, is: Under area scoring, does 5.5 komi equal 4.5 or 6.5?
Suppose the scoring without komi was B for black, W for White.
So the game result is W - B + komi (positive is White winning).
Note that W - B must be an odd integer because there are 361 points on the board.
Here’s a table a few examples for W - B and komi
W-B 4.5 5.5 6.5
-7 -2.5 -1.5 -0.5 ==> all komis give victory to Black
-5 -0.5 0.5 1.5 ==> komi 5.5 or 6.5 give victory to White
-3 1.5 2.5 3.5 ==> all komis give victory to White
So, to answer your question: under area scoring, komis of 5.5 and 6.5 give the same game result
) from 19 x 19 komi. I don’t think it’s vastly unreasonable to assume that the komi for, let’s say, 14 x 14 would be within 1 point from the komi used for 13 x 13. However, I also grant that it might not be possible to infer from my line of questioning whether a komi of 6 or 8 would be closer to the desired goal…