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Number of legal 18x18 Go positions computed. One more to go

tromp.github.io

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Re: Number of legal 18x18 Go positions computed. One more to go

#31

Post by tromp »

MichaelGG wrote: post #24
tromp wrote: post #15

Earlier quoted context omitted.

Few people can believe that there are as many as 386,356,909,593 games on the tiny 2x2 board. Needless to say, nothing is pruned there either. A game could visit as many as 48 of the legal positions and have dozens of passes (but only 2 consecutive ones, which ends the game).

Well it "ends" the game but play can resume. Plus, there's the crazy hypothetical play in the way-over-complicated Japanese rules. I think, in theory, you can play multiple almost-compete games after the game is "over". Each hypothetical play is just to resolve one group, as I understand.

Indeed, the Japanese rules are not suitable for mathematical analysis of the game; see https://en.wikipedia.org/wiki/Rules_of_go#Counting_phase

That's why our paper "Combinatorics of Go" assumes the so-called Logical Rules at http://tromp.github.io/go.html, which do end a game on consecutive passes.

Re: Number of legal 18x18 Go positions computed. One more to go

#32

Post by NhanH »

motbob wrote: post #26
everyone wrote: post #11

Anyone here play? It is pretty much the ultimate boardgame. Its like game-theory the game. From the very start you are embroiled in interesting risk/reward and provoking you opponent to overextending type stuff. Great place to play is gokgs.com I actually cant play many strategy games anymore because I realize this is like go with a load of crap thrown on it. My friend and I call this 'false complexity' the game isnt…

What makes complexity "false"? Is it "complexity I don't find interesting"?

I read "false complexity" as "complexity as imposed by a set of rules", as opposes to "complexity as an emergent behavior from very simple rules and interaction". Of course, adding any rule will add more complexity of the former, and probably the latter too. Whether one is more interesting than another is a matter of taste.

Re: Number of legal 18x18 Go positions computed. One more to go

#34

Post by Orangeair »

motbob wrote: post #26
everyone wrote: post #11

Anyone here play? It is pretty much the ultimate boardgame. Its like game-theory the game. From the very start you are embroiled in interesting risk/reward and provoking you opponent to overextending type stuff. Great place to play is gokgs.com I actually cant play many strategy games anymore because I realize this is like go with a load of crap thrown on it. My friend and I call this 'false complexity' the game isnt…

What makes complexity "false"? Is it "complexity I don't find interesting"?

I think 'artificial' would be a better word here. For example, in Magic the Gathering, there is a very basic turn structure and set of rules that define the game (draw a card, play some cards, attack, play some more cards, done) that is convoluted by several factors, including an increasingly large dictionary of terms relating to abilities and powers of the cards, and a correspondingly dense set of rules to handle the inevitable complexity of all those things.

For example, creature cards have power and toughness. Simple enough. But then at some point, cards were printed that allowed you to modify those values. Now you have to mentally keep track of the actual state of the card. Then consider what happens when you have two effects like "add two to toughness" and "switch power and toughness" applied at the same time. Which one happens first? Much as in software, each new feature of the game inevitably has interactions with other features that have to be analyzed and handled appropriately.

Going back to the main point, this complexity is 'artificial' because it is not an emergent property of the rules themselves, but rather a consequence of the fact that so many rules have been piled on over time.

Re: Number of legal 18x18 Go positions computed. One more to go

#35

Post by baddox »

everyone wrote: post #11

Anyone here play? It is pretty much the ultimate boardgame. Its like game-theory the game. From the very start you are embroiled in interesting risk/reward and provoking you opponent to overextending type stuff. Great place to play is gokgs.com I actually cant play many strategy games anymore because I realize this is like go with a load of crap thrown on it. My friend and I call this 'false complexity' the game isnt…

I'm not super familiar with Dota, but I have thought a fair amount about game theory as it applies to RTS games, and Dota (being a MOBA) has many similarities.

The main thing (from a game theoretical standpoint) that I believe sets RTS games apart from (most) strategy board games is not the real-time nature, but the fact that RTS games are not perfect information games.

Incorporating knowledge about your opponent's playing style is important in chess (and I presume Go), but I believe it is vastly more important in RTS games, so much so that in high-level competitive games it is a primary driver of both players' decisions in the game.

Of course, from a broader (not game theoretical) standpoint, the bigger and more obvious difference between strategy board games and RTS games is that the latter, being real-time, requires substantial physical speed and coordination, which is mostly not the case with the former.

Re: Number of legal 18x18 Go positions computed. One more to go

#36

Post by hasenj »

NhanH wrote: post #32
motbob wrote: post #26

Earlier quoted context omitted.

What makes complexity "false"? Is it "complexity I don't find interesting"?

I read "false complexity" as "complexity as imposed by a set of rules", as opposes to "complexity as an emergent behavior from very simple rules and interaction". Of course, adding any rule will add more complexity of the former, and probably the latter too. Whether one is more interesting than another is a matter of taste.

Also: arbitrary rules.

Concrete example: castling[0] in chess

[0]: http://en.wikipedia.org/wiki/Castling

Re: Number of legal 18x18 Go positions computed. One more to go

#37

Post by CurtMonash »

everyone wrote: post #11

Anyone here play? It is pretty much the ultimate boardgame. Its like game-theory the game. From the very start you are embroiled in interesting risk/reward and provoking you opponent to overextending type stuff. Great place to play is gokgs.com I actually cant play many strategy games anymore because I realize this is like go with a load of crap thrown on it. My friend and I call this 'false complexity' the game isnt…

I love Go. But from a game-theoretic view it is theoretically rather trivial, as are chess, checkers, and any other game in which players with perfect information alternate moves.

The winner of a Go game is whoever more reliably predicts the ultimate result of various potential intermediate positions. The only interesting game theoretic aspects at all arise to the extent one can predict one's opponents' likely errors, or that one "knows what one doesn't know" in terms of one's own calculating ability.

Re: Number of legal 18x18 Go positions computed. One more to go

#38

Post by ctdonath »

tromp wrote: post #15
chizthtor wrote: post #5

They got 57 legal position for a 2x2 game of go. They're counting all the symmetries. They're not pruning anything. facepalm

Few people can believe that there are as many as 386,356,909,593 games on the tiny 2x2 board. Needless to say, nothing is pruned there either. A game could visit as many as 48 of the legal positions and have dozens of passes (but only 2 consecutive ones, which ends the game).

That...is ridiculously intriguing.

I'm afraid to ask for pointers to understanding that statement, as it would mean spending hours pouring over the details (and likely writing & running software to analyze it) just to understand a ... 2x2 go board.

Seems to fall into the category of "grand unified theories" in any topic, where prolonged advanced study of complex systems tends to lead students thereof to develop zen-like simple-yet-profound expressions of the subject.

Now I want a 2x2 go board. "What's the point of that?" "There are a third of a trillion possible games that can be played on it. Care to try one?"

Re: Number of legal 18x18 Go positions computed. One more to go

#40

Post by esgoto »

everyone wrote: post #11

Anyone here play? It is pretty much the ultimate boardgame. Its like game-theory the game. From the very start you are embroiled in interesting risk/reward and provoking you opponent to overextending type stuff. Great place to play is gokgs.com I actually cant play many strategy games anymore because I realize this is like go with a load of crap thrown on it. My friend and I call this 'false complexity' the game isnt…

I've been playing on and off for a few years. I got to around 1 dan, and hit a wall because I need to actually study regularly in order to improve now, but I'm too lazy. I've been taking a break and planning on creating some sort of routine for doing tsumego every day and pro game reviews.

I've always loved the way it becomes so complex through such seemingly minimal and simple rules (although superko rule and komi aren't particularly simple rules).

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