Some time ago I posted some observations about the game of Go, in which I compared the complexity of Go to that of chess. I said:

Go is combinatorially many orders of magnitude larger — the number of possible chess positions (the so-called “Shannon number”, since it was first estimated by Claude Shannon in a1950 paper on computer chess) is “only” about 10 to the 43rd power, which pales in comparison to Go, which has about 8 times 10 to the 100th power possible board positions.

Turns out that estimate of 8 x 10100 was way low. Some folks whose level of determination is truly impressive to behold have managed to calculate, after “9 months of computation and 4 petabyte of disk IO on a Dell PowerEdge R280 server” the exact  number of legal Go board positions on an 18 x 18 board (one row/column shy of the 19 x 19 standard board). The answer, explained here, (which I have to split into three lines, but it’s just one number) is:


or approximately 6.7 x 10153. Based on that, the estimate of the number of positions on the 19 x 19 board is about 2.1 x 10170. Plans are apparently underway to nail down the exact number for the 19 x 19 board once the required computing resources (10 to 13 servers for 5 to 9 months) can be found.

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