Yes, Arimaa has a branching factor of about 20k which is bigger than go with about 400, but I'm thinking bigger! For example if you were allowed to play an arbitrary number of stones in go then the maximum branching factor would be about 2^400 which quite a bit larger. I'm wondering if such games exist and are playable.

edit: http://senseis.xmp.net/?OtherGamesConsi ... ogrammable has a discussion of this, but doesn't really seem to solve it, except perhaps for "mind ninja" which has a very high branching factor on the first move but then settles down (I think), so doesn't seem that complex, by my definition.

Haha yeah, my feelings exactly.

If there are an infinite number of choices for each (or even just one) move, then voilà, the number of possible games is infinite.

Examples:

• Go on an infinite board
• Go on a board without lines

(I am not claiming that any of these are good games.)

The problem with infinite boards is that the game never ends (as well as the cost of materials to build them).

Perhaps that's where a bit of misunderstanding is coming from. I see Robert's remark as a direct response to Jhyn. Whether or not you agree with Jhyn, it's a bit strange to question Robert for discussing game complexity as a separable attribute when he was responding directly to a statement that did the same thing (which you in fact agree with).

With regards to whether complexity is irrelevant, I can see your point, but also suspect that we can actually feel the difference between "complex enough" games even if they are all beyond our ability to completely solve. For example, even 5x5 is complex enough that humans can't exhaustively search without the aid of computers, but 9x9 and 19x19 feel considerably more complex (and in my opinion, much more interesting). There are definitely other factors at play (e.g. balance between third and fourth line), but having played 15x15, I definitely think there is more depth and allure in 19x19 comparatively. Not quite sure whether expanding the board further would make the game more interesting - possibly the added game length and the already astronomical complexity of 19x19 doesn't really make it worthwhile, but wouldn't be surprised if it turns out that 21x21 and even larger board sizes could be amazing if they become popular.

p.s. I agree that your statement wasn't a personal attack, just didn't really want to steer the discussion down that route.

Edit: Changed "territory and influence" to "third and fourth line".

I fail to see where I appeared to be mocking Robert (which was definitely not my intention), so if you can point to what I said that gave you this impression, I would appreciate it.

Robert disagreed with the sentence that you quote, and while I technically agree with him, he associated a meaning to my sentence that I did not intend in this context. This is why I tried to clarify what I meant in my next post. You seem to ignore this second post and quote again my first post to say something I did not mean.



The short answer is: less combinatorially complex is not straightforward, in the same way that a slightly greyer shade of black is not white.

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La victoire est un hasard, la défaite une nécessité.

I did not imply that you were mocking Robert :p Apologies if my phrasing is unclear.



Sorry - I tl;dr'd your second post initially as the intent of my first post was to defend Robert's response to your first post. I don't fully agree with your second post (please refer to my previous post - I would expect the game tree complexity of chess to be closer to 13x13), but understand your frustration for my continued quote of your initial post which you clarified in your second. Again, the intent was to give context to Robert's statement rather than critize yours (and I can definitely see the point of your second post even though I slightly disagree).

All right, thank you for your clarification (also I can see how the second part of my post could be seen as an answer to Robert's statement, which it was not).

I don't think 13x13 or 15x15 go are "19x19 with less combinatorial complexity". Other aspects of the game, for example the fuzzy notion of the "strategy/tactics balance", are also changed. I have heard many times the argument that 19x19 hits a sweet spot in terms of this balance; this is not a mathematical proof but as you said 21x21 is not really played, and I tend to believe adding more intersections will yield diminished returns. In short, I agree with hyperpape: we can't measure the effect of more or less complexity all other things being equal, so we have a discussion about intuitions and impressions with no definitive answer.

In short, I think using the complexity argument to claim a kind of objective superiority between games is an error, because many other aspects of the game are more important with regards to what it brings to us; I see it as similar as claiming Bach is superior to any other compositor because his music is more complex. I have no problem if you prefer Bach, but this is a lazy (and falsely objective) argument imo.

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La victoire est un hasard, la défaite une nécessité.

I agree (and I suspect Robert also thinks it's silly to claim Go is objectively superior to Chess due to complexity since he clearly stated that both are outside human capacity). Personally, I think complexity of 19x19 does add to the game (though I do get overwhelmed by its size pretty often). I definitely agree that there is more to just complexity since I also prefer 9x9 over 13x13 - can't really say why exactly, just that the "balance" of 13x13 feels a bit off to me (whereas 9x9 isn't really about balance). When comparing between 13x13 and 19x19 I feel like the "depth" component is more important to me than the "balance" component, but of course this varies by person.

The go game tree is complex, that some people are enthusiastic about it, well I don't see that as a problem.

There are many 'problems' in the go community, one, for instance, might be 'amateur syndrome', people who say they want to improve, but really just want to play for fun.
Instead of doing things like counting, and making sensible plays, they like to get into crazy fights because it is fun, then they'll complain how they are stuck at X level, and when they get a review that tells them where they made mistakes they take it personally and decide to ignore it, and do whatever they want anyway. And if someone says something, they'll point out how it is wrong because pros do X all the time, etc.

Is it a problem? Not really, everyone engages with go at some level, and for the individual it may be annoying that they don't increase they're level, but then they play another game and get into a fight, and kill a big group and feel better anyway.

If someone is excited about the game tree complexity, just give them a high five, and then play a game with them.

Accept that the game tree complexity in go is mind boggling, and let it go.

Complexity has several aspects. For some complexity aspects, Go is superior to Chess (among them: it requires more AI techniques to let a program beat a top player) - for others, the two games are equal. Complexity is just one of the topics that can make games interesting.

The number of first move possibilities is 361, but please keep in mind that most people do not play on the first line or second since it generally does not lead to a good outcome. So just quoting numbers does no good. Chess has 20 possible opening moves. But some are not used because of the weakness thereof. Both games have a complexity that dwarfs the human minds ability to fully grasp. And that is why we have GO and Chess tournaments and not tic tac toe....

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Walla Walla GO Club -(on FB)

We play because we enjoy the beauty of the game, the snap and feel of real stones, and meeting interesting people. Hope to see ya there! お願いします!

Anthony

I think that the problem is now dead. It was the case that Go players would overstate this complexity aspect, lumping in the pants-on-a-stick ability of the state of the art software alongside. Such days are past.

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North Lecale

Something which narked me slightly in all the AlphaGo press was the "Go is so complex, there are more games than atoms in the universe" spiel. I seem to recall Demis Hassabis said this in his presentations as well as being reported in newspaper/website articles. That atoms in the (observable) universe number is about 10^80, which is less than chess complexity (about 10^120) so it's rather a naff comparison. If every atom in the universe was replaced with a copy of the universe, and then every atom in those copies was replaced with another copy of the universe and then every atom in those copies of copies was replaced with a copy of the universe and you then counted all the atoms in those 4 levels of universes, then you'd have about 10^360 atoms which is Go's complexity. Exponentiation makes big numbers!