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January 24, 2016 04:00 pm

Finally Calculated: All the Legal Positions In a 19x19 Game of Go

Reader John Tromp points to an explanation posted at GitHub of a computational challenge Tromp coordinated that makes a nice companion to the recent discovery of a 22 million-digit Mersenne prime. A distributed effort using pooled computers from two centers at Princeton, and more contributed from the HP Helion cloud, after "many hiccups and a few catastrophes" calculated the number of legal positions in a 19x19 game of Go. Simple as Go board layout is, the permutations allowed by the rules are anything but simple to calculate: "For running an L19 job, a beefy server with 15TB of fast scratch diskspace, 8 to 16 cores, and 192GB of RAM, is recommended. Expect a few months of running time." More: Large numbers have a way of popping up in the game of Go. Few people believe that a tiny 2x2 Go board allows for more than a few hundred games. Yet 2x2 games number not in the hundreds, nor in the thousands, nor even in the millions. They number in the hundreds of billions! 386356909593 to be precise. Things only get crazier as you go up in boardsize. A lower bound of 10^{10^48} on the number of 19x19 games, as proved in our paper, was recently improved to a googolplex.(For anyone who wants to double check his work, Tromp has posted as open source the software used.)

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