Chess and Draughts Club

From all appearances this Club is coming into its own again. After passing through two or three years of small membership, and, for the most part, except on the part of a few, little interest, the Club, on account of the cessation of hostilities, has had returned to it several of its oldest and most enthusiastic members. Although no formal evenings have yet been held, mainly owing to the lateness of the general meeting and capping activities, yet players have largely availed themselves of the privilege of going to the common room and having a game at any time. It is hoped that very shortly some evenings will be held and competitions encouraged. All those who intend joining this Club and have not done so are asked to give in their names to the secretary as soon as possible, and they will be given a key to the cabinet.

A chess-board and chess-men are of such a nature as to afford many problems for mathematical analysis. But in an ordinary game the number of possible moves and combinations is so great that the analysis becomes hardly less than a mathematical tangle. Thus, there are 20 ways of making the first move, and 400 ways in which the two first moves of each player may be made. It has further been shown that the first four moves (two on each side) may be played in no fewer than 197,299 ways, and that72,000 different positions may arise after these four moves have been played, of which 16,556 arise when the players move pawns only. Some of our enthusiastic members (who are not sitting for the November examinations) might find it interesting to try and obtain these numbers.

The relative value of the pieces may also be determined mathematically. The relative value of a piece may be estimated by the chance that if it and the king are put at random on the board, the king will be in check, i.e., a simple check, in which the king may or may not be able to take the piece in return. On whatever square the piece is placed, there are 63 other squares on which the king may be placed. It is equally probable that it will be placed on any one of them, and hence the chance that it will be in check is 1-63 of the average number of squares commanded by the piece.

For example, a bishop, when placed on any of the ring of 28 boundary squares, commands 7 squares; when placed on any of the 20 squares of the next ring it commands 9; from any of the 12 squares of the next ring it commands 11; and when placed on any of the 4 middle squares it commands 13 squares. Hence, if a king and a bishop are placed on the board, the chance that the king will be in simple check is (28 × 7 + 20 × 9 + 12 × 11 + 4 × 13) / (64 × 63), that is 5/36.

Similarly, for the rook, knight and queen, it may be shown that the chances are 2/9. 1/12. and 13/66 respectively. This gives the relative values of the queen, rook, bishop and knight as 26, 16, 10, and 6.

In many of these possible positons, however, the king might take the piece in return, as it certainly would do in practice, and thus the relative values determined in this way are purely theoretical.

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If safe checks only are considered, i.e., checks in which the king has no opportunity of taking the piece in return, it may be shown by a method exactly analogous to that given above that the relative values of the queen, rook, bishop, and knight are 37, 24, 13, 12. These more nearly agree with the practical values 40, 22, 14, 12 (approx.) given by Staunton, and estimated empirically from a wide experience of the game.