More On Wei Ch'i.

Granted it's been a while since I've played, and I'm fairly certain that I'm not as good as I once was, but I still pick up a chess board every so often just to keep myself sharp. I'm still pretty good. I've played at the national level, and did quite well; I finished in 143rd place out of over 3000 competitors.

So when I tell you that Go makes chess seem like the strategic equivalent of tiddlywinks by comparison, I want you to understand my full meaning.

Let's take your average chess game of, say, 120 moves (60 per player). On any one move, the largest possible number of available configurations is 121, broken down as follows; not counting the squares the pieces are sitting on at this moment:

pawns: 2 possible squares each (a total of 16 new possible configurations, at the absolute most).
King: 8 possible squares (eight new possible configurations)
Queen: 27
Bishops: 13 each (for a total of 26)
Rooks: 14 each (for a total of 28)
Knights: 8 each (for a total of 16)

Add 'em together and you should come up with 121. And the vast majority of the time, you will have far fewer than 121 available. For the first move, for example, there are only twenty possible moves, period. Not twenty-one, not nineteen. Twenty, exactly.

But since this is all very rough, that means that in a 120-move chess game, the configuration of the board is approximately 121^120; which gives you something on the order of 8.6x10^249.

On the first move playing Go on a 19x19 board, black has 361 possible moves; white, 360, and so on. Now, this is all approximate, but since I was generous enough to use the absolute best-case scenario for Chess, I'll do the same for Go. Your average Go game on a 19x19 board lasts about 300 moves. So the number of possible board configurations that are available looks something like this:

N=361!/61!; which gives you something on the order of 2.82x10^684 possible board configurations.

That's a really big number:

2820000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000

Give or take a zero or two

How many of these are actual legal board configurations is anyone's guess. I've seen estimates between 5 and 20%. Which, when you're talking about numbers this big, doesn't make a whole hell of a lot of difference.

So I'm beginning to understand why nobody's ever written a computer program that plays a decent game of Go. The numbers are just too big.