Deep in the Mind of the Spirit Divine
The idea for what we call chess was conceived
It soon came to birth manifested on earth
The design for which had been decided on high
It would be based on the unending circle
At best "Chess is an expression of Pi"
One might conclude that I have no right to speak with such certainty on this matter, but I would attempt to justify myself by revealing the foundation on which chess is built upon.
I'll begin by stating my case upon a formula that came apparent to me as I was creating what I called "The L7 Chess Lesson." My love for the game of chess made me want to teach others how to play it. Looking for the best way to explain to others the most important ideas in chess caused me to look at chess from a mathematical point of view. It became clear to me that everything in chess had a numerical value. This included the pieces, the squares, and each tempi or each opportunity a player has to move a piece. I sought for a way to accurately determine these values.
First I decided to use what had become the accepted numerical value given to each pawn, that being one. Next, I determined that piece mobility was the most accurate measure for determining its value. I decided that the rule or formula must be that the number of squares that a piece can reach from the center of an empty board times the numerical value of a square equals the numerical value of the piece.
Using this formula a square would have the numerical value of .33 as a pawn can move to no more than one of three different squares on 80% of its possible moves in a chess game. Then, of course, was not always the case as the rules have been changed allowing a pawn to advance two spaces forward on its initial move. This unfortunate change led to the making of another rule "in passing" which was never meant to be and takes away from the purity of the game. I said all that to say that pawns should only have three squares that they could possibly reach in a move.
About a year after coming up with the formula it came to me that whoever created chess did so with pi in mind. They were squaring the circle and creating pieces and giving them movement based upon the same. I could see that each square must have the numerical value of .314 and when I began using that value the values of the pieces came into harmony.
· Queen reaches 27 squares. 27 x .314 = 8.478
· Rook 14 squares. 14 x .314 = 4.396
· Bishop 13 squares. 13 x .314 = 4.082
· Knight 8 squares. 8 x .314 = 2.512
· King 8 squares. 8 x .314 = 2.512
· Pawn 3 squares. 3 x .314 = 0.942
One Rook plus one bishop equals one queen
4.396 + 4.082 = 8.478
One bishop plus one knight plus two pawns equals one queen
4.082 + 2.512 + 1.884 = 8.478
One bishop plus one pawn equals two knights
4.082 + .942 = 5.024 . 2.512 + 2.512 = 5.024
One knight plus two pawns equal one rook
2.512 + .942 + .942 = 4.396
The formula demonstrates numerically what the chess community has known for a long time and that is that:
Two bishops plus one knight are greater than one queen
4.082 + 4.082 + 2.512 = 10.676. 8.478
Two knights plus one bishop are greater than one queen
2.512 + 2.512 + 4.082 = 9.106. 8.478
The formula also demonstrates that:
Two bishops plus one pawn are greater than one queen
4.082 + 4.082 + .942 = 9.106. 8.478
This information speaks only to material strength. A poorly placed piece will probably not be working at full strength.
Time or tempo is very often the deciding factor in a chess game. When two average strength players (1600) face one another, a point is usually reached where one of them can strike the others camp quicker than the other can adequately respond. Even more often than that it happens that an endgame is reached where one player enjoys a single tempi lead that proves to be decisive. Still, a tempo is a tempo is a tempo. What advantage does white have at the beginning of every chess game? White has the right to strike out at the enemy camp first. The right very often does not result in a material advantage nor a space advantage. So while it is difficult to prove what the generic value of a tempo is, I give it the same numerical value of one square (.314). It is essentially worth the value of the square that the piece being moved lands on. It makes no difference what piece is being moved nor how far that piece travels. One tempo is worth .314 and like many other things in chess, the importance of each tempo grows as the game progresses. Small advantages loom large late in games.
I have put more time into this than I wanted to and I'm sure I've taken up more of your time than you wanted to give me. I hope that you understand how much the formula means to me and what it should mean to the chess community. I am convinced that if the chess community makes a big fuss over the formula more people will become interested in chess and they and the existing community will be better for it.
Lemuel John Taylor