Chess and Math

The reality is it can not be effective only with numerical works. To solve problem of chess, one must have genuine idea which can relate chess effectively.

Numerical works are beauty of chess and chess of math but it is not the math of chess. Only Math of chess can help us. So we need to develop  new kind of scientific method to solve problems of chess.

Soon i will propose a system which will be accepted internationally.

I'm beginning to mentally swag too, but I'm still following the concept. Is there anyway to calculate the best move, without leaving the mathematical approach?

The excpected answer is of course that chess engines are using that kind of mathematics already. But as a human I need shorter algorithms and theorems.

What math and chess share in common can be made more explicit:

Let  Φ be a first order logic formula with 2n free variables X1,Y1,X2,Y2...Xn,Yn. Let Ψ be the formula ∀X1 ∃Y1 ∀X1 ∃Y1...∀Xn ∃Yn Φ(X1,Y1,...,Xn,Yn).

 Consider the following game: We fix some set S (we assume basic set theory if needed), Alice starts and picks some object x_1 in S. then Bob picks y_1 in S. Then Alice picks x_2, Bob picks y_2 and so on. The game stops after n steps. We evaluate F=Φ(x_1,y_1,...,x_n,y_n) and say Alice wins if F is wrong, and Bob wins if F is true. What is interesting here is that:

Ψ is true in S if and only if Bob is able to win every game.

more interestingly, an explicit (reliable) winning stategy for Bob is the same thing as a rigorous logical proof of Ψ.

(I admit the above is cumbersome and frankly pedantic but intuitively it is what every player do when he tries to ensure he's playing the right move)

If you are unable to innovate, create it. That is my inspiration.

To make my words understandable by all, i avoid complexity. Do not make  irrelevant post please. I choose simplicity rather than complexity. Add any simple relevant idea which will help me.

http://www.amazon.com/Mathematics-Chess-Dover-Recreational-Math/dp/0486294323/ref=sr_1_1?s=books&ie=UTF8&qid=1438457617&sr=1-1&keywords=chess+mathematics

http://www.amazon.com/Corridors-Geometry-Physics-Mathematics-Chess/dp/1465361731/ref=sr_1_5?s=books&ie=UTF8&qid=1438457418&sr=1-5&keywords=chess+mathematics

Probability Equation Concept

Let it be,

Probability for conquerence by white = Pwc
Probability for conquerence by Black  = Pbc

Probability for losing by white = Pwl
Probability for losing by Black = Pbl

If so,

then,
Pwc = Pbl ......1
and
Pbc = Pwl.......2

Now, Equation (1)+ Equation(2) :

Pwc + Pbc = Pbl + Pwl

Theorems:

• Pwc and Pbl are positively related, if Pwc increases, Pbl will also increase and vice versa
• Pbc and Pwl are positively related,
  if Pbc increases, Pwl will also increase and vice versa
• Pwc and Pbc are negatively related,
  if Pwc rises, Pbc will fall and vice versa
• Pwl and Pbl are negatively related,
  if Pwl rises, Pbl will fall and vice versa

Suppose, A game is being played----

 at beginning, balance will be    0+0=0+0

   
                           Pwc + Pbc = Pbl + Pwl

1.at the beginning:   0     +   0    =   0   +   0

2.at move 10
white gain 10%
winning chance        10    +   0   =  10   +  0  [1st theory]

3.at move 16
white lose
5% chance              0        + 5    =  0    + 5

.....                       ............................

Finally                  15            =     15  

http://www.amazon.com/Math-Theory-Chess-S-Version-Parts/dp/4871877086/ref=sr_1_12?s=books&ie=UTF8&qid=1438458559&sr=1-12&keywords=chess+math

http://www.amazon.com/Mathematical-Theory-Chess-Collin-Carbno-ebook/dp/B00HAVJN8W/ref=sr_1_13?s=books&ie=UTF8&qid=1438459223&sr=1-13&keywords=chess+game+theory

Turbo fish, have you read these books ?

No, but I would definitely like to when I have time.  I'm already working on about 10 books on mathematics, chess, and buddhism that I need to finish first before I add anything else to the queue.  If anyone is curious about the contents and/or reviews, just follow the amazon.com links (hey, they even let you peek inside the books for free!)

Turbofish,
i am pleased to see that you are working on fantastic affairs.

Thanks for your encouragement.  I forgot to mention that I'm also reading "Quantum Mechanics: the Theoretical Minimum" by Leonard Susskind (the most difficult subject I've ever studied).  I'm still trying to understand why I like difficult things?

Add more things like programming and electrical engineering. you will be famous.

Funny you should mention programming.  I recently started learning the programming language Python.  But so that I don't brag to much, I must admit that I'm a beginner, and have written only simple programs for my own amusement.  There are plently of very advanced programmers among the members here whose accomplishments I can only dream of.

And electrical engineering?, forgettabout it!  I tried but got stuck on Maxwell's equations.  Got my degree in organic chemistry instead, which requires shape-oriented thinking (in away that reminds me of chess) rather than advanced quantitative math.

I'm learning Python too!  And pre-calculus.  I'm not that good, I'm only going into 7th grade, I should be learning Statistics and Game Theory, not simple pre-calculus.  I'm also horrible at python.(And kinda-bad at geometry.)

You should be excited about your potential, you're young!  Your brain is fresh, and if you avoid falling into bad habits, there is so much that you can accomplish.  Don't let the dramas of the teenage years get you down.  If you work hard in school, everything else will naturally work out fine.

I'm 55, my time is running out.  And I wasted too much time worrying about nonsense as a youth.  I wish I had studied programming at your age -- I think I could have accomplished so much more than I will be able to now.

Python is a great choice, such a clean and beautiful language.  Good luck with all of your projects.

      Google, "Dana MaKensie Blog". He's a mathematician and an NM.