Contradictory AI theory, plus the value of Komi

[Elom0]

AI doesn't care too much about giving the opponent influence since it could easily Cho Chikun it's opponent's areas. But the AI always opens with starpoints and influence oriented moves in it's corner patterns. So which is it? Also, given the known horizon effect, should we really have as much trust as we do in AI evaluation? With the perfect Komi of 6 points in territory rules, Katago gives 52%. So I guess we can assume AI is 2% from God if we want be simplistic. While endgame shenanigans might mean the actual Komi multiple is anywhere between 5 and 7, it is likely it is actually 6 points since it's still harder for white to find perfect play, so white still at disadvantage with 6, which means Komi is definitely not 5, but a Komi multiple of 7 instead of six would mean the difference per stone is 14 points instead of 12, which definitely seems too large.

[Schachus]

For the first question: I do not think it is either. AI does value influence. It dosent get „scared“ of huge Moyos as humans do, cause it knows the opponent can still get his fair share, but that does not mean it does not value the influence.
And yes, I do think that depending on your ability, you might need to invade 1 move earlier than AI recommends, because you cant Sabaki as well 1 move later, but I dont think it should affect your Joseki choice.

As for playing 4-4 points, AI considers the joseki after 4-4 and 3-3 invasion to be even. It is not so, that the invading player got advantage, because influence wasnt worth anything. On the contrary, the 4-4 chose the influence with its first move and you invade 3-3 not because it is so much better for you, but because you say ok, you want influence thats fine, then I‘ll take whats left (territory). If that is not your style, you can still just keima Kakari, but AI just considers it as tiny concession, because the corner you give away is a tiny, tiny bit bigger than it would be „fair“ in its view. Very similar to the high approach vs 3-4, which also allows taking the corner happily, but its no desaster at all.

As for the Komi, I‘m not convinced 6 is fair at all. For all intents and purposes, I consider the value of the first move to be 13. Now I know fair komi cant be 6,5 (most probably, depending ob the ruleset maybe it could even theretically be 6,5, with perfect play resulting in some kind of „no result“, that neither side could escape without conceding a half point loss) but to me that is a rounding effekt due to whoever will get tedomari in the endgame with perfect play and doesnt concern me practically.

I handle it like this, because I‘m reasonably certain that 7 is the right komi in chinese rules (7,5 favors white and 5,5 favors black, also evident in results). Therefore the first move should be 14 in chinese counting, so 13 in Japanese counting. This is a good enough approximation to me.

[Elom0]

The Komi of 7 in Chinese rules is 6 + black having an extra point at the end that is a constant rather than a multiple.

When calculating the actual Komi multiple, it could be ±1 from the Komi because you have to account for any shenanigans of the ruleset. If in Chinese rules the there must always be an odd number of dame left on the board before counting, then Komi would be 6, therefore the true komi multiple in Chinese rules is 6 points. Think of it this way, the rule change I mentioned changes the Komi by a single point regardless of anything else. Therefore there's no way that rule change could actually make it so that playing with a 12 point Komi after the tweak is the same
as playing with 14 points before the tweak. The 6 points is actually based on sente first move advantage, while the extra point has nothing to do fundamentally with the first move advantage. The part of Komi based on on being the last to play is a constant while the part of Komi based on advantage derived in the early game from the first move is a multiple.

Similarly, while it's possible to have a territory ruleset as simple as area rules, one with lots of semi-arbitary shenanigans like Japanese and Korean may also adjust Komi by a point, or even half a point in the example you mentioned, but fortunately none seems to have done so, but for a non-perfect player it is more difficult to find the correct moves for white with 6 Komi.

My main query with AI is why doesn't it start with 3-3 as much as it starts with 4-4? If it doesn't think moyous are that impressive, why would 4-4 be better than 3-3? I don't know . . .

[Schachus]

I disagree, because to me, I‘m not sure Japanese Komi is correctly 6. In my mind, it could just as well be 7, I just dont know. Thats why I prefer to thing of the 7 chinese komi to be fundamental and 1 point potentially missing to be a „boundary effect“ that I can round to half a point.

For the other one, I‘ve wondered that before. I think it would help you to play a game against AI(or just the opening) where you play 3-3, see what it does against it and then compare the sequences arising from 3-3 to those from 4-4 with AI to get insight, why it likes 4-4 better. I dissgree with the comment that AI wouldnt like moyos. It might like them less than you do, but that is a different thing.

[Elom0]

I'm not quite sure what you're saying, if the Komi of 7 includes a boundary effect

Let's forget Japanese rules or any territory rules and just focus on Chinese rules or area rules in general. AI and humans 7 points is the correct Komi. We know 1 point of that is entirely due parity. So the parity independent sente komi is 6 and the parity Komi is 1

Let's say you decide to give a point handicap equivalent to a one stone handicap, twice true komi. If you think the sente komi is 7, then you think one stone is worth 14. But if we tweak the rules slightly so that black can't be last to play, Komi is 6 and suddenly one stone is worth 12 points. How can that make sense, since parity at the end of the game has nothing to do with sente advantage at the beginning of the game?

In terms of AI, yes I might see if I can give that a try, but I am woefully incompetent with all the AI hocus pocus of actually using the darned things. It just goes over my head. I have negative talent for programming or how many playlists a GPU has blah blah blah. I just use the Shibano Toramaru strategy of freeloading off others experimental work like a pure theoretical physicist

[Schachus]

I'm not quite sure what you're saying, if the Komi of 7 includes a boundary effect

Let's forget Japanese rules or any territory rules and just focus on Chinese rules or area rules in general. AI and humans 7 points is the correct Komi.

I agree until here.

We know 1 point of that is entirely due parity. So the parity independent sente komi is 6 and the parity Komi is 1

I disagree. The“parity effect“ is worth 0 points if white gets the last move, 1 point if black does. In games of mine, that will be 0,5 point on average. With perfect play, its either 0 or 1, I just dont know which.

Let's say you decide to give a point handicap equivalent to a one stone handicap, twice true komi. If you think the sente komi is 7, then you think one stone is worth 14. But if we tweak the rules slightly so that black can't be last to play, Komi is 6 and suddenly one stone is worth 12 points. How can that make sense, since parity at the end of the game has nothing to do with sente advantage at the beginning of the game?

In terms of AI, yes I might see if I can give that a try, but I am woefully incompetent with all the AI hocus pocus of actually using the darned things. It just goes over my head. I have negative talent for programming or how many playlists a GPU has blah blah blah. I just use the Shibano Toramaru strategy of freeloading off others experimental work like a pure theoretical physicist

In terms of the 14 points(2*7), 1 of that is due to the extra point each move is worth in chinese rules. Subtracting that, I arrive at 13(equivalent subtracting half a point of paurity komi).
In the perfect game it wont be 13, but rather 12 or 14, but I dont know which, and I dont care. The fact that it needs to be even is only vecause the empty board is symmetric between black and white, but I‘m less interested in precisely the value of a move on the empty board and more in similar board positions( like an empty corner early in the opening). That could be 13 without a problem.

[Elom0]

I disagree. The “parity effect“ is worth 0 points if white gets the last move, 1 point if black does. In games of mine, that will be 0,5 point on average. With perfect play, its either 0 or 1, I just dont know which.

Oh, okay, I think you just made a mistake when calculating averages that require weighting, essentially, in instances where multiple scenarios are not equally likely to occur, you multiply the value of each scenario by the probability it will occur and then add all those values together. This is why changing komi from 5.5 to 6.5 is almost pointless in Chinese rules, so they changed it to 7.5. Because black is much more likely to be the last to play since white is only last to play in relatively rare games that have an odd number of dame!

For this reason why Katago Thinks perfect Komi in Chinese rules is 7 points, it does not treat 6 and 7 points as equally divergent from 50%.

In terms of the 14 points(2*7), 1 of that is due to the extra point each move is worth in Chinese rules. Subtracting that, I arrive at 13(equivalent subtracting half a point of parity komi).
In the perfect game it wont be 13, but rather 12 or 14, but I don't know which, and I don't care. The fact that it needs to be even is only because the empty board is symmetric between black and white, but I‘m less interested in precisely the value of a move on the empty board and more in similar board positions( like an empty corner early in the opening). That could be 13 without a problem.

Oh yes, I completely forgot about that! You're right, yes in Chinese rules each stone is worth 6*2 + 1 extra point = 13 points.

[Schachus]

No, white is last to play in games that have an odd amount of territory between both players (plus liberies in seki, that are very unlikely, as you say). And that is more or less 50/50 to me.

With the komi 5,5 vs 6,5 its different, because black winning by 6 in territory rules already implied white isnt last to play. And those are precisely the cases where 5,5 vs 6,5 would make a difference.

[lightvector]

Right, black and white are roughly equally likely to get the last play in area scoring rules.

Because black is much more likely to be the last to play since white is only last to play in relatively rare games that have an odd number of dame!

This is probably the misunderstanding. Imbalanced chance of who makes the last play, and imbalanced chance of even vs odd dame, is not the reason why area scoring ends up with an odd score. Neither of those have a highly imbalanced chance, and yet it is still the case that the area score is typically odd.

Let's actually write down all the cases, then it becomes clear. Let's make all the usual assumptions (odd dame sekis don't happen, no deferred ko-dame fight, players are far from perfect play, yadda yadda), and examine the point when the game has just finished except for dame, and where both players have played equally many moves on the board (if black makes the last positive-territory-value move then have white fill one dame so that both players have played equally).

Then all of the following cases are roughly equally likely, with very gradually diminishing of likelihood as you deviate to more extreme scores in each direction:

...continued...
* Black wins by 5 points territory on the board, and there are an even number of dame on the board. (So under area scoring white will get the last move and black will win by 5 points area on the board).
* Black wins by 6 points territory on the board, and there are an odd number of dame on the board. (So under area scoring black will get the last move and black will win by 7 points area on the board).
* Black wins by 7 points territory on the board, and there are an even number of dame on the board. (So under area scoring white will get the last move and black will win by 7 points area on the board).
* Black wins by 8 points territory on the board, and there are an odd number of dame on the board. (So under area scoring black will get the last move and black will win by 9 points area on the board).
...continued...

We can see that:
* The area score on the board is always odd.
* The territory score is roughly equally likely to be even or odd.
* It is roughly equally likely whether the number of dame on the board is even or odd, it is NOT the case that one is much more likely than the other.
* It is roughly equally likely who will get the last move under area scoring, it is NOT the case that one is much more likely than the other.
* Among all cases where black would win by 7 area on the board, black will win about half of them by 6 territory and about half by 7 territory.

The last observation means that if we suppose that 7 komi area scoring produces an equal practical balance of wins and losses among all the games that aren't draws, then 6.5 is the precise value of komi for territory scoring would be expected to produce equal practical wins and losses, because 6.5 results in half of the area-scoring draws becoming territory losses and half of the area-scoring draws becoming territory wins. And in that case, it's also true there isn't any integer value of komi would be practically fair under territory scoring.

There also need not be any practical fair value of komi at all, regardless of integer or noninteger. An intuitive way to see this is to suppose it were the case that the practical frequencies are something like 45% B+5 or less, 4% by B+6, 4% B+7, and 47% B+8 or more. Then no matter where one places komi to divide the above cases into wins on one side and losses on the other (with possibly some draws in between) there simply isn't a division that ends up with equal wins and losses on each side. This of course assumes placing komi itself doesn't alter those frequencies by altering how players play, but it still illustrates the general kind of counterexample. (and if komi itself affects the frequencies, or if we relax some of our earlier assumptions, it only becomes even easier to construct counterexamples).

[Elom0]

Yes, thanks for correcting me regarding dame, silly me, but! In cases where the score is even black gets an extra free point, excluding rare mutual life changing the parity of the Dame.

If territory scoring Komi is 6, Area Komi is 7. If territory scoring Komi is 7, Area Komi is still 7. In the case of perfect play under Area rules, black would be either 6 or 7 points ahead in territory, unless shenanigans of the ruleset make it 6.5. Even among strong enough engines, there's no reason to believe that of the number of times black wins by 7 points the territory score is equally 6 or 7, it's more likely significantly more of one or the other.

Therefore we have no idea if the correct Komi is 6, 6.5 or 7, and it makes no sense to assume any one of these values when we know they all lead to an Area Komi of 7.

[Harleqin]

Removing odd parity should be done explicitly at the end of the game. This decouples it from the komi question.

Either: »If White passes first, White gets one extra point.« (Also known as button go. To wit, this transforms area scoring into territory scoring.)
Or: »White must make the last move (board play or pass). Every pass transfers a prisoner to the opponent.« (As in AGA rules, IIRC. This transforms territory scoring into area scoring.)

[Elom0]

Removing odd parity should be done explicitly at the end of the game. This decouples it from the komi question.

Either: »If White passes first, White gets one extra point.« (Also known as button go. To wit, this transforms area scoring into territory scoring.)
Or: »White must make the last move (board play or pass). Every pass transfers a prisoner to the opponent.« (As in AGA rules, IIRC. This transforms territory scoring into area scoring.)

To me, transforming Area scoring into territory scoring is better! The button could be a see-through neutral stone, or a stone decorated with the ying-yang symbol if one wants to be fancy.

[Elom0]

* Black wins by 6 points territory on the board, and there are an odd number of dame on the board. (So under area scoring black will get the last move and black will win by 7 points area on the board).
* Black wins by 7 points territory on the board, and there are an even number of dame on the board. (So under area scoring white will get the last move and black will win by 7 points area on the board).

But now to me it seems there's no reason for the parity of dame to be less likely than not to match the parity of territory difference.

-> Black wins by 6 points territory on the board, and there are an even number of dame on the board. (So under area scoring white will get the last move and black will win by 6 points area on the board).
-> Black wins by 7 points territory on the board, and there are an odd number of dame on the board. (So under area scoring black will get the last move and black will win by 8 points area on the board).

So . . .

[lightvector]

* Black wins by 6 points territory on the board, and there are an odd number of dame on the board. (So under area scoring black will get the last move and black will win by 7 points area on the board).
* Black wins by 7 points territory on the board, and there are an even number of dame on the board. (So under area scoring white will get the last move and black will win by 7 points area on the board).

But now to me it seems there's no reason for the parity of dame to be less likely than not to match the parity of territory difference.

-> Black wins by 6 points territory on the board, and there are an even number of dame on the board. (So under area scoring white will get the last move and black will win by 6 points area on the board).
-> Black wins by 7 points territory on the board, and there are an odd number of dame on the board. (So under area scoring black will get the last move and black will win by 8 points area on the board).

So . . .

Did you forget about this?

Let's actually write down all the cases, then it becomes clear. Let's make all the usual assumptions (odd dame sekis don't happen, no deferred ko-dame fight, players are far from perfect play, yadda yadda), and examine the point when the game has just finished except for dame, and where both players have played equally many moves on the board (if black makes the last positive-territory-value move then have white fill one dame so that both players have played equally).

So we're specifying that we stop to count the evenness/oddness of dame at a point where both players have made an equal number of moves on the board, allowing white to fill one dame if necessary so that it's black's turn again.

How do you imagine that we've managed to make Black wins by 6 points territory (including stones they've captured) before komi, and yet both players have played an equal number of moves, and there are an even number of dame on the board? And no sekis or other unusual situations, just a normal endgame. There are an odd number of spots on the board, we can't have all of these be even at the same time.

[Elom0]

So we're specifying that we stop to count the evenness/oddness of dame at a point where both players have made an equal number of moves on the board, allowing white to fill one dame if necessary so that it's black's turn again.

How do you imagine that we've managed to make Black wins by 6 points territory (including stones they've captured) before komi, and yet both players have played an equal number of moves, and there are an even number of dame on the board? And no sekis or other unusual situations, just a normal endgame. There are an odd number of spots on the board, we can't have all of these be even at the same time.

Oh, that's what I missed, an even number of moves and imperfect play

But in an actual game, where the number of moves may or may not be even, a komi of 6 shouldn't be the same in practice as a komi of 5.

I'm also perhaps wondering more about perfect plsy, since the aim is to determine whether inherent komi under territory rules

I wonder what the proportion of self play games KataGo trains on use Area vs Territory rules? I assume it's 50/50, correct? Or maybe 55% territory to make up for KataGo initially training on Area rules so the number of territory games need to catch up?

And it seems a difficult task representing the rulesets properly. So training KataGo with 50% Territory Scoring and 50% Area Scoring and 50% Territory Scoring, the distribution might be 33% Chinese, 33% New Zealand 33% AGA 25% Korean and 25% Japanese.

If I Remember correctly, under territory rules KataGo under a komi if 6 gives 52% for black and under a komi of 7 gives 55% fir white, which suggests the true komi under perfect play is indeed 6, but white is harder to play so for imperfect players 6.5 is fairer

Thanks for answering my noob KataGo questions!