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Re:Re: About brute force and knowledge...
Henrik Rydberg wrote:
>
> A agree with Antii's statement that perfect play probably is
> inconcievable even to the best human players. As he points out,
> it does rise some hope, too; Just as humans, a good program
> should learn to avoid really complex situations, which should
> be a quite substantial part of the state-space.
>
I agree too.
> At this point, it would be interesting to make some kind of estimate
> of how large that part really is. To answer that question, we first need
> a measure of complexity.
[Lyapounov exponents explanation snipped]
> For instance, if after playing lots of different sequences from
> a position one finds a large spread in outcome, it would be a hint that it
> might be hard to find the perfect sequence from that position, hence a
> large complexity.
That's an interresting approach. If chaos (Lyapounov exponent) is small then it
means that go is more a "local" game than a "global" one, that is, most stones
played have "natural" local follow-up. That's what intuition suggests, too.
>
> The relation of this measure to the Luapunov coefficients requires a
> clarification on what state-space we are talking about. Assume that we
> know the sequence of truly perfect play from a certain position, and
> know
> the outcome of that sequence. A handful of moves might be sufficient.
> Also
> assume that we can evaluate the new board position exactly. Now assume
> we
> make a small change to the initial position, for instance by placing the
> last stone at some other point. Again assuming perfect play, we might
> now
> after a couple of moves end up in a completely different position, and
> in a
> completely different evaluation. The magnitude of the change in those
> two
> entities, summed over all possible adjustments to the initial position,
> would be the Luyapunov coefficients of the position, and the rate of
> change
> of the evaluation function, correspondingly. Summing over all initial
> positions would be the Luyapunov coefficients of the game of Go itself.
> A comparison to Chess, for instance would be quite interesting in this
> respect. Antii's argument and my own actually indicate, in my opinion,
> that Go is *played* less chaoticly than Chess, although the game it self
> might not need to be.
>
> Henrik
>
> --
> Henrik Rydberg (http://fy.chalmers.se/~rydberg),
> Department of Applied Physics, Chalmers University of Technology.
I think the game itself is less chaotic than Chess. In chess, deplacing the
King, or even a simple pawn, changes completly the nature of the following game.
In Go, a single stone position has far more importance. But perhaps one move at
chess is "equivalent" (in term of the game structure change the move will
produce) to several (4 ? 5?) Go moves. The "granularity" of Go is smaller, and
therefore so is the Lyapounov Exponent. But if you take this in account, you
have to add a constant to Lyapunov exponent for Go to be able to compare
chaoticity for the two game, and then you might find in the end that both games
may be *played* at same (relative) chaoticity level after all...
Perhaps even, if we can "renormalize" their Lyap. exps. by building a relative
"granularity" scale of moves, we could find that ALL games are played by human
at same chaoticity ! That would be be a "constant of human Brain"...
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