Author: KarinsDad
Date: 12:23:33 01/15/99
Go up one level in this thread
On January 15, 1999 at 13:42:15, Dann Corbit wrote:
>On January 15, 1999 at 00:34:40, KarinsDad wrote:
>
>>On January 14, 1999 at 20:20:51, Dann Corbit wrote:
>>>
>>>I have a notion about solving chess equations. Chess looks very much like a
>>>fractal equation to me (in n-space). If we could find a fractal equation for a
>>>given position, we might be able to solve forward. Perhaps we could even
>>>differentiate the function and glide down the maximal slope.
>>
>>Wow Dann, you are way beyond me here. I take it you are not being serious. If
>>you are, I would be interested in you posting more on this. Knowing what I do
>>about fractals, I cannot even begin to imagine a solution here (except maybe in
>>extremely limited endgames).
>>
>>Now don't be pulling an old man's leg here. It isn't polite to make fun of your
>>elders.
>It was largely tongue in cheek in a sense. I clearly don't think it is doable
>right now. But when you look at chess, everything about it says fractal.
>Self-same similarity (but not exact -- look at how king & queen are reversed),
>reflections, transpositions, taking off in new directions with similar themes
>being repeated. We can consider an epd string as a big binary number. The
>rules of the game allow certain trajectories (I'm visualizing the Lorentz
>Transformation butterfly right now -- and thinking of the butterfly effect at
>the same time {I wish I could do that in a haiku}).
>If there is to be a *revolution* in chess algorithms, it will be the encoding of
>chess as a fractal.
>The slope thing was just a joke. I doubt if the equation would even be
>differentiable since chess hardly seems like a smooth, continuous function.
>In another sense it was a teaser. I was kind of hoping someone might have a
>brainchild from it. Maybe you?
>;-)
I doubt it. I'm just not that smart. The only doable thing I can think us is to
improve upon the tablebases by having the solutions encoded within some form of
fractals, and hence having them drastically compressed. If each "idea" within an
endgame solution could be expressed via an equation (fractal or otherwise), then
the actual solution to the endgame would not be in the tablebase, rather, the
mechanism to get to each link in a series of ideas would be there. The engine
itself could look 6 or 8 ply to accomplish the next idea. However, this would
probably take a lot of work.
An example: KR vs K
This example is extremely simple to people who have been playing chess for a
while, but if you can remember back to your beginning days (I cannot), there was
a point early on when this was difficult.
There are several simple ideas when you break this down:
1) Attempt to get your king 2 squares away from your opponent's king (do not
grab opposition) with the rook covering the squares in between.
2) Whenever possible, use your rook to minimize the number of squares the
opposing king can "eventually" reach (as opposed to currently can reach) either
with a well timed check, or whenever the king retreats.
3) If the opponent's king attacks your rook, move the rook a substantial
distance away on the same rank or file that is keeping the king trapped within
the current minimum number of squares.
4) Once the opponent's king is backed up to the edge of the board, continue to
use steps #1 and #3 until the opponent's king "grabs opposition" from you in
which case you move the rook to mate in 1.
This is probably more difficult to clearly explain (I really butchered it) than
it is to show across the board, however, using these ideas would enable the
chess engine to ignore moves which did not follow the "plan". It isn't required
to have the actual solution in the tablebase. Just the ideas and whether it is a
win, a draw, or a loss.
A more advanced idea is to have complex equations to determine the behavior of
each piece and how they relate to others. You would then have close to a perfect
evaluator and would not require a search engine. But I would have no idea on how
to do such a thing for the KR vs. K problem, let alone implement it for all of
chess. However, if you could implement this type of solution for simple endgame
problems, you may eventually be able to use it for all of chess since you would
be building an equational relationship type of database between pieces and not a
solution to a given set of pieces database (like the current tablebases).
KarinsDad
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