>Take the combinatorial questions, for instance: At the beginning of a >game of Go, there are 19^2(=319) possible legal moves
Except that 19^2 is 361, and that the starting board has 8-way symmetry, so the number of first moves is closer to 90.
>Most moves in Chess create the possibility of new moves on the >following turn which were not legal on the present turn. >[snip] >Most moves in Go reduce the number of legal moves (for both players).
Well, once you take the symmetry into account, chess and go are very similar. The first move of go erases one or more axes or symmetry, causing the number of second moves to jump from 90 to 180 or 360.
It's still true that the branching of Go is more front-loaded than in chess, but that just makes the tree bigger.
>Indeed, in Go there are many situations when only one possibility need >be considered as the consequences of failure to respond to a >particular attack can be so catastrophic.
Except that to really see the "consequences of failure," you have to look ahead. Most "move here or the giant group dies" moves aren't ever even ALLOWED to happen by good players, except during ko fights. And ko fights are strategically complex by nature; with each player forced to choose between two different battles.
>While Bridge and Go afficiados may love to think of their games as >more difficult than Chess, neither has had a fraction of the >theoretical effort lavished on it that Chess had.
I just don't buy this.
How much of the "theoretical effort" we put into chess was really Chess-specific? I'm sure that in the process of making Deep Blue, someone came up with some good chess heuristics, but that is a mere footnote in the greater scheme of everything we've learned about game AI in the last few decades. And even without good heuristics, Moore's law would have caught up to chess sooner or later.
From a purely theoretical "what if you had unbounded computing power" perspective, Go and Chess are equally difficult. They are both just search trees, giant but finite, with completely public information. If you can search to infinite depth, you don't need heuristics at all.
From a practical "which one would Moore's law catch up to first?" perspective, Chess is clearly the simpler game.
Bridge, on the other hand, has hidden information, which makes it a different (though not necessarily harder) problem.
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>Take the combinatorial questions, for instance: At the beginning of a
>game of Go, there are 19^2(=319) possible legal moves
Except that 19^2 is 361, and that the starting board has 8-way
symmetry, so the number of first moves is closer to 90.
>Most moves in Chess create the possibility of new moves on the
>following turn which were not legal on the present turn.
>[snip]
>Most moves in Go reduce the number of legal moves (for both players).
Well, once you take the symmetry into account, chess and go are very
similar. The first move of go erases one or more axes or symmetry,
causing the number of second moves to jump from 90 to 180 or 360.
It's still true that the branching of Go is more front-loaded than in
chess, but that just makes the tree bigger.
>Indeed, in Go there are many situations when only one possibility need
>be considered as the consequences of failure to respond to a
>particular attack can be so catastrophic.
Except that to really see the "consequences of failure," you have to
look ahead. Most "move here or the giant group dies" moves aren't
ever even ALLOWED to happen by good players, except during ko fights.
And ko fights are strategically complex by nature; with each player
forced to choose between two different battles.
>While Bridge and Go afficiados may love to think of their games as
>more difficult than Chess, neither has had a fraction of the
>theoretical effort lavished on it that Chess had.
I just don't buy this.
How much of the "theoretical effort" we put into chess was really
Chess-specific? I'm sure that in the process of making Deep Blue,
someone came up with some good chess heuristics, but that is a mere
footnote in the greater scheme of everything we've learned about game
AI in the last few decades. And even without good heuristics, Moore's
law would have caught up to chess sooner or later.
From a purely theoretical "what if you had unbounded computing power"
perspective, Go and Chess are equally difficult. They are both just
search trees, giant but finite, with completely public information.
If you can search to infinite depth, you don't need heuristics at all.
From a practical "which one would Moore's law catch up to first?"
perspective, Chess is clearly the simpler game.
Bridge, on the other hand, has hidden information, which makes
it a different (though not necessarily harder) problem.