So it makes sense to me that under area scoring, there is no difference between 6.5 and 7.5 komi (unless black is last to pass, right?).
My question (and I know this should be trivial, but I cant quite wrap my head around it) is: If we play with integer komi to enable ties, does a komi of 6 always give the same result as a komi of 7 (provided that white is last to pass)?
No, 6 is the same as 5.5. (all numbers between 5.01 and 6.99 are just tie breakers for 5 in area scoring)
5 will be less white wins, 7 will be more.
Thanks!
EDIT: Hang on, just to verify: So 6.5 komi for area scoring is identical with 5.5 (rather than 7.5)?
Correct! Thatās why they jumped to 7.5. Originally both used 5.5 but black was still deemed to have an advantage. Japanese moved up to 6.5 but in area scoring 6.5 gives the same result as 5.5 so their next step was 7.5.
Follow-up question - does that mean that in territory scoring, 5.5 komi is equal to 4.5 (provided that white passes last)?
No. In territory scoring each point of komi is significant. 3, 4, 5, 6, 7, and all their half-point tie-breaker counterparts all have unique results.
Territory and Area scoring are giving the same result if white played the last stone and neither player passed before.
Since there is a difference of 1 point in area scoring depending on which player fills the last dame, I have trouble to find the reason why area scoring should give always odd scores, but territory not. (If whites last move would always be filling the last dame, territory and area would be equal, if whites last move would always be filling her own territory, area would be odd and territory always even (or odd since white wouldnāt actually play it under territory), or if territory is both even and odd, then area should be as well. 
(There are still differences in rulesets regarding points in seki, ā¦ , but they shouldnāt matter in most cases)
When area scoring is used (as in Chinese, Ing, AGA and New Zealand rules), the winning margin without komi is always odd, unless there are an odd number of points in seki. Since seki is fairly rare, and since a komi of 5.5 points has proven insufficient in professional play, and since a komi of 9 is generally considered far too much, it seems likely that the perfect komi is 7.
It does not matter who played last. There are an odd number of points on the board and so there must equally be an odd difference in score (unless there is an odd total amount of points in seki on the board)
Consider an evenly played game with no komi, from the 361 available points say black gets 181 and white gets 180. The difference is 1 (odd).
Now, letās add a single point to blackās winning score, however, there is still a maximum of 361 points, so white also loses a point. The new total is 182 for black and 179 for white. The difference is 3 (still odd). Since each point one player gets, the other also loses, a total point shift of 2 happens each time, and the difference before komi and without seki is always 2n+1 (odd).
I feel dense here, but why is the same not true for territory scoringā¦?
Because stones are not scored. All area scoring games have a total score of 361 points but in territory every stone played is dame. In this way, a player could take a point away from his opponent without gaining one himself, thus switching the difference in score to even instead of odd.
How is each stone a dame?
[1001] The Japanese rules define a dame as an open point that is not surrounded by live stones of only one color.
Senseiās - Dame
I guess I misused the term dameā¦ in my head it is just any point or area that wonāt become territory. So I guess by the definition you listed above it stops being dame once a stone is put on top but in my head its status of dame remains even after a stone fills it because whether itās open or closed itās still not territory.
Sorry if I caused any confusion 
No worries. I just wanted to make sure I wasnāt missing anything. Your responses in this thread have been extremely helpful to me. Iāve never understood why Komi worked differently between Territory and Area, or why there was a one point difference between Chinese and Japanese. I sincerely appreciate your time in this thread. I have found it very educational and interesting 
Thank you very much for your kind feedback at the time I was concerned I was just regurgitating what others had already saidā¦ so Iām glad to hear I brought something unique and beneficial to the discussion
This is an awesome explanation; I canāt believe this wasnāt obvious to me before, which is a good heuristic for a good explanation.
Right - ā¦ but I thought this would always even out after counting once you figure in prisoners? My understanding was that (complicated seki cases etc aside) the only times territory counting would result in a different score than area counting was if a ruleset was used in which white doesnāt have to make the final pass. As far as I remember, the entire idea of AGA rules is that you can score a game by either method and get the same result as long as white makes the final pass.
So either the premise that territory and area scoring deliver the same result after counting (if white makes the final pass) is incorrect, or the conclusion that every point of komi matters for territory scoring is incorrect (unless the ruleset doesnāt force white to pass twice after black fills the last dame) ā¦ Rightā¦?
Territory allows for even score differences and area doesnāt https://online-go.com/demo/view/418890
In AGA rules they also use 7.5 komi, if they tried to use 6.5 it wouldnāt work.
The demo board specifically mentions Japanese rules, which (if I understand correctly) donāt have a provision regarding pass stones. As far as I understand, under any other kind of territory scoring ruleset (such as AGA), black would have passed a stone to white at move 13 and the difference in score would still be uneven.
Correct. That is precisely the reason for the existence of the AGA ruleset. To force territory scoring to match area scoring by making passing cost a stone and forcing white to pass last.
Youāre trying to say territory is the same as area because thatās how it works in AGA, but AGA was invented specifically TO make territory the same as area.
If that were inherently true to begin with, AGA would not exist.
Just miscommunication all around, I guess 
From my first post in this thread onward, I kept asking if a 1-step increase in komi could make a difference under territory scoring if there was a pass stone provision. Iām glad to hear that the answer is no and would like to re-raise the question I was trying to ask from the start - given such a pass stone provision, does a 6.5 komi equal 5.5 or 7.5? (Again, I feel like the answer is trivial, but it seems to escape meā¦)