Under a suitable formalization of “Japanese-like” rules (for instance “when a position is repeated for the third time, it’s a no-result”, making the game finite again), I believe you can prove something similar to Zermelo’s theorem, you just get some additional cases.
It is still the case that there is a least integer komi for which White can force a win (from White’s perspective, just treat no-result as a Black win and apply Zermelo’s theorem), and similarly for Black.
For similar reasons as before, these two integer komis must differ by at least 2. (in this case, they may also differ by more, since there could be a whole range of komi where either side can force no-result to avoid losing)
For concreteness, let’s assume that with komi 5 black can force a win and with komi 7 white can force a win. Then there are these different possibilities for komi 6:
The result will be either draw or no-result, black can force either.
The result will be either draw or no-result, white can force either.
Either player can force a draw: it will only be no-result if both players want that outcome.
Either player can force a no-result: it will only be draw if both players want that outcome.
It will always be draw. Neither player can force no-result.
It will always be no-result. Neither player can force a draw.
(I think that covers all the possibilities, let me know if I missed any)
And if you have a whole range of komi where neither player can force a win, you could conceivably have multiple of these possibilities come up at different komi.
What remains true is that there is at least one komi where neither player can force a win.
This was not a rigorous proof, I’m just saying that I believe that a proof can be made along these lines
If I may be allowed to say, in my opinion, the difference between Chess and Go is the same as between boxing and jujutsu. The goal of a boxer is to knock out an opponent, and this can be compared to checkmate in Chess. The purpose of the jitser is to gain a dominant position in the fight, and this does not require punching the opponent in the face. This can be compared to Go, where the task is not to destroy the opponent, but to surpass him, even if only slightly.
I hope it’s clear what I mean. I hope we don’t start figuring out which is better, boxing or jujutsu.
Not quite sure Go is more complicated than chess. Ok, sure on a purely mathematical standpoint yea but realistically no one play by mathematical standpoint, no one here is a computer (well…I hope).
Realistically, both are played by following a bunch of concept and rules of thumb… And both have quite a few layers of complexity. One could say than spotting the good move in Go by having good fundamental is basically the same as spotting good move in chess by having good eyes for tactics.
And realistically, it can take years to develop a similar level of skill in both game. Both do require quite heavy capacity to focus as well. It’s kinda like comparing banana to orange…both are fruit and both are liked by lot of people, both get good side and cons but it’s hard to say one fruit is better than the other from any objective standpoint
Now, I could say than I love about Go than there is no draw…and than I like about chess than game are generally faster (especially fun when you get opponent dragging lost game forever). But it’s more byproduct of the game design than anything’s else and hard to say it’s really an objective advantage or making game better or worst.
In my opinion good way to judge the complexity of a game in a human relevant way is the spread of the Elo ratings. If I’ve just learned the rules of go I can find a player that can beat me 9 out of 10 times and they can find a player that beats them 9 out of 10 times etc. For a more complex game there should be more of those steps until we reach top human play (or alternatively the standard deviation of the Elo distribution to avoid dependence on the number of players).
This of course also depends on the player base and intensity of professional study, and draws might distort this metric at the top levels of chess (a sufficiently good player can essentially force a draw even against a stronger player), but I think it’s still a good baseline for complexity according to which Go > Shogi > Chess > Gomuko > Checkers > … > Tic Tac Toe (with very quick and careless research into the Elo distributions of those games).
Such a metric also would rate “best-out-of-5 Chess” as being significantly more “humanly-complex” than Chess, as it would also have many more steps of skill as measured by Elo or similar ratings spread. (“best-out-of-5 Chess” is the game where you play 5 subgames of regular Chess in a row alternating colors, the winner is the one who wins more subgames).
Generally, this kind of metric is fairly correlated to just the average length of the portion of a game that allows for meaningful decisions. One might be happy with this, or not, depending on the intended purpose of such a metric.
The question of complexity from a human point of view seems to come down to the question how good a game is at measuring the difference in people’s ability to perform complex reasoning.
After all, if you ask how complex it is for humans to play, people playing any game to the highest humanly possible level will presumably be developing mental structures of roughly equal complexity, if their brains and training are comparable, and if you insist on measuring complexity by how hard it is for us to achieve. On this basis, play in all games too hard for perfect play by humans would rate as equally complex. This is why I feel it is more interesting to look at how well the game results measure the complexity of thought. That seems to come back to looking at how many levels of skill the ranking can distinguish; which seems to favour Go. Taking @hexahedron’s point about a 5-game series, one could all how many games of chess are equivalent to one of Go.
I suspect I am making a few assumptions which would be interesting to examine.
Didn’t read the whole thread. Did someone already reply with …
… apples are better than oranges?
(BTW in German it is apples vs. pears.)
The probably most true (for me) and probably most incendiary could be …
Go is better than Chess like macOS is better than Windows.
NOTE: Although, as said, this bears truth FOR ME, it was meant as a joke (meaning that I ROTFL’d), NOT to start a platform war I don’t need that: I run Windows and Linux in virtual machines, where they belong