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PhilGoetz comments on Rationality Lessons in the Game of Go - Less Wrong
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Comments (145)
Try redoing the calculation with geometric averaging: 300 moves, 150 of which are yours, suppose the final score is 80 to 70:
I don't think that's an improvement. As I said in another comment just now, I think that in go having a small advantage does not make you more likely to gain additional advantages.
Then why does handicapping work? Giving someone 3 stones on star points at the start of a game will have a much larger impact than giving them 3 stones on star points at the end of the game.
I finally saw your point-- moves are more valuable at the beginning of the game, mistakes come at a more or less constant rate, therefore the margin of victory shouldn't be divided up evenly into every move of the game. Yes.
I tried to put a blanket disclaimer in my post that started this thread ("There are some problems with averaging things like this which I probably don't need to point out to you all...") in the interest of brevity but perhaps that was a mistake.
There are problems with my calculation that yours does not solve. Namely, mistakes do not tend to be small and come at a constant rate. If I lose by 10 points it's entirely possible that I made a single 20 point mistake and my opponent made 10 single point mistakes. (well, for example only. In reality amateurs make a lot more mistakes than that)
That said, now that I understand why you suggested it, your calculation does represent the situation more accurately.
The escalate/accumulate/linear/exponential discussion threw me off, as did the fact that I was looking for an answer expressed in points (it's easier to visualize what that means), and the fact that I have seen this calculation done by stronger players than I am. Obviously an answer expressed in points can't be constant throughout the game, and I should have seen that.