The Mathematical Equivalence
of Counting Methods
Posted by: roscivs, in Uncategorized
Tomorrow some people at work are meeting together at lunch to play Go. There will likely only be a handful of people there, but I’m hoping that we can start a regular thing, and maybe even attract some new players to the game! It’s a very easy game to learn, and I think it has a special appeal to computer programmers because of its prevalence in the AI world. Plus it’s gaining popularity in the West anyway.
So, to help attract other players, I was planning on printing out some handouts to give to people who might happen by, drawn by the pleasant “click” of the stones, interested in finding out what exactly the black and white patterns on the board meant. So far I only was able to finish one handout, a list of the Rules of Go (with a few explanations of each one). I emailed the handout to the other members of our newly-forming Go club requesting feedback. There were many good comments, probably none that I’ll be able to incorporate into the handout before tomorrow, but many good comments nonetheless.
An interesting thread was started by a Japanese player who refused to believe that area scoring is the same as territory scoring. The issue is this: there are two common ways of scoring a completed game of Go. One is to count all the “territory” (empty points surrounded by your color of stones), and add “prisoners” (the stones you’ve captured of the other player’s). The other way is to simply count all your stones on the board and all the empty points surrounded by your stones, and ignore prisoners altogether.
The counterintuitive part is that these two methods end up being exactly mathematically equivalent (given some assumptions about who plays last and no extra passing). Crazy, eh? But this guy refused to believe it even after I tried (rather poorly, I’m afraid) to explain it several times. He believed the scoring change would result in a completely different game, where it was more to one’s benefit to build up bulky shapes in the center with little territory, rather than building territory in the corners and sides with few stones.
Suffice it to say this is not true. But perhaps he will come to the Go Lunch tomorrow, and I will be able to show him first-hand, with stones on the board, the mathematical equivalence of territory and area scoring.
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