18 September 2012

Lesson of the Week

Today marked the initial meeting of my chess classes for home schooled students during the 2012-2013 school year. My after school clubs begin in October. Part of today's lesson will be used again in October.


Complexity and Truth

I seek to impress young chess players with the staggering complexity of chess, as well as to impress upon them a simple idea: the truth of the position. Every conceivable chess position* has a truth that may be discovered. White or Black may have a decisive advantage, or a slight advantage. The position may be equal.

In the starting position, White is generally regarded to have a very slight advantage because White moves first. From that position, each player has twenty legal moves. After each player has moved, there are 400 possible positions. In some of these, the advantage has shifted to Black, or the position is closer to equal. White often retains a slight advantage, particularly in the openings employed by masters.

After the second move, there are 72,078 possible positions. In four of these positions, White is in checkmate. The truth of each of those four is determined easily. In the game as a whole, there are perhaps 10^43 possible positions (estimates vary because the precise number is very difficult to determine). Most of these positions never have been seen on a chess board, neither in play between humans nor in calculations by computer. Some positions have been known, and the truth about each has been known for hundreds of years. Some positions have inspired debate as strong players attempt to determine the truth.

Each playing session usually results in many previously unseen positions. Chess players have the opportunity to seek the truth in each of these new positions.

Chess offers astounding possibilities for problem solving. Chess players are on a quest, searching for the truth of every position.


Illustrative Position

After this brief introduction, we looked at a position from a historic game. The position appeared in a game that is featured in Irving Chernev, The Most Instructive Games of Chess Ever Played: 62 Masterpieces of Chess Strategy (1965).

Position from Rubinstein -- Duras, Vienna 1908

White to move
r3kb1r/p1q1pppp/2n2n2/1p6/1PN3b1/P3PN2/1B3PPP/R2QKB1R w KQkq - 0 11

Black just played 10...b5??

Chernev presents the next several moves as "a spectacular combination" that is "brilliant and clear-cut" (34). My approach differs. I emphasize the truth of the position. Prior to Black's move, the position was close to equal. After Black's 10...b5, White has a clear advantage. Using my computer prior to class, I examined the next six moves. All the moves by both players were the top choice of Hiarcs 12.

The game continued: 11.Nce5! Nxe5 12. Nxe5 Bxd1 13.Bxb5+ Nd7 14. Bxd7 Qxd7.

Here, we also examined 14...Kd8 15.Rxd1 e6 16.Nc6+ Qxc6 17.Bxc6++-.

15.Nxd7 Bh5 16.Ne5.

White has won a pawn and has a clear plan: force the exchange of pieces, and use the extra pawn to create a decisive advantage in the endgame. The endgame will be next week's lesson.


*A chess position differs from a diagram, which is the arrangement of the pieces on the board. In a position, we also know which side is on move, and whether castling or en passant is legal. For instance, the following diagram is two positions: 1) White to move, and 2) Black to move. If it is White's move, White has a decisive advantage. If it is Black's move, the game is even--Black draws with best play.


My data on the number of possible positions comes from the work of Fran├žois Labelle: http://wismuth.com/chess/statistics-positions.html.

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