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John Tromp and the Big Numbers of Go

Some years ago, Dutch computer scientist John Tromp (right) and his colleagues reported that the longest possible game of go would last longer than the universe is likely to. Now, the culmination of their work on Go Combinatorics—the science of counting—is reported on in Peter Shotwell's latest essay, "John Tromp and the Big Numbers of Go: The Possible Positions, Games and the Longest." One finds that the number of possible games "is more than a googolplex, which is a number that cannot physically be written down in the available space of the universe." Also, with highly advanced computer power since that last report, Tromp and his team finally found the exact 171-digit number for 19 x 19 boards. "A 13x13 board has as many possible positions as the approximately 10⁸⁰ atoms in the universe and the ‘L19’ number is more than 10⁹⁰ times greater than this.” In other words, as one science writer quipped, “Saying that there are more go positions or games than atoms in the universe is like saying the national debt is more than a penny.”