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as far as I know the more complex a position is:
1- the more is sharp
2- more possible solutions are available
3- the deeper the combinations have to be calculated
In theory if such measure exists it could be possible to identify the most complex chess games ever played
In mathematics a solution to a problem has to be less complex than the problem itself, otherwise the problem has no solution. This is not pie-in-sky theory there are mathematical problems where the solution is more complex than the problem therefore they are theoretically unsolvable.
Analysing the complexity of some chess positions may sometimes lend itself to the theory of unsolvable problems. As GM Natalia said in a different blog, the complexity of a position may not lie in the depth of combinations, but the evaluation of the position after the transactions. Evaluation being HOW does this position benefit me or my opponent. The transactions involved may be simple but the position arrived at may be difficult to evaluate, hence many GM draws where both parties decide that a seemingly simple looking position is frought with too much uncertainty and no one wants to risk the journey
no there is no way to be certain.
but the engines can calculate evaluation scores from a position so you could find a measure of complexity as a function of these scores for example isn't it?
I am guessing engines use algorithms that are designed by Humans... so the engine is just as good as the programmers algorithms and even the strongest engines have serious flaws to that end.
However Deep Blue once went for a pawn munch with Kasparov hovering ominously over its King. The machine, an emotionless piece of software evaluated correctly that Kasparovs attack was not fatal and that the extra pawn was worth it. NOW i don't think any GM in his right mind would go for a pawn munch with the great champion hovering over their King, no one would risk it, but the machine did its calculations and made its decisions to go for material. Even the commentators were aghast. So maybe there could be some positions that are better analysed by machines.
Anyway after the loss Kasparov chose deep strategic play, well beyond the machine's calculating ability and never gave the machine any chance to oucalculate him, so some positions the human mind can assess complexity better.
The engine can't really tell you how complex a position is. Take a look at some middlegames in the Sicilian Najdorf Poison Pawn variation for examples of the most complex positions you can get in chess. The lines after black accepts the pawn are so complex that not even a supercomputer could find all the correct moves in one look.
you could choose an horizon limit of moves beyond it you don't calculate . for example the starting position is complex but it's not sharp because you can choose among many moves without compromising your game.
In mathematics a solution to a problem has to be less complex than the problem itself, otherwise the problem has no solution.
For example : http://en.wikipedia.org/wiki/Fermat's_Last_Theorem
The current version of the proof is a couple of hundreds of pages, densely written, which only specialists of the domain can understand.
Does it mean the problem has no solution ?
good so with this program it should be possible to identify the most complex games which should be the "best" in terms of raw computation if not the most spectacular. I wonder how much correlation there is between this score and the difficulty score of tactics puzzles
Fermat's theorem was not a mathematical problem, it was a mathematical conjecture (a unproven statement).
example: "there are no blond girls with brown eyes." Well to prove that to be true I may have to travel around the world and look at sample all blond the girls. In math of course they had to use complex branches of geometry, ellptical functions etc.etc.
Example: Instead of looking for blond girls with blue eyes, let as look for the genes that make brown eyes and see if that gene can coexist with the gene for blond hair. If they can, then there must be a blond girl with bbrown eyes somewhere in the world.
So it was a proof of a statement not a solution to a specific problem. Capisce?
A complex position.
yes, and it is called the level of difficulty you have evaluating a position.
One can over-complicate anything. In fact, there are some who would go so far as to suggest that trying to find a formulaic approach to quantify positional complexity in chess is a kind of over-complication in and of itself.
Moves make position less COMPLEX , especially pawns' move.
Because when you move, you choose one posibility from 10+ possibility and that make something no need to be calculated and some position never happen.
And what is more , the initial position is deepest than any other position.And the initial is very sharp because the first move you make affacts the whole game quite much.For example, we all know something like 1.g4 1.b4 leads a sharp game, so if a position has moves which lead to sharp games , that position is sharper and more complex.
But why you feel not so sharp? Because you just remenber or are told which first move you need to make or response.
When you play Chess960 and face a init position you never saw, you will find it sharp/complex.
So the initial position is the most complex one or in the set of the most complex ones.
Yes. I'm not sure how to implement this in games, but on playchess.com if you go to add kibitzer engine while watching a game, it shows you two little dials that come up. Hotness (complexity) and Mate-O-Meter. I"ll let you know when I find out how to use this in the regular program.
Ok, I found it, under view>measurements it has these two odometers that show the level of hotness in the position and the possibility for checkmate. I'm not sure what the latest program you have to download to get this but I'm guessing its been around a while.
I would guess a rough estimation of a positions "complexity" might be related to the size of the decision tree for all possible moves forward - with the trees ending only in mate or stalemate. Blueemu's post of the starting position as "complex" is a good example.
For humans, this might also invove the number of "positional changes": exchanges or "significant" pawn or piece moves.
Not exactly true. For example, an end-game position with a lot of alternate forward moves would not be "complex" if humans looking at it could tell didn't matter much what alternate paths were taken as only one or two leads to a win.
Just remember, when using these tools (if there is one) it cannot be use during live or online games.
Umm... there is a tool. and here it is. http://www.flickr.com/photos/95651238@N03/8728536856/in/photostream
As for doing it your head... I guess this meter can help you identify complex positions by giving you more of a feel for when the meter may go up or down.
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