Number of Legal 18x18 Go Positions Computed; 19x19 On the Horizon 186
johntromp writes It took about 50,000 CPU hours and 4PB of disk IO, but now we know the exact number of legal 18x18 Go positions. Seeking computing power for the ultimate 19x19 count. And it's not a heat-death-of-the-universe kind of question, either, they say: "Thanks to the Chinese Remainder Theorem, the work of computing L(19,19) can be split up into 9 jobs that each compute 64 bits of the 566-bit result. Allowing for some redundancy, we need from 10 to 13 servers, each with at least 8 cores, 512GB RAM, and ample disk space (10-15TB), running for about 5-9 months."
How Much Does it Cost? (Score:1)
How many cryptocoins could be mined for that amount of computing power?
Re: (Score:2)
Re: (Score:2)
Not that many, the general purpose cpus are poorly suited to cryptocurrency and the low core count would hamper the number of threads.
Either thread heavy GPU's, incredibly cheap SOC's or well suited FPGAs return much more coin for the buck than what they are asking for here
If you went to Dell for this, it would run just under $200k (list price, using local disk), but there is probably an awful lot of suitable gear that is being aged out or abandoned by bankrupt companies out there that could be picked up fo
Re: (Score:3)
Instead of going to Dell, why not use Amazon EC2? Probably do it way cheaper and you could set it up in a couple hours.
Re: (Score:2)
It's Go ; it's more important than mere finance.
There is a ha-ha-but-serious school of thought about Go that it's not a matter of life and death, but something much more important. You'd be harder-tested to find a room full of Go players who could meaningfully give an opinion on whether Go was more important than the heat death of the universe. I suspect that given such qualified people, you'd get an affirmative on the question.
Re: (Score:2)
Fair enough, then what is the 'benefit' of solving this?
Fame, better game design. pursuit of knowledge?
Just saying that if you want to get donations for a pile of computing power, it is helpful to know how much it will cost and what the selling point to the donors is
Re: (Score:3)
Fair enough, then what is the 'benefit' of solving this?
Guessing they needed to heat their apartment and having the server run flat-out for 9 months helped - a lot.
Re: (Score:2)
dont think of ROI in a negative context here. the researchers are invested in learning more about the world and sharing this knowledge and this is what they want. they're not looking to "monetize it". a better question is, why would somebody pay $200k to solve this problem?
Re: How Much Does it Cost? (Score:4, Interesting)
Yeah, $200k seems a bit steep. I mean, if it was for national defense, pushing data against the stock market, or even running a moderately sized corporation's ERP stack it would be a totally acceptable expenditure
It is an interesting problem to posit how it would be possible to get the same gear for a fraction of the cost, say 10%, or $20k
This may seem wildly optimistic, but in the dot-com meltdown I remember seeing gear with million dollar price tags going for $10k on ebay
The chassis, processors, and potentially even disk arrays may be easily obtained. I have worked at companies where they were shoved out the loading dock door on a monthly basis, because newer gear had smaller footprints and we could stuff ten times as many processors or terabytes into the same constrained space that we were stuck with
RAM may be a problem since they are asking for 512GB per machine. This would probably be in 32GB sticks, which are as easily traded as gold, and even if a company was shit-canning them, the more enterprising techs should be expected to be grabbing them at every opportunity
The common nexus for this gear would be the computer salvage companies that get paid to haul it away and make a secondary profit off of reselling what they can. How would these go-crackers find a salvage company with similar leanings? If that connection could be made, they may get away with it for the discounted cost of re-sold RAM
Which leads us to the next issue, supplying 15KW of juice to run these on, the additional power to pull that heat out of the space and enough battery supply to handle a power outage without losing your entire data set. In the corporate world, this is another $50k of Liebert gear and a diesel generator. And your gonna have somebody on-call to monitor, tune and otherwise tend to their wants and needs...
in cheapo-town... this could be a garage and a stack of deep-cell batteries with the over-worked go-crackers reheating pizza on the top of a server
I think that it is an interesting exercise to figure out how to deliver a half-million dollar hardware solution for next to nothing, anybody else have their 2-bits to throw at it?
Re: (Score:2)
And what exactly is the financial incentive to solve the number of 19x19 Go positions?
Re: (Score:2)
Re: (Score:2)
What was the financial incentive for Deep Blue and champion chess programs?
PR for IBM, plus they did actually play chess with it, not just calculate the potential number of games.
Re: (Score:2)
Re: (Score:3)
Re: (Score:2)
When I started playing go, somewhere around 1987/1989, there was a price money offered for the first computer program that was able to beat a 1st Dan go player.
The price was a million dollars. It took decades until one managed to write such a program and farm in the price money.
I'm pretty certain we have a new price for a program beating a 4th Dan.
Someone with a better internet connection than I have right now, might want to google for that.
A go implementation that is somewhere around between 1st and 2nd Da
Re: (Score:3)
How do you justify the cost of a book, movie tickets, money spent on vacation travel or, going further, a degree that's not an engineering degree? Because if you run your numbers, there's no financial reason for any of those things.
Yes, there is absolutely no financial reason to be a doctor, lawyer, accountant, architect, dentist, vet, banker, real estate agent, marketer, economist, fashion designer, Army General, rock star, Hollywood actor, actuary, quantity surveyor...they're all just hobbies rather than jobs where you can earn any money.
I know it is a bit late in life... (Score:4, Interesting)
However, I think I'd like to learn to play this game. I played chess at an amateur level and did rather well at it during and even after college. I don't know if any of the skills transfer but I've been told that the mentality transfers. Being able to look a half dozen or more moves ahead and being able to picture all the moves my opponent can make are, as I have been told, something that does transfer.
Re: (Score:2, Insightful)
I played chess and go when I was a kid in China, and sucked at both. From my limited experience, chess is more tactical and analytic, while go is more strategic and holistic, although local territorial fights in go can be just as intense, where skills in chess can somewhat "transfer". Because of its holistic nature, kids sometimes excel in go. If you start as an adult, it'd be difficult, if not impossible to attain master level performance. But in any case, go is trivial to learn and more fun to play.
Re:I know it is a bit late in life... (Score:5, Insightful)
I played chess and go when I was a kid in China, and sucked at both.
There are approximately 100 people in the world who don't suck at chess, and even they make silly mistakes. Don't play chess in an effort to be the 'best', play chess because it's fun.
Re:I know it is a bit late in life... (Score:5, Interesting)
To be honest, as a kid I enjoyed chess and played with my friends right up to the point where you suddenly had to start memorizing openings and other canned sequences. At which point it felt more like a school subject than an escape from it.
Re: (Score:3)
You never needed to memorize. Push toward a position you're comfortable with, especially if you happen to know your opponent prefers a different type of position. An open player can f2f4 in a complicated position which can be very jarring and put the opponent into time trouble simply because he wants to figure out what you think you see. Or g2g3 and locked pawns can frustrate the hell out of an open player. At my absolute best I was 1800, and I memorized very very little. You're no Fischer and I'm no Capabl
Re:I know it is a bit late in life... (Score:5, Interesting)
I have to agree with this. I loved chess as a little kid -- probably started playing when I was 4 or so. Always just played for fun and liked the way it was more complex than something like checkers. I also occasionally enjoyed puzzling out some of those chess puzzles in the newspaper, which usually involved endgame scenarios. But then, early in middle school, I played against someone who actually "knew what he was doing," which included things like memorized openings, basic tactics, and canned strategies. He was kinda dumb but nonetheless beat me handily. I spent a month or two learning openings and such, and suddenly I could beat most of my friends (including those quite a bit older) pretty consistently too, just from the improved board positions.
At that point I realized that becoming a "real chess player" was very different from the fun I'd been having, and I completely lost interest. I've only played a handful of times since, mostly because it's really hard to have any fun playing with my knowledge -- not enough to play "real chess" against anyone who studied strategy, but too much to play against the people who know the basic rules but never learned that stuff.
I admire the grandmasters, because they have both that amazing set of memorized knowledge AND the incredible logic/intuition. But I have absolutely no desire to play the game anymore because while I'm somewhat interested in the latter, I can't be bothered with the former. It's permanently ruined for me.
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
as a kid I enjoyed chess and played with my friends right up to the point where you suddenly had to start memorizing openings and other canned sequences.
The world champion doesnt do this... prior champions certainly have but the current one isnt looking hard for an advantage in the opening...
Re: (Score:2)
This is how I felt learning a rubix cube.
It was really cool learning how to solve it, but learning all of the more efficient way to do it just took the fun out of it for me.
Re: (Score:2)
"fun"?
easy for you to say
then you lose to your little sister
Re: (Score:2)
Re: (Score:2)
I once lost a game of chess to a guy who was partially stoned, and who didn't know the complete ruleset. Yes, I'm that sloppy.
That said, I once did beat the reigning extended family chess player with a very very risky move that required me to sacrifice my queen and have a couple moves after that. Very risky. That's my fave fame of pretty much anything ever because of that.
Re: (Score:2)
I once lost a game of chess to a guy who was partially stoned
Probably because he was stoned. The downsides to being high, as it relates to chess, can be managed.. while the upside remains.
(the downside is that you are more prone to overlook things, the upside is that you can focus quite well on specific things.. "wide" vs "deep")
Re: (Score:3)
Ignoring the assholes making fun of you for being interested and explaining why, you can start learning right now:
igs: http://pandanet-igs.com/commun... [pandanet-igs.com]
kgs: https://www.gokgs.com/ [gokgs.com]
I know you can play the Gnu Go Server on kgs, if you want to avoid playing with a person for a while. You can also install it on your computer: https://www.gnu.org/software/g... [gnu.org]
Re:I know it is a bit late in life... (Score:5, Insightful)
I'm bad at Go (about 19k AGA, which is quite bad), but I really enjoy it. The Go community differs radically from the chess community. My experience (yours may vary) is that the Go community is more supportive, understanding, and genteel. There's a lot of tradition and protocol in Go and I think it means something.
You can be a clueless beginner (the writer raises his hand), go to a club (or online) and almost always find someone willing to give you a teaching game. If there is a club in your area, meeting some other players is a giant plus, but there are many great online sites.
I play for fun, which is the best reason, and I enjoy it immensely. Will I improve? Of course. Will I ever excel? No, but that's not the point for me.
Re: (Score:2)
Much thanks. I will start this evening I think.
Re:I know it is a bit late in life... (Score:5, Informative)
Having played both nothing transfers. The strategy level is different. Go is about unit formations and patterns. Chess is about unit tactics. There is a Japanese equivalent to Chess i.e. Shogi.
Re:I know it is a bit late in life... (Score:5, Funny)
Having played both nothing transfers. The strategy level is different. Go is about unit formations and patterns. Chess is about unit tactics.
I can play both at an intermediate level, and I agree with this. The mentality is very different. If you are starting as an adult, you are very unlikely to ever be a master, but you can easily learn the game well enough to have fun. Go has a handicapping system that allows for competitive games between people with a wide skill gap. Besides, Go tournaments, like chess tournaments, and model railroading conventions, are a great place to meet chicks.
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
It is kind of like the difference between playing a Total War game vs X-COM but only worse.
Re:I know it is a bit late in life... (Score:5, Funny)
Re: (Score:2)
I manage to completely forget all those moves I foresaw so brilliantly, and make the absolute worst possible move I could have made instead.
In chess thats called Kotov Syndrome
In Kotov's 1971 book Think Like a Grandmaster, he described a situation when a player thinks very hard for a long time in a complicated position but does not find a clear path, then running low on time quickly makes a poor move, often a blunder. [wikipedia.org]
Re: (Score:2)
"I'm so smart that I can't take my mind off porn and popcorn."
I'm glad I'm not as smart as you.
Well it's for sure you're not as funny.
My two (Score:3, Interesting)
I also took chess quite seriously for a few years, reaching approximately 1800. The pervasiveness of rote openings discouraged me a bit, but I always loved the game and still do. However, I abandoned it for Go, where I hold a shameful but enjoyable rating of 6-7kyu. I have never found any aspect of Go, other than scarcity of oponents , worth complaining about. It is, perhaps, the world's only perfect game. Just remember to lose your first 50 games as quickly as possible. Afterwards, expect a lifelong compan
Re: (Score:3, Insightful)
Re: (Score:2)
Chess is a battle. Go is a war.
I'm all out of mod points, but this is an excellent summary of the difference.
Re:I know it is a bit late in life... (Score:5, Interesting)
Chess mentality doesn't transfer very well to go in my observation. Since go has vastly more plausibly good moves, chess players often find themselves not understanding how to choose where to go next. Most people I've known who like go a lot hate chess. I've known one person who likes both, and he was never able to get very good at go. Generally speaking, chess can be learned by someone who can think logically and learn the standard opening sequences. Go is more like painting. Its not necessarily a superior skill, but not all intellectually-smart people are smart in the right way.
But by all means learn, its easy to get a game on the internet. If you like it its worth it. And if you do it for ego and discover you suck, sometimes that's worth something too.
A Game Worth Playing (Score:2)
A game for adults http://www.sharedwisdom.com/ar... [sharedwisdom.com]
http://www.amazon.com/The-Mast... [amazon.com]
Not much to transfer the other way (Score:2)
I can tell from my experience, having played Go decently, but being a calamity at Chess.
To give an example, I wrote a chess-playing program (a simple alpha-beta minimax with a value function pilfered from SunFish ...). When I set it to just 4 plies (that is two moves ahead) it absolutely destroys me. Basically, to be a decent chess player, you must have the ability to picture the board in your head and be
https://github.com/thomasahle/... [github.com]
No iterative deepening, no transposition table, no null-move search, no
Re: (Score:2)
There's a version of blindfold Go where both players use the same colour of stones. They can see all the stones placed on the board so it's theoretically still a full-information game. They remember who played which stone or they can work it out from the pattern.
Re: (Score:3)
Agreed, there is "one color go" as you describe it.
The point I was trying to make is that while this version of go is not very popular, any chess player starting at about National Master level (and certainly for those at IM level) is capable of playing blindfolded.
This ability is simply a by-product of their training, not something they specifically aim for.
For Go players, the ability to play with the same color stones is not something that follows naturally from their training.
Go and Chess expand different
Re: (Score:2)
I know it's a bit late in life, but I was thinking about learning how to make mead. I know it's a bit late in life, but I was thinking about training to run a marathon. I know it's a bit late in life, but I met this woman and we've decided to get married...
You don't have to be the world's best at something, just to do it at all. There's a certain generation of geeks I guess that grew up playing particular games (modern warfare and the like) where those who weren't in the top tier would have a hard time h
Re: (Score:3, Funny)
doesn't sound like the game should be called go (Score:3)
we need from 10 to 13 servers, each with at least 8 cores, 512GB RAM, and ample disk space (10-15TB), running for about 5-9 months
sounds pretty slow to me
Re: (Score:2)
4PB of disk IO
How many Libraries of Kokuritsu Kokkai Toshokan [wikipedia.org] is that?
Re: (Score:2)
it might sound like an exercise in how much CPU can we tie up for no discernible reason, but it does have applications in encryption and chaotic systems analysis, a lot of which is directly related to the actual calculation being discussed.
Number of legal positions (Score:5, Informative)
6697231142888292128927 401888417065435099377 8064017873281031833769694562442854721810521 43260127743713971848488909701 11836283470468812827907149926502 347633
Why they chose to present it like that, instead of scientific notation, I'll never know but there it is. It's so long Slash-filter won't let me post it without adding spaces.
Re:Number of legal positions (Score:5, Funny)
I'm not quite clear how 6.697231142888292128 927401888417065435 099377806401787328 103183376969456244 285472181052143260 127743713971848488 909701118362834704 688128279071499265 02347633e151 is much of an improvement, to be honest.
Re: (Score:3)
Re:Number of legal positions (Score:5, Funny)
How can you know I didn't just guess?
Re: (Score:2)
Re: (Score:2)
I might just be lazy, and 151 is a reasonable-size prime number :)
Re: (Score:2)
Because the real answer is 6.697231e+152
https://www.google.co.nz/searc... [google.co.nz]
Re: (Score:2)
google being stupid again, you are wrong:
"It is customary in scientific measurements to record all the definitely known digits from the measurements, and to estimate at least one additional digit if there is any information at all available to enable the observer to make an estimate. [wikipedia.org]"
Re: (Score:2)
google being stupid again, you are wrong: ...
I'm confused. Are you saying: (punctuation added) ... ...
(a) Google, being stupid again,
(b) Google "being stupid" again,
Because those two interpretations seem very different.
Re: (Score:2)
If, you, understand, b, you, should, do, what, b, sais.
Re: (Score:2)
No, that answer has thrown away more than 10 ^ 142 combinations.
If you would gift me a billionth of a penny for each combination you threw away, I likely would still be the richest man of the world.
Re: (Score:2)
Better than the post I was replying to, that was off by a factor of 10.
Re: (Score:2)
How can you know I didn't just guess?
Maybe you did - my text editor says 152!
Re: (Score:2)
Because now I know it's 151 digits. Had no idea before.
... but it's 153 digits, not 151. Or at least that's what grep -P -o '\d' | wc says when I paste the number into it...
Re: (Score:2)
Internet GO (Score:2)
Now let's give each position an IPv6 address. Ooops!
Re:Number of legal positions (Score:5, Informative)
Why they chose to present it like that, instead of scientific notation, I'll never know but there it is.
This is a discrete mathematics problem. There are exactly that many positions. Not one more, not one less, with no measurement error nor variance. And the question they set out to answer was what precisely was this exact number. To not report the result in full would be absurd.
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
JanneM also did it wrong. [slashdot.org]
Re: (Score:3)
Binary?
Re: (Score:2)
Re: (Score:2)
Are you sure the correct answer is "it's generally not possible to represent numbers accurately using that format"? Where "accurately" means "the correct answer".
Yes.
Re: (Score:2)
I have exactly 2 feet.
of 2.00000000 x 10^0
kind of both mean the same thing
"Kind of" is correct.
They are not exactly the same thing.
Re: (Score:2)
pedant: anything raised to the zeroth power is equal to one.
So, 2x10^0=2x1=1.
So you're saying that 2 feet is equal to 1 foot.
OK.
(ergo, 2 feet != 2.00000000 x 10^0) :)
Re: (Score:2)
So, 2x10^0=2x1=1.
You might want to check your math.
I predict a face palm in your near future. :)
Re: (Score:2)
oh snap.
Re: (Score:2)
1 Googol is in fact less than a 10^51-th of this
Re: (Score:2)
Re: (Score:3)
The reason is obvious. Scientific notation is mainly used for approximate results, and integers are exact.
Re:Number of legal positions (Score:4, Funny)
Damn! They guessed my pin number. I hate it when that happens.
They should give both (Score:2)
It's interesting to see the exact number, but we obviously can't grok it. We want to know how many digits that number has.
Re: (Score:2)
Pffft, Cobolers
Just found that out today (Score:4, Funny)
My Computer:
"For no reason at all, would you like to play a game of Go today?" *casual indifference*
Me:
"Sure, 20x20 board?" *smiles*
Computer:
"Never mind" *sulks*
Re: (Score:2)
Computer: Would you like to play "Total Thermo Nuclear War"?
Meh: sure
And the point is ....? (Score:2)
Besides curiousity, why was computing power (read: energy) spent on this?
next milestone (Score:2)
compute the number of nodes and CPU-hours required, hence the system cost, of a 20x20 system.
That's before you even start calculating the actual positions.
Re: (Score:3)
Sure we can brute-force it, we'll just spit out a whole bunch of random machine code, and check each set to see if it solves the boolean satisfiability problem, and then see if it solves it in polynomial time. This approach just depends on P == NP being true in order to work. :)
Re: (Score:2)
There's no way to bruteforce P = NP isn'it ?
We just need a genius to work on it for 10 years.
I've been working on it for 10 minutes, and it's patently obvious that P=NP when N=1, since 1 x anything is anything.
Not quite sure what all the fuss is about.
Re: (Score:3, Interesting)
hey man, don't be a prick
go is super interesting from a formalistic perspective given that it has an extremely large amount of emergent behavior.
that is, the rules are so simple, that it should really be as easy to analyze as connect 4
but its likely the most complicated full-information game created by man
so, no, the exactly number isn't particularly interestingbut give the guy a break. 'mathematical go' by berlekamp is pretty
boring and trite and focusses on some really uninteresting endgame positions. but
Re:In case anyone was wondering... (Score:5, Informative)
Although a lot of knowledge is assumed on here, Go is one of the most well-known and popular board games worldwide. Probably more popular than chess, even.
Othello/Reversi, however is, not only a poor comparison but relatively unheard of. (I'm a massive fan of Othello, it has to be said).
Go is NOT like Othello at all. You have to put coloured stones on a grid-like board, 19x19 for standard Go, in such a way to "enclose" a block of your opponent's pieces. The complexity of Go is RIDICULOUSLY high, so much so that just to hold work out how many board positions there are takes months of computing time. Imagine how good the AI players are in such a circumstance!
When I was at university, 15 years ago, one of my professors (Professor Wilfred Hodges) was working on Go. It was his introductory lecture to describe the complexity of the game. It's astounding. At the time, the most powerful computer player in the world couldn't come close to beating even a seasoned amateur. They're a little closer now but nowhere near the way that Chess can be dominated by a single machine.
Go is one demonstration of how a human's pattern-matching and simultaneous processing can far outweigh anything that a computer can do at the moment. No doubt, with breakthroughs of thought and ever-increasing speed of computers, we'll eventually get there, but a human brain has been able to be there for, well, probably thousands of years already. And on a "puzzle" that's entirely logic-based and effectively ternary (white, black or no stone at all on each space).