A hypothesis about Chess vs. Go

Chess is a game that is further evolved than Go. But it is not simply due to the board size.

Chess has evolved at a far quicker rate due to the growth of Europe and the Americas, and that played a massive role in the understanding of it. Go, on the other hand, was like many games banned by Chairman Mao, and most of the best players had to leave the city for the countryside in their resettlement programs. The only real player was Japan, and they only had a simple understanding of the game.

The last one hundred years have resulted in most of the openings and half of the middle game ideas in chess already being understood by humans. We did not need Stockfish to understand this part of the game. The middle game and the end game is the real fertile ground for the chess engine of today.

Alpha Go, on the other hand, has shown the Go masters that they understand very little about the game and big inroads are now underway, but this progress was hampered by the social conditions in Asia, and not the Go players' mind or how hard the game is.

Online is always different, has nothing to do with the game. Classifying "chess players" or "Go players" in terms like "generally" sounds very un-wise ...

If you are trying to stay on topic and that topic being your re-stated hypothesis above, then it seems to me a fairly shallow and rather circular argument: 

Given two problems, A and B:

Assumption 1: problem A is more complex than problem B

Assumption 2: solvers of A are equally intelligent (whatever that means) as solvers of B

Conclusion: Problem A will be more completely solved than problem B

In the case of Go (A) and chess (B), neither assumption is necessarily true. 

The second assumption is ill defined and incomplete. What is intelligence? are certain cognitive skills more conducive to solving Go than chess? Is there any reason to believe that humans are innately as proficient at solving both? The assumption is incomplete in that it further assumes an equal number of solvers devoting equal time,effort and resources to solving. 

So:

IF Go is more complex and IF an equal number of solvers, equally proficient at solving both games are devoting equal time, equal effort and equal resources at solving, then yes, chess will be more completely solved. But this is merely a functional definition of complexity and so simply a circular argument. You will need to examine and prove all the inherent assumptions before your conclusion is valid

I think you got me there ...

But let me add, the way I put it in my post wasnt meant to get it closer to a scientific approach (too shallow for that, you are right). I was just trying to express the base idea in the most simple way since the first participants in the thread didnt seem to understand it at all.

Personally I think the idea could be solidified if someone put enough effort in it (consider the parameters you named, and more), but yeah, nobody got time for that and it´s just my personal opinion.

Just because something is easier to understand doesn't mean it's played on a higher level. For example, a fairly complex algebra problem like solving three independent equations in order to determine the values of x, y, and z is not solved on a "higher" level than a barely comprehensible calculus problem like the solution to Schrodinger's equations applied to the two electrons in an negatively charged hydrogen ion, even though the Schrodinger equation has strange stuff in it like the square root of -1.

1) I dont think this is comparable. I am using the terms "more researched", this is something else than "levels of solving mathematical problems" (how are you measuring this now? could be plenty of different ways to measure that ...).

2) What´s so strange about imaginary numbers?

It depends on how you define skill level. Is it an absolute or a relative value?

If it is a relative value, that means relative to the possibilities you have in chess, chess is definitely played on a higher level: Since there are less possible moves in chess, you have a higher chance of playing the right move and a lower chance of making mistakes. I believe, Magnus Carlsen makes more often the best move than the Go world champion does. This math example is a good example to prove this point. While a simple equation is 100% solved, millenium problems are not 100% solved, that means people are better in solving the simple equation than they are in solving the millenium problems.

If you see skill as an absolute value, though, I believe, chess is still played on a higher level (simply because it is older, I believe, and more popular), but once chess is solved, Go players can play Go on a higher level. Just like someone, who soled Schrodingers equation is a better mathematician than the one who solved the simple equation, the Go Player is better in board games and calculating and all the abilities chess and Go require, than the chess player. 

It might be older, but it came out of Asia in the 20th century, so I think, people spent more time in total studying chess than they did in studying go.

This is a great question. And comparing similar games can lead this discussion down a useful path. Someone already mentioned Tic Tac Toe, which is a great example. I think the complexity of any game can be quantified assuming there are finite parameters. Alas, my interest in this wanes as measuring the complexity of complex things becomes... quite complex. You can find various game complexities measured on Wikipedia here https://en.wikipedia.org/wiki/Game_complexity. There, you'll see Chess (without the 50-move drawing rule) and Go both rank as "EXPTIME-complete", which is described here https://en.wikipedia.org/wiki/EXPTIME

The Wikipedia article is mostly about the characteristics of the decision tree, and confuses game complexity with the decision tree shape, so the comparison is apt only for approaches based on exhaustive search.  What it doesn't address is how hard positional evaluation is (which is the pragmatic issue in game evaluation).  The decisions made in a game of chess are quite different to those made in Go and the characteristics of the positions are quite different.  In Go, in my view, there is more consideration of, and more opportunity for, positional advantage at various scales (aji and sabaki) than there is in Chess.  In Chess, again in my view, the individual moves represent higher stake plays.  Tenuki, seizing the advantage by playing elsewhere on the board, is hard to do in Chess, you just can't get that far away.  What has been interesting is how the emergence of AI has changed the way that Go is talked about and has changed the way that people view the balance between aji (opportunity) and territory.  There wasn't that kind of shift with the emergence of AI in chess, the balance between combinational play and positional play in chess shifted long, long ago.  AI has forced some re-evaluation of known positions and plays because AI tends to value potential more highly than people do.  The point of this is, that if the decisions in the two games are quite different, then they are not really comparable, no matter what the statistics of say. 

Go uses both sides of the brain chess only uses one side 

https://www.eurogofed.org/index.html?id=96

@cheytac,

I might quibble a bit with your OP, but I think you have a point.

Both games are sufficiently complex that full comprehension is beyond human grasp.  Both are played seriously and with great study by people.  So, the full range of human comprehension is a little bit closer to complete understanding of Chess than it is to complete understanding of Go.

The best way to test a hypothesis is to experiment, so go play some chess.

I do not know if people are still looking at this discussion, but I do have something I would like to add. For perspective, I am an 8 kyu go player and I believe I am much worse at chess than go when compared to other players.

I have devised a thought experiment that might help to reveal the differences between go and chess. If we imagine that there was an all-knowing master of games that devised a test for the best human players of both chess and go, we could compare which result indicates a "better understanding" of their game. The only issue is the varying complexity of the games changes the effective results.

Let us say the chess master is given a 10 question test where each question represents an equal portion of knowledge to determine their mastery of the game. If all of the questions are extremely difficult, but they manage to answer 5 of them correctly, leaving 5 questions remaining. That would be a 50% score out of the "complete understanding" of the game.

Then let us say the go master is given a test, where the questions are made to represent an equal amount of knowledge than those of the chess test. Because go is more complex and there is more to master in all areas of play, it has 15 questions on it. Of those questions, some of them are likely to be easier than others because there are likely a greater number of easier parts in go than chess as well as more difficult parts. If the go master answers the same amount of extremely difficult questions as the chess master on his exam, but also answer 3 questions that happen to be easier on the go test, he would receive a higher score of 53% despite there being 7 questions remaining, meaning there is a large amount of knowledge left to master.

This result would indicate that there is both more knowledge needed to learn about go compared to chess and that they have mastered more knowledge than chess. This definitely creates problems when comparing who has an overall "better understanding" of the game. We would have to look for some other way to compare for a satisfactory definite answer.

This example was meant to demonstrate how there could more understanding about one game out of all understanding possible, and also have more understanding remaining to achieve for the same game.

Sadly, I do not think this example is an accurate portrayal of what would happen. If it were questioned whether it was possible to be completely master either of these games, I would have to admit that it is more likely for chess to be masterable. As of right now, it seems human intelligence is the main limiting factor for go players to keep improving. As was mentioned before, it seems Magnus Carlsen does play the "best move" more often than the best go player does. I believe this is because it is actually too difficult for the human brain to determine the "best move" in a game of go, but it is much easier to see where to play in chess.

If we are to assume that the players of chess and go are equally intelligent, I would agree that chess players have a "better understanding" of their game because go is too complex for the current intelligence to understand and improve upon its knowledge of go.

I am not very happy with your proposed thought experiment, because it contains a lot of seemingly random assumptions and unequal formalities. However, we seem to agree, that chess players might have a better percentaged understanding of their game. I say percentaged, because in either game, no human will ever be able to achieve mastery (I dont know how much you know about chess - and I dont know much about Go, this is true. But about chess I can tell you, that good play is mostly brute force calculation, and this is where the human brain very quickly taps out - even the biggest computers can not compute chess variations at a near satisfactory level). What I want to say is:

Picture to swimmers, the Go and the chess player. We tell the chess "swimmer" to swim through all the oceans of the world. He will drown quickly. Now we increase the ocean by a certain factor, that is the factor by which Go is estimated to be more complex in terms of variations and possibilites. Now we tell the Go swimmer to swim through this enlarged ocean. He will drown just as quickly.

One could summarize: We humans apply our cognitive abilities on the two games that are quite different but each in its way very complex. Our abilities are nowhere near of gaining something like absolute mastery in those games, so we just enjoy them as the endless sandboxes they are for us.

I agree. I think it is good enough just to enjoy the games and not worry about how much we don't know.