I'm not questioning that he's able to checkmate me (which, with perfect play, he'll probably be), I'm questioning the fact that a human being can memorize 10^120 combinations of moves.
Of course not. But perfect player is never a human. Humans are retarded little stupid fuckers who re deluded into thinking they re the most important thing in entire universe.
Perfect player is a computer (or perhaps a hamster?)
kkkkk. i dig that.
Nice Mandelbrott fractal,I've made a lot of them myself. Imaging this is made by repeatedly calculating Z = (Z*Z)+C for a specific C .
Our world and everything in it can be understood using physics. Physics can be expressed if formulas using math. Math can be expressed using math. Everything is math and therefore effectively just numbers.
Isaac Newton said something like this when he wrote his Principea.
Math is pure and objective . It is our greatest gift.
But chess is art . You cannot use formulas to come up with a good (best) move. No math here I'm afraid. The good Lord must have created chess before he made the world.
Chess is a math problem. There are at least 2 ways of solving it. The 1st is using the tree as most chess engines do. The 2nd is using a discrete graph like endgame table bases do.
Your argument is invalid.
I would say that chess is quite far away from math when it comes down to the "goals" of chess versus math. 
In math you strive for an answer. The way to get there may vary alot but it doesn´t matter. In chess however, you may strive for different things. E.g. a draw or just to improve your play and hence play "unsafe". The process is usually the most important part. You don´t really see GMs play to a mate either.
If only computers were fast enough to allow for say a 250 ply deep search , the engines will be able to answer the horrible question : Is chess a draw ? The best engines available now can reach upto 40 ply , using a lower depth of min. 16 ply and on my 1GHz laptop this results in evaluating 2000kN/sec positions. Very impressive software.
Most engines work like this : You generate a list of legal moves and then start a depth D search . When this is done,you sort the list on best-score and , when time enough left , you repeat the process , but now for a depth D+1 search. And so on.
Now it has been estimated that on average there are M=30 legal moves in a position. When an engine does a depth D search it builds up a kind of tree.Every node (except for an end node = leaf ) in this tree is followed by M branches indicating the moves of the other player. The total number of possible positions is : P = M^D . So for a 3 ply deep search , you need to evaluate P = 30^3 = 27000 positions. This doesn't look like much , but try to stick in D=16 giving P = 30^16 positions.
The explosive growth of the tree can be dealt with partially by making use of some clever logic-based algorithms called alfa-beta pruning and it has been mathematically shown that (and how) it works. Basically the number of positions (evaluations) are reduced to P' = M^(D/2) or 30^3 for a D=6 ply depth search.
Evaluating a position is mostly done by counting the material and adding to that some weight-factors representing the contribution of static properties like : Pawn-structure , Centre-control , King-savety and Development to name a few. When the position is unstable , lots of trades and checks possible , a simple routine will find out if there is loss/win of material to be expected. If so , this is also added to the evaluation as a bonus-term. If the position is too unclear , then the routine advices you to search deeper (if allowed).
You have to tell an engine how deep it is supposed to search and to get an answer in a reasonable time , you have to limit this depth. This means the engine will examine all positions up to that depth and is then forced to evaluate the position. This leads to a so-called horizon effect . The engine has to evaluate , but it is possible that a criticial move exists beyond that depth.
The engine actually returns a Both-Optimum line (mainline) of some length , the first move being the one to play. Don't forget , the value of this move is the evaluation-value of the final position (of the mainline) reached after D ply .
Thus all you can say about the move the engine came up with is that it's the move leading to the optimal position within this D depth. Now this is not rigor mathematics , it's a nobel guess . Very usefull , still a guess.
@McNastyMac :
Yes , I was aware of the incompleteness theorem and yes I understand algebra. The symbols (letters) you speak of represent any number , but still a number. I take back the word pure .
Since you do Physics , you might agree that quantum-theory proposes that nature roughly consists of particles and fotons interacting with one and another. They can be represented by a set of quantum-numbers and/or a wave-function containing some parameters and arguments. Both particle and foton are thus represented by a set of numbers. And I said that numbers are the domain of mathematics. I also said that math deals with more than numbers alone,it also deals with proof , to be able to generalize it also deals with abstractions .
@rmurray ,
Well yes , the last part does sound silly , it also deals with proof was intended. And to be able to generalize was an attempt to start a new line saying it also deals with abstractions. I somehow ran out of crayon.
Thanks for pointing this out . I will correct it right cow .
I think proving a proposition is one of math's basic responsabilities and to make it usefull. When something is proven once , it is true and true forever after that. Sometimes the same counts for some lines in chess.
@fmurray having her period :
"it more often" is what you wrote, and that sounds a bit vague considering it's math? it either deals in proof, or it doesn't, or is there some type of math that deals in proof when it feels like it?
Like I said , I was actually in the midst of writing it . It wasn't finished/corrected yet .
"it more often" is gone. It no longer exists , I edited my comment . Satisfied now ?
Chess problems in math.
Define the objective:
1. Checkmate the King.
2. Win material.
3. Maximize space covered by all chessmen.
4. Promote pawns.
5. Defend attacks.
6. etc.
The problem: Maximize the objective value due to a chess function, depth, and time allocated.
Solution: Computer programs.
@smurray :
Why did Daisy have to leave while Buford was the one being a nuisance ?
Math isn't characterized by numebrs or proofs but by deductive reasoning based on axioms. That's where it gets a little messy with chess and math. Chess is surely an axiomatic system (the axioms are simple stuff like the rules of chess) and it's even finite state. That means that theoreticaally all chess questions can be answered using deductive reasonging from the rules. Unfortunately, that is beyond our ability for most interesting chess questions (although not the questions answered by tablebases) because chess is so big.
So we try to make do with heuristics like "two bishops is better than two knights" and "rooks belong on files that can be opened" and "material is good". But these don't come from very rigorous arguments based on axioms so most of the way we play chess is not particularly mathematical.
@smurray wrote :
Florida ain't all sunny beaches, and disney world. it's got a lot of back woods, and all manner of crazy stuff goes on out there.
I've been called a Troll on the Forum once and I had to look it up to see what it meant . Now I'm familiar with a lot of myth-class dudes like Hobbit,Dwarf,Elf doing crazy stuff but a Troll I never met . I thought they also lived in the woods. The things they do in there , is that what Buford did to Daisy ?
Hi Mr. Bean !!!.........
oops...keep going everyone....
Hi Indiana. well, well, well.
Math and chess ...... problem solving.
You can model a chess game as a vertex-edge graph in which each node is a particular game state and edges represent transitions (i.e. moving a piece) between game states.
Feeling that this is more philosophy than anything else, I must say (as an undergraduate in Mathematics and Physics) that Mathematics is axiomatically incomplete, that is, given any mutually coherent set of axioms, there will exist propositions that cannot be proven true nor false.
http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
I would expect more care and precision from a mathematics student. Your statements are just false as stated. Propositional calculus is complete and consistent, and there are many other examples, as I'm sure you know, because Gödel's results don't apply to "any mutually coherent set of axioms".
Chess is in someway related to math, not the other way around. If you are good at math, you don't necessary good at chess.
Math is much broader and much more developed than chess. Application of math has reached Arts and languages. Using math you can do some artistics figure like the one below: a fractal art. You can't do that with chess.
Chess is an art. Allright. I won't argue with this.