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Number of Legal 18x18 Go Positions Computed; 19x19 On the Horizon

Posted by timothy on from the now-we'll-call-it-gone dept.

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."

4 of 186 comments (clear)

  1. Re:I know it is a bit late in life... by cheesybagel · · Score: 4, 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.

  2. Number of legal positions by phantomfive · · Score: 4, Informative

    Here is the number of legal positions:
    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.

    --
    "First they came for the slanderers and i said nothing."
    1. Re:Number of legal positions by vux984 · · Score: 4, 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.

  3. Re:In case anyone was wondering... by ledow · · Score: 4, 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).