> The news flies under the radar because for most people Go is now solved (compare to what happened after Deep Blue's win).

"Machines reaching a level of play that is consistently better than humans" and "the game is solved" are two completely different statements and it isn't particularly useful to conflate them.

We will likely never be able to solve Go in the formal sense.

The key though is "for most people". We live in a post-fact society, remember? ;)

I don't think there is a factual disagreement here, just a terminology issue. Mathematical jargon is not quite the same language as plain English. In the former, 'solved' by default means you have found the mathematically perfect solution. In the latter, 'solved' by default just means you have found a solution good enough for practical purposes.

Quite. gcp is lamenting the same conflation as msbarnett.

Go on smaller boards is solved (5x5). Solving on 9x9 or larger is likely not possible.

>"Machines reaching a level of play that is consistently better than humans" and "the game is solved" are two completely different statements and it isn't particularly useful to conflate them.

Very good point

>We will likely never be able to solve Go in the formal sense.

I'm not sure if it would be precise to say chess will be solved either. The number of outcomes in a 50-move chess game approaches Graham's Number--a number larger than the number of atoms in the observable universe.

In a 100-move game, the number would be many orders of magnitude than an already incomprehensibly large number. So chess also will probably in a precise definition of the word, also never be solved.

Edit: It's kind of mind boggling to think about every atom in the universe representing one position in a game of chess and there not being enough atoms in the universe to represent each one.

The number of outcomes in a 50-move chess game does not even come close to the Graham's Number.

10^(number of outcomes in a 50-move chess games) also does not come close.

Even 10^10^10... (repeat this the number of outcomes in a 50-move chess game) does not come close to Graham's number.

Thanks, I was wrong about that. I swore I read that somewhere, turns out it was on a chess forum--not a source I should have committed to long-term memory.

I did find this interesting statement about Graham's number (unsure of the veracity):

> Graham's number is greater than all of the Planck lengths in the universe. There literally isn't room in the universe to write it out in numerical form.

Edit: It looks like we confused Graham's Number for Shannon's number: https://en.wikipedia.org/wiki/Shannon_number

But according to the Wiki on Shannon's number, a the number of possible outcomes in chess does still far exceed the number of atoms in the universe: >Allis also estimated the game-tree complexity to be at least 10123, "based on an average branching factor of 35 and an average game length of 80". As a comparison, the number of atoms in the observable universe, to which it is often compared, is estimated to be between 4×10^79 and 4×10^81.

This is a bad kind of argument. There are more 16x16 sudoku boards, and ways of dealing a deck of cards, than there are atoms in the Universe too, but Sudoku and many card games are easy for computers to solve.

Well, you should volunteer on the Stockfish engine and show everyone how it's done.

I don't believe your comparison between fundamentally different games is sufficient to support your conclusion that an extremely large number of calculations does not pose a challenge for computer programs to solve.

Rather, to the best of my knowledge, to support your conclusion what you would need to do is to prove there exists a method or formula for reducing the number of permutations to a manageable number while still coming to an optimal solution. Apparently if Sudoku is easy to solve, that exists in Sudoku, but it certainly does not yet exist in the realm of human knowledge in chess.

The fact is that Sudoku and many card games are easy to solve, while chess is in fact a much, much more challenging problem for a computer program, and there are a lot of very smart people that have worked on that problem.

I don't disagree that Chess, and Go, and very hard. I don't believe without a major mathematical breakthrough we will see either solved, ever. There just isn't enough possible computing power in the universe.

HOWEVER, arguing that they aren't solvable purely from a point of view of "the number of possible games / states is greater than the number of particles in the universe" type arguments is that there are many problems we routinely solve with massive search spaces.

Your comment kind of bothers me. Probably because it is both wrong yet says in a rather frank, matter-of-fact way that my argument is bad.

Well, you could just do a Google search for yourself to see why your reasoning is wrong. The problem with using a computer to play Go is precisely what I described, the extremely high number of permutations involved, and it's the same concept with chess (Go just has even more of them): https://www.wired.com/2016/01/googles-go-victory-is-just-a-g...

Well, your comment bothered me, so we are all bothered!

I still disagree with your argument. The problem with Go isn't just the high number of permutations involved, there are real-world problems, with just as many permutations, which have been solved.

The extra problem with Go (and chess to a lesser degree) is that's it's incredibly hard to be sure, with any certainty, to be sure that a move is a "good" choice.

Comparing to the sudoku example again, when "playing" sudoku it's usually obvious as soon as you make a bad move, you've put two '1's in the same row/column/box for example. With Go if we want to play well, or perfectly, we really have to explore the entire search space.

What you're describing is this:

Sudoku is a game, and in which to solve it, a computer program has an obvious method to limit possible permutations to compute in finding a solution. In other words, it is not faced with the challenge of a requirement to compute permutations > 10^86 (roughly atoms in the observable universe).

In contrast to sudoku, chess and go are games which have no yet discovered or theoretical method to limit permutations to solve, therefore to solve them you would be required to computer permutations > 10^86.

So the problem is still with the number of permutations.

Like I said in my other post: if you could develop a technique to reduce the number of permutations while still solving the optimal solution then you would be onto something. Right now no one has been able to dream up such a theory and there are a lot of very smart people who have worked on this problem.

> It's kind of mind boggling to think about every atom in the universe representing one position in a game of chess and there not being enough atoms in the universe to represent each one.

Chess players mentions this a lot. And then they consider chess a sport. For a sport, it shure is a mind boggingly low number of game states :)

(ps: I don't mean to start an uninteresting sport-or-not debate. It is what it is.)

Something else- today you can run programs that play chess at superhuman levels on your phone. At the time of DeepBlue's win against Kasparov the same kind of system could run on off-the-shelve hardware [1]. Very soon after AI programs running on ordinary laptops demonstrated dominance against human masters (that's in Russel & Norvig, somewhere, I can dig it up if you like).

So the fact that Cho Chikun won against a less powerful machine is not necessarily an indication that the entire system is weaker than DeepMind's one. To know that you'd have to run Zen against AlphaGo.

______________

[1] A big hint of why it didn't is that, at the time, IBM was still selling more hardware than software.

>> Cho Chikun had the large advantage over Lee Sedol that his opponent (Zen) and similar programs (Crazy Stone, Leela) are simply available for him to practice against and probe for weaknesses.

That's an argument against Go having been solved by AlphaGo, not for. If Lee Sedol could beat AlphaGo given the opportunity to practice against it, then nothing is solved.

Also, for a system to dominate against humans in a game it must be able to beat any opponent every time. AlphaGo hasn't demonstrated this yet, so while in the popular opinion AlphaGo "dominates", in the technical sense it does not, and Go won't be "solved" conclusively until it has.

> There's a small blemish in that Ke Jie is still rated higher than AlphaGo.

This is false. Ke Jie is far far below Lee Sedol.

Lee Sedol has no equal. Well, AlphaGo beat him but we are talking about player ranks.

Speed of the hardware is significant to discuss. A human, given sufficent notebook paper & time, could think ahead for thousands of years and thousands of turns -- this is effectively what a machine is doing.

With much tighter time constraints, I don't believe machines would do as well because they are using full-breadth search (to my knowledge) -- searching every possibliity. Whereas humans use visual pattern recognition, and we can run this programs quite fast.

machines use aggressive tree pruning. they don't evaluate all positions

Thanks. Even so, they still compute the full value of the move, right? Queens are 9 points, pawns are 1 etc, this position is worth X