I’ve been working on my slides for my thesis defense talk, and it reminded me of this particular observation.
The game of Go presents incredible freedom of choice to its players. At any juncture, a player my place his stone on any unoccupied vertex of a 19 x 19 grid. That means there are 361 possible first moves, and for each one there are 360 possible replies, and 359 possible replies to each of these, etc, until the game finally ends, typically about 300 moves later.
So how many unique games of Go are there? The simple way to describe this number is to write 361!
The exclamation point, a rather fitting piece of math notation, is called a factorial, and what it means is take every number between 1 and 361 and multiply them together. Try it on your calculator: it’ll probably explode. The result is roughly 10^700, which is another way to express the same number, but really doesn’t give much more intuition as to its actual size than 361! did. We are way beyond the realm of what humans are capable of wrapping our little heads around.
Consider this: if you decide to take every possible game of Go and play them out side by side on separate boards, you couldn’t do it. You run out of matter fairly early on in the process. There are, after all, only 10^80 atoms in the universe, and if you used them all to build Go boards, you’d still come up woefully short.