Questions I would ask God about the game of Go
fuseki.net
fuseki.net
> What openings do aliens play?
I love these questions about if anyone else in the universe is playing Go. My gut response would be yes -- it's a simple enough game (regular game grid of any size roughly 5x5 on up, one type of piece, two players take turns alternating placing pieces, and any that are surrounded are removed). I suspect other simple enough games that likely exist elsewhere in the universe would be tic-tac-toe, connect-N, dots and boxes, and Othello/Reversi -- any others?
Contrast with, say, Chess, which has too many different types of pieces, all with specific movement rules, and with a specific initial layout. I wouldn't be surprised if Chess only existed here, though I also would expect plenty of games similar to Chess to exist out there in the universe, i.e. a game on a regular board with multiple types of pieces and different rules for moving the different pieces. If Shogi, Checkers, or Stratego weren't human games I wouldn't be surprised to learn them from aliens.
It's a great question -- what is the most universal board game? What board game has been independently invented the most times throughout the universe? What if it's a game that we haven't even come up with?
Even if some aliens think so differently from us that the concept of a square is unknown to them, surely there are plenty of aliens that would think similarly enough?
Hell, maybe there's aliens that don't enjoy games per se but that use them for other purposes, like deciding legal guilt or who gets to rule.
Once you start looking into the rules for specific games that only use dice, the rules are many and pretty specific (e.g. street dice), and it's the Chess problem again. I guess a dice game that probably exists pretty widely in the universe would be the simple children's dice game, namely, two players roll N-sided dice and the higher number wins, or you accumulate multiple rolls and play first to a given total, but that's not a very interesting game, and there's no strategy.
I'd guess no, since there doesn't seem to be another human culture / civilization that independently invented it.
I don't want to get into arguing Drake's equation here, but if you accept that aliens exist, then you're granting that there's a lot of them; it makes no sense why we would be, e.g., one of only two intelligent species in the entire universe.
It may be wrong, but "aliens" is not a response to it.
The intention of the GP was - given that Go was not invented again on Earth, there's no real indication that it would be invented again at all. That doesn't imply that it cannot be invented again because it is too complex.
Also, it's kind of silly to count something not have being reinvented against it, because things almost by definition cannot be reinvented. Look at how popular board games are right now; if Go hadn't yet been invented, it's quite possible that it would be invented now. But instead it has already been invented, so people already know about it, and any would-be inventors end up not being inventors; they either already know about it or are told that what they've come up with already exists.
Well, they can, but the opportunities are limited to cultures where the game has not been introduced yet.
I would also point out that we don't know that Go was never invented independently on earth, just that it was never invented and popularized in a manner that left a cultural or historic record of which we are aware. If Go were played by a small clan of prehistoric people using different color berries and a grid scratched out in the dirt, what evidence would be left?
So that REALLY limits the opportunities to cultures that left a significant historic record but had no cultural exchange with china.
Not quite. It's making a must out of an is. The relevant distinction is "true by necessity" vs "true by coincidence", not "factually correct" vs "morally correct".
Dozens, if not hundreds, of other abstract games were, and I don't think there are many as simple.
It's not so obvious that anyone would have noticed how good a game it can be.
I want to say that board game players are pretty good at recognizing strategic depth, and that good games naturally rise to the top and become widespread, and their mechanics are reused and evolved in further board games. You certainly see this with Euro-style board games at least.
Chess, by contrast, propagated rapidly throughout the Old World.
I don't have an explanation for this. It seems curious.
Korea had Sunjang Baduk: https://senseis.xmp.net/?SunjangBaduk
Tibet had its own variant: https://senseis.xmp.net/?TibetanGo
I didn't meant to imply that chess didn't mutate as it travelled around. It's still striking to me that Go was unknown anywhere which didn't use Hanzi to write.
If earth is visited by Aliens some day, we should assume they play on larger board than us. It would be laughable that we get visited by 9*9 players.
This only makes any sense if you're also confident that, should we visit an alien world some day, we would have updated the rules of Go to require a larger board.
If we can play on a 19x19 board for historical and sentimental reasons, aliens can play on a 9x9 board for historical and sentimental reasons.
Which proves it's not gravity -- gravity would move the same speed always (assuming a vacuum game stage), or would move proportionally to air resistance (so based on shape), etc.
Clearly the real answer is that Tetris is played in a weightless vacuum, and that pieces are shot at a constant speed from somewhere offscreen.
Obviously not, since the speed increases as the game progresses (of course the planet could have increased its mass in the meantime).
Obviously the tetrominoes are being fired by a variable speed railgun and the current is being increased with each round.
> Board size - gravity rules - scoring etc. are arbitrary
So 'gravity rules' refer to falling speed, which is unimportant and doesn't fundamentally change the game, same with board size.
There's dozens of Tetris variants, all with tiny little differences at this level, and they all contribute to different strategies.
As an aside, my favorite variant of this is from an old game Puzzle Pirates: https://www.youtube.com/watch?v=XRQIHyC__kc
Why do all theories about aliens start with the implication that they're similar enough that they developed the way we did, they think like we do, have similar senses, brain structure and locomotion.
Any aliens that have evolved to any kind of level of intelligence would have done so under the conditions specific to their planet. Given the huge variation of life on Earth over its existence and that humans in their current form, or even animals in their current form, have existed for such a tiny insignificst fraction of time that it seems kind of preposterous to assume aliens elsewhere are anything like us in the slightest.
Humans have problems anthropomorphizing animals as it is, but when it comes to aliens it just seems like everything starts with, well of course they must do the things we do....
Our simplest board games aren't that far removed from the realm of the purely mathematical. And yet aliens won't all have their own completely different mathematical systems; such a thing isn't possible.
I think the body shape part is relevant here because it determines what kinds of games are possible or practical. A species of intelligent octopuses might play games involving changing their pigment (in wavelengths we can't even see!) or manipulating eight things at once. Bird games might involve flying competitions etc.
Edit: I guess the important part here in a species inventing Go, is having a body that can make a board game (or similar representation). Hands are pretty good for crafting tables and moving small pieces around. Beaks and snouts less so. (I'd put my money with the octopus.)
It's worth pointing out that Go is a purely mathematical game. You don't need a board at all to play it, especially not if your memory is good enough. Chess Grandmasters don't need boards to play Chess, for example; they can simply say the moves to each other and both will have the same image of the board in their mind.
So you could have intelligent aliens playing Go entirely verbally. Considering how many alien species there are likely to be, perhaps this is almost a certainty?
We might one day have octopuses play Chess with us. But there may be other alien games we'd learn from them as well. Or not.
Is it common to be able to play Go without a board? That seems to require storing 361 bits in your head. I guess it’s much sparser than that for most of the game and has more structure than just 361 random bits, but that still sounds hard.
Here’s a (strong?) amateur who claims to be the only person who can play this way [1].
But yes, there are even some people that can play Go in their head. You're wrong about the amount of information though; each piece on the board has 3 potential states, not just two. Though you can chunk the board pretty effectively and it becomes more about memorizing larger patterns than the state of every single spot on the board. Plus, the board never fills up, so you only need to remember the spaces with pieces in them, not every space.
Also, 400 bits of information is about two sentences.
I think the assumption there is that the alien race is smart enough and dexterous enough to create machines. Wether they use tentacles, fingers, snouts or talons, it makes sense that such a species develops board games at a moment
The little-known Star Trek IV: The Voyage Home centers its plot around the idea that Earth whales are themselves aliens. A crisis occurs when a whale probe comes to check on the Earth whales.
While not exactly movie and not specifically sea creatures/birds, there are plenty of anime series and visual novels with intelligent non-humanoid alien species. Parasite from Parasyte, some forms of BETA from Muv-luv, aliens from Stellvia, (NSFW to Google) Saya from Saya no Uta (real form). Dragons are also often portrayed as intelligent race originating from space (e.g. Final Fantasy XIV & Kumo Desu ga, Nani ka?). Many of these usually have a way to appear as humanoid to make conversing with mankind easier though (and likely to make it easier for readers/watchers to relate).
Anyway, since probably won't know anytime soon, and perhaps never, this kind of speculation is a bit useless. But if we ever found an alien species, it seems unlikely we would be able communicate with them any more than we can communicate with a piece of rock.
You're making a lot of assumptions about things that you claim are impossible or would never happen, without explaining how you're coming to those assumptions. And the "communicate with a piece of rock" bit is just flat-out bad argumentation, as rocks aren't intelligent and thus cannot communicate by definition.
I think the variety among the possibilities for other intelligent species (if any) would far outweigh the number of them. Hence it might be probable that there would exist two similar ones, but it would be very improbable that any of them would be similar to humans.
The point about "communicating" with a piece of rock was exactly that we cannot communicate them. Even if we would run into an alien species (which seems unlikely), it seems very improbable that any meaningful communication could happen.
Unless we're going to argue that Earth has some sort of unique concept of "playfulness" built into the original single cell, it's not that hard a guess that a good chunk of aliens out there might recognizably "game".
Is everyone who thinks we stand no chance of communication really comfortable claiming that we're just soooo unique that we won't be able to communicate with anything? Because it's the exact same claim, just from a different viewpoint. Personally I think it's just fashionable misanthropy that will dissolve the instant you spin it in a direction where it might perhaps look like one is claiming it in a way that makes humanity look special.
However, it could be probable that there are two life forms in the universe which are similar. But then they would probably be too far apart from each other to ever be able to communicate.
For the same reason the laws of nature are the same around the universe.
Logic is not really that negotiatable, so thinking creatures will end up with the same kind of logic as us, even if they look differently. All forms of life are also not equally good at developing thinking and tools, so that's another pressure to converge to something similar-ish and e.g. not an underwater fish-like creature or some thing without a means to grab stuff and manipulate it (even if it's not opposable thumbs).
>Humans have problems anthropomorphizing animals as it is
I don't think anthropomorphizing is really a problem, or unscientific. In fact "anthropomorphizing" as a bad thing is probably based on religious inspired dichotomy between the man and the animals, where man is basically just another animal for 99% of intents and purposes.
There's a bad form of anthropomorphizing animals (the Disney or pet owners way, which puts into animals exactly the human characteristics they lack more or don't have at all), but that aside, we share all kinds of insticts, physiology, deep brain structures, etc with animals.
I wonder how much is cultural though? Go depends on a 2d grid, but is it possible that some alien Grade 9 math tends to use, say, distance and angle from origin instead of x, y? In that case the intuition for Go might not be there because they don't use grids, even though the math is ultimately the same.
Or a culture that likes to use hexagons for their board games (hexagonal Go tends to be more shallow than grid-based Go).
There are a plethora of abstract games that have been invented that are not played very much, but seem to have the potential for extreme depth of play. I would be willing to bet that some of those neglected games are played by Aliens somewhere in the Universe, and enjoy the level of success in their society that Chess or Go enjoy here.
On your turn you can either move your piece, or place a wall. You have 10 walls to place.
The one non-obvious rule that completely changes the strategy of the game is that you cannot make it impossible for the other player to win (you can't simply box them in).
So a common theme is to try to maximize the amount of paths your opponent has while minimizing the number of paths you have, so that whenever your opponent commits to a path, you block it and force them to backtrack.
But say your opponent has 2 paths, and they begin to commit to one. You are waiting for them to commit further so you can block it and force them to backtrack. But before you do it, they block the other path themselves. Now it is illegal for you to block their only remaining path.
On the face of it, the branching factor is much higher than chess. On each turn one has 100+ possible moves. I have written pretty highly optimized minimax AB-pruning type AIs for it and have never managed to make an AI that can search deeper than 7 moves or so in a reasonable amount of time, and my AI was the strongest (by far) of any I could find online (and better than any human player in my friend group).
It's pretty computationally difficult due to the "cannot make it impossible to win" rule. If you do it naively, that involves an A-star search for each possible move. You'll max out around 4 moves deep with that strategy. A few observations will get you a bit higher. e.g. A wall cannot possibly block a path unless both ends of the wall touch another wall (or edge of board).
There might be some sophisticated graph cutting algorithms I am not aware of that could make this tractable, but I haven't found any that mapped too well onto the problem.
I think Quoridor is actually really ripe for an AlphaZero type approach (due to the high branching factor and expensive compute needed to determine move legality), and I would love to see a superhuman game played.
You can play against someone's javascript AI here: https://danielborowski.github.io/site/quoridor-ai/display.ht...
I think this AI does a depth 2 or 3 search.
I think dice combination games are going to be popular as well.
Sickle - Brick - Foil
Hell, if the players are far enough away from each other and shouting out their answers, you can solve the simultaneity issue. By the time you've heard the other player's move you're already halfway through saying your own move, and can't pretend you were going to say something else.
Bottom line numbers:
280 gomoku
356 hex
483 dots and boxes
572 go
622 checkersAny idea where Chess would stack up? I'm assuming it'd be greater than Checkers in that list, but how much greater? And would Nim be simpler than Gomoku (Connect-N)?
I wonder, would it make sense to encode the idea of a square and hex grid with pieces of two different colors as a library of sorts, such that this basic grid implementation doesn't count against each game individually? The boards are very widely reused, generic, mathematical concepts. This would give something like Go or Connect-N a fairer shot of competing against something like a Nim, which only needs a single integer accumulator to represent its game state.
Most of the complexity is in what changes players are allowed to make to the board.
Have you considered defining the complexity in terms of the number of bits required to implement the game, and not just the ruleset? Go requires a potentially very large list of past board states.
It's played on a grid of overlapping circles, without counting the origin as an intersection.
Every intersection has exactly four liberties, so it adds an optional move of a stone after each placement. Liberties are counted after both the placement and the move, so a player can't occupy a point with no liberties and then slide to capture.
Anecdotally, it's enjoyable.
Thing is, I came up with it in the year 2000, and it doesn't appear to have existed before that. This experience has left me skeptical that it's obvious that an alien race came up with Go. They might have.
If there are enough intelligent aliens than it's just a numbers game.
But would it be more than half? I doubt this. Sure would be fun to find out.
This naturally introduces the idea of a "universality constant" for any given game, i.e. what percentage of species will have invented that exact game. For obvious reasons this figure is likely to be much higher for, say, Go, Connect-N, or Hex, than for something like Chess.
It definitely seems like the kind of thing that could be independently invented. It's so based in random chance.
Every NxNxN cube of space has a finite state space. Assuming an infinite universe, there are an infinite number of such spaces. If a state is likely enough to occur once, it ought to occur an infinite number of times.
This supposes not only a game functionally (if not superficially) identical to chess, possibly with differently shaped or colored pieces. It also supposes a world identical to Earth, called Earth by the English speaking humans who live there, who play a game called chess which functions exactly like chess, with knights that are called knights and bishops that are called bishops.
Which leaves us in an interesting conundrum. We can't ask which game is the most common, because many games occur infinitely many times: infinity doesn't let us make comparisons like that.[1]
Then we start asking questions like which games occur finitely many times? Of the finitely numbered games, which was the most common? Least? What does the probability curve look like? (This is honestly the most interesting to me. Is the peak at 1 unique copy which then exponentially decreases, or are there very few unique games which grow to a peak and then rapidly drop to zero, or is it a uniform distribution that just... Keeps going, or is it a boring normal distribution?) Which game had the most variations but still recognizable to a player of a middle of the road variation? Are there any ring species [2] of games, and if so, which has the largest ring? Is Star Trek 3D chess played unironically?
Other questions we can't ask: are there infinitely many games? There are not. Life is almost certainly bounded in size, which means there are a finite number of states. This gives us a finite number of creatures, and therefore a finite number of unique ideas.
Infinity is a fickle mistress.
[1] https://en.m.wikipedia.org/wiki/Hilbert's_paradox_of_the_Gra...
Is go played anywhere else in the universe, and was it discovered by chance there? What openings do aliens play?
Our Universe is a huge place. I think it was Nature Magazine that had an article estimating 20,000 worlds with earth like conditions and life. My formal education is in physics and personally I subscribe to the multiverse hypothesis so with a potential infinite number of universes these questions have meaning.
My older brother taught me to play Go when I was eight and I played actively in the 1970s. Two years ago, on a whim, I decided to go to the US Go Open. I drastically overestimated my own rating when registering, played too strong of players and lost every game. A good lesson in humility and I made some friends. To lick my battle wounds, I paid a South Korean Go professional for lessons for three months and I feel like that really helped my game.
We have a sample size of one and what must be, in the grand scheme, a primitive understanding of physics and chemistry and biology. Throwing around numbers and probabilities for the existence of other life is frankly ridiculous. The best we can intelligently talk about is what the number is given some guess about other numbers. But remember, we have no good numbers for the emergence of life, the survival of life, the likelihood of evolution into intelligent life, etc. Any number multiplied by a totally unknown factor can be literally anything.
And before someone throws the infinite universe argument at me, of course. Any probability above zero times infinity is infinity. (Though it’s also possible that there is still no extraterrestrial life even in that case, that outcome always has a non-zero probability!) If we accept a probabilistic emergence of life, then we need to talk about useful things like “in our solar system”, “in our galaxy”, “in the visible universe”, and such. Though it is theoretically possible that the conditions for the emergence of intelligent life are so narrow that only planets exactly like ours, so exactly like it that someone else on that planet has or will typed out this exact comment, have it. In a truly infinite, random (hmm, another bad assumption perhaps?) universe, there would be infinitely many such exact replicas of Earth and its entire visible universe. This isn’t a very useful concept.
> Is there a safe way to prevent Mirror Go?
> A really sad result of talking to God about go would be that there is a way to just play mirror go and win. If that was all god did, it would be really annoying. If mirror go doesn't actually work, how does God defeat it? Do the variants where W is just not allowed to mirror fix the issue?
The first way I was aware of was that the primary player could surround the center. They'll capture the mirroring player's stones one turn before the mirroring player can surround theirs, and the mirroring player loses the stones they need to do a mirrored capture.
Sensei's Library [0] has a few other ways as well.
I would think not, because when you have perfect play, you either win, lose or draw. So you just have "winning opening moves", "losing opening moves", and "draw opening moves". You cannot really rank them.
Maybe the ranking would be the number of different games that lead you to a win, in a monte-carlo tree search fashion. Which could then be useful if you can't play perfectly (highest probability of winning).
So, if you have a very clear path of how to win by 1 point, or a risky way to win by 10 points, does it make sense to try the risky path ?
I like how he used the word "discovered" and not "invented".
Some of the rules neatly map onto it.
Since AlphaGo plays itself, it could have been set to play itself with a handicap, such that the win rate was 50%. I want to know what that handicap would have been, because wouldn't that indicate a pretty accurate measurement of what komi should be?
There are a few open source implementations of the alphago algorithm and some new work being done to improve it for go. Check out lizzie, which is a nice front end to leela zero.
I do think we already have good evidence the best komi is 7 or 7.5, but it's not definitive.
The question of what the best ko rule is value based (different rules have different consequences/aesthetics for gameplay).
Komidashi https://en.m.wikipedia.org/wiki/Komidashi
"Komi in the game of Go are points added to the score of the player with the white stones as compensation for playing second. Black's first move advantage is generally considered to equal somewhere between 5 and 7 points by the end of the game. Standard komi is 6.5 points under the Japanese and Korean rules; under Chinese, Ing and AGA rules standard komi is 7.5 points. Komi typically applies only to games where both players are evenly ranked. In the case of a one-rank difference, the stronger player will typically play with the white stones and players often agree on a simple 0.5 point komi to break a tie in favour of white."
Does not apply to questions about aliens.
Ladder is a fundamental technique that is easy for humans but hard for both monte carlo and neural network static analysis. It is plausible that an equally strong but more ladder-aware player would have very different tactics from the current best computer players.
The original AlphaGo actually had a hand-crafted ladder feature input layer. It was removed in Alpha Zero. We know from Leela Zero and ELF Go game records that they don’t understand ladders very well, so likely Alpha Zero didn’t understand them either.
That having been said, I think it's fascinating that most of these questions are just that, but are impossible to answer at present. The probability space is just too large. It's one of the fascinating aspects of go. It's a very simple set of mathematical rules that yields incredibly complex behavior and is practical impossible to brute force "perfect" gameplay as a result. I.e. you can't search the full space, you have to learn to predict optional strategies and always wonder if there isn't a better solution somewhere.
For example i wrote a 3 page article. Even would be surprised be surprised if a person came and tell me if we took all the characters at prime number it would be a valid sentence about an event going to happen in future.
Below is a text version:
Here is an attempt to describe the rules of Go precisely. This is actually for a generalization of Go that I call MANGO, which stands for MAth Nerd Go
Equipment
To play Mango, you need the following:
• A countable set, I.
• A set, C, whose members are subsets of I, each of which contains exactly two members of I.
• Three subsets of I, called E, B, and W, such that their union is I, and the intersections of any pair of them is empty.
• A real-valued function F, whose domain is I.
• A function, T, whose range is {0,1}, that is defined on the real numbers.
Definitions
• If P is a finite subset of C, and n is a member of I, then the INDEX of n in P is the number of elements of P that contain n.
• A finite subset, P, of C is called a PATH if the following conditions are met:
1. Each element of I has an index in P of 0, 1, or 2.
2. There are exactly two elements of I whose index in P is 1.
• An element of I whose index in a path is 1 is called an ENDPOINT of the path.
• An element of I whose index in a path is 2 is called an INTERIOR point of the path.
• Let S be one of the sets B or W. Let s be a member of S. Let L be the set of all members, e, of E, such that there is a path whose endpoints are s and e, and whose interior points are all in S or E. Let z be the sum over L of F. Then s is ALIVE if T(z) = 1.
• The ordered triple (E,B,W) is called the CONFIGURATION.
Playing
The players must first obtain a Mango set. This consists of agreeing to the sets I, C, E, B, and W, and the functions F and T.
The players must agree to an initial score for each player.
The players than decide who shall have the first turn. Players alternate turns.
On a players turn, that player may do one of two things:
• The player may PASS. It then becomes the other players turn.
• The player may make a LEGAL MOVE.
Note that a player MUST either pass or play a legal move. If there is no legal move, the player is forced to pass.
A MOVE consists of performing several actions. In the following, if it is Black's turn we will use the symbol M to refer to the set B and the symbol H to refer to the set set W. If it is White's turn, M will be W and H will be B. Here are the actions that are taken by a player on that players turn:
• A member, n, of E is selected.
• n is removed from E and added to M.
• All members of H that are not alive at the end of the above step are removed from H and placed in E.
• All members of M that are not alive at the end of the previous step are removed from M and placed in E.
A move is a LEGAL MOVE if the configuration, (E,B,W), produced by the move is new.
The game ends when two consecutive turns are passes.
Scoring
Each player uses the following procedure to compute his score. We will use the symbol M to refer to B if the player is Black, and to refer to W if the player is White.
We use the symbol H to refer I-(E union M).
The player starts with the initial score agreed upon at the start of the game.
For each m in M, the player receives F(m) points.
A player receives F(n) points for each member, n, of E for which the following conditions both hold:
• There exists a path with n as one endpoint and the other endpoint in M, and which contains no members of H as interior points.
• All paths that contain n as one endpoint and a member of H as the other endpoint contain a member of M as an interior point.
The player with the most points wins.
Example
To play ordinary 19x19 Go, with a 5.5 point Komi, the players might agree to the following:
• I = { (x,y) | x and y are integers in [1,19] }
• C = { {(x,y),(u,v)} | (x,y) and (u,v) are in I, (x-u)^2+(y-v)^2 = 1 }
• B = W = {}
• E = I
• The initial scores are 0 for Black, 5.5 for White.
• It is Blacks turn.
• F((x,y)) = 1
• T(z) = int((z+360)/361)
To play a Go-like game on an infinite board, the players might agree to this:
• I = { (x,y) | x and y are integers }
• C = { {(x,y),(u,v)} | (x,y) and (u,v) are in I, (x-u)^2+(y-v)^2 = 1 }
• B = W = {}
• E = I
• Initial scores are Black:0, White:0.
• It is Black to move.
• F((x,y)) = exp(-x^2-y^2)
• T(z) = 1 if z > 1/1000, otherwise T(z) = 0