> Go is a deeply complex strategic game — famously far more complicated than chess, with 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible board configurations.
The correct number of legal Go positions is over twice as much, or to be exact [1]:
All these digits are only making it more obfuscated. Using the order of magnitude it's 10^44 for chess versus 10^170 for Go. Thus, Go is 10^126 times more complex than chess.
For reference, the estimated number of individual atoms in the universe is thought to be between mere 10^80 and 10^83.
> All these digits are only making it more obfuscated.
I think that using these numbers as as stand-ins for difficulty is itself a form of obfuscation.
The truth is that, despite the massive number of potential board states, Chess and Go are some of the easier games to solve, thanks to their nature (perfect information, zero randomness, alternating turns where each player plays exactly one move). And trying to use board states as a proxy for complexity and complexity as a proxy for difficulty doesn't generalize to other categories of games. Compared to Go, what's the complexity of Sid Meier's Civilization? If I devise a game of Candyland with 10^180 squares, is that harder to devise an optimal strategy for than Go just because it has more board states?
The reason that we're still using board states as a proxy for difficulty is because historically our metric of "this is difficult for a computer to play" was based on the size of the decision tree and thus the feasibility of locally searching it up to a given depth. In the age of machine learning, surely we can come up with a more interesting metric?
Number of possible game states is a poor measure of complexity. How many game states does soccer or basketball have, when you consider flight of ball and movement of players? Does that tell us anything about whether basketball is more complex than Go?
Complexity of the game has nothing to do with the number of legal positions. It's very easy to design a game with arbitrary number of positions which is very simple. While go might be more complex than chess using a more reasonable measure this argument was used to for arguing nonsense in scientific papers in the past (that some poker games are more complicated than chess because they have more possible states).
Wording like “game is more complex” overal seems incorrect. Game is not complex by itself (for example go rules are extreemly simple), all the difficulty and challenge depends on the skill of your oponent.
Game only allows the opponent to demonstrate the skill.
Are you sure that the complexity of a game has absolutely nothing to do with the number of legal positions?
I mean I am open to hear the justification for this, but I was fairly certain that all measures of game complexity are a function of the number of legal positions. Now certainly there are other factors, namely the cost of computing the transition from one legal move to another legal move so a simple game might have a very low cost transition function while a complex game has a very complex transition function, but I can't conceive of a game where the number of legal positions bears no weight on the game's complexity.
Go is played in a a bigger board though and has this kind of recursive nature where a subset of a go game is also a go game while chess is more ad-hoc.
To my knowledge AlphaGo models never became meaningfully available to the public, but 8 years later the KataGo project has open source, superhuman Go AI models freely available and under ongoing development [1]. The open source projects that developed in the wake of AlphaGo and AlphaZero are a huge success story in my mind.
I haven't played Go in a while, but I'm kind of excited to try going back to use the KataGo-based analysis/training tools that exist now.
What stuck with me is Lee Sedol's strong emotional reaction, leading him to leave professional Go playing.
It's understandable he didn't expect AlphaGo to be that strong. Or that (for him) losing to a machine took the 'soul' out of the game.
But come on... I've been cornered by Pac-Man ghosts many times. That doesn't make Pac-Man less fun to play.
Nor does losing to the crude 'AI' steering those ghosts. Instead, you play, aim for a high score, see how long you can survive, how many levels you can complete, or how many fruits & ghosts you can eat in a game.
And (if you care) compare how those 'metrics' stack up against other players.
If a machine with superhuman Go-playing ability isn't fun or challenging, then stick to human opponents.
Of course it's his views and choices, and I respect that. But other than providing extremely challenging opponent, I don't see how human-beating machine would take the fun out of a game. Rather the opposite: new tactics, new insights, a raised upper bound for a Go player's strength (human or otherwise), etc.
Some people connect their ego tightly to their accomplishments. Others are emotionally fragile to what they perceive as negative experiences. Some achieve great things by what they perceive as great sacrifices, and have a lot of difficulty maintaining what they have achieved. Some at or near the top of a field perceive their accomplishment primarily as being "best", and are consumed with angst when they are no longer best. The public explanation they give may not describe how they are different than someone trying to understand.
Open up how you frame personality types and life experiences, and you can think of possibilities beyond "I don't see how".
Michael Redmond, to my knowledge the highest ranked English-speaking Go player, does youtube analyses of Go matches, including Pro vs AI games, which are very insightful.
Great PR for Google from Lee! It totally isn't mostly for advancing Google's commercial interests, the bottom line being:
"I believe that humans can partner with AI and make great progress. As long as we can set clear principles and standards for it, I am quite optimistic about the future of AI technology in our daily lives."
Readit News
The correct number of legal Go positions is over twice as much, or to be exact [1]:
208168199381979984699478633344862770286522453884530548425639456820927419612738015378525648451698519643907259916015628128546089888314427129715319317557736620397247064840935
Indeed far larger than the ~ 4.8 x 10^44 legal chess positions [2], that is in between the number of legal 9x9 and 10x10 Go positions.
[1] https://tromp.github.io/go/legal.html
[2] https://tromp.github.io/chess/chess.htm
For reference, the estimated number of individual atoms in the universe is thought to be between mere 10^80 and 10^83.
I think that using these numbers as as stand-ins for difficulty is itself a form of obfuscation.
The truth is that, despite the massive number of potential board states, Chess and Go are some of the easier games to solve, thanks to their nature (perfect information, zero randomness, alternating turns where each player plays exactly one move). And trying to use board states as a proxy for complexity and complexity as a proxy for difficulty doesn't generalize to other categories of games. Compared to Go, what's the complexity of Sid Meier's Civilization? If I devise a game of Candyland with 10^180 squares, is that harder to devise an optimal strategy for than Go just because it has more board states?
The reason that we're still using board states as a proxy for difficulty is because historically our metric of "this is difficult for a computer to play" was based on the size of the decision tree and thus the feasibility of locally searching it up to a given depth. In the age of machine learning, surely we can come up with a more interesting metric?
Yes, but what are the estimated number of states of all these atoms?
Wording like “game is more complex” overal seems incorrect. Game is not complex by itself (for example go rules are extreemly simple), all the difficulty and challenge depends on the skill of your oponent. Game only allows the opponent to demonstrate the skill.
I mean I am open to hear the justification for this, but I was fairly certain that all measures of game complexity are a function of the number of legal positions. Now certainly there are other factors, namely the cost of computing the transition from one legal move to another legal move so a simple game might have a very low cost transition function while a complex game has a very complex transition function, but I can't conceive of a game where the number of legal positions bears no weight on the game's complexity.
I haven't played Go in a while, but I'm kind of excited to try going back to use the KataGo-based analysis/training tools that exist now.
[1]: https://github.com/lightvector/KataGo
Truly a must watch! (just look at the video comments to be convinced)
What stuck with me is Lee Sedol's strong emotional reaction, leading him to leave professional Go playing.
It's understandable he didn't expect AlphaGo to be that strong. Or that (for him) losing to a machine took the 'soul' out of the game.
But come on... I've been cornered by Pac-Man ghosts many times. That doesn't make Pac-Man less fun to play.
Nor does losing to the crude 'AI' steering those ghosts. Instead, you play, aim for a high score, see how long you can survive, how many levels you can complete, or how many fruits & ghosts you can eat in a game.
And (if you care) compare how those 'metrics' stack up against other players.
If a machine with superhuman Go-playing ability isn't fun or challenging, then stick to human opponents.
Of course it's his views and choices, and I respect that. But other than providing extremely challenging opponent, I don't see how human-beating machine would take the fun out of a game. Rather the opposite: new tactics, new insights, a raised upper bound for a Go player's strength (human or otherwise), etc.
Open up how you frame personality types and life experiences, and you can think of possibilities beyond "I don't see how".
"I believe that humans can partner with AI and make great progress. As long as we can set clear principles and standards for it, I am quite optimistic about the future of AI technology in our daily lives."
I hope he got paid well.
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