On the Advantage of a Plus in Pieces.
First Proposition: The Plus of a Rook suffices to win the game.
When one is Checkmated the pieces that are inactive onlookers of the disaster, however many they might be, are of no avail. Pieces that cannot aid in staying a danger are of no value. Let us, however, consider the question of a Plus in pieces under a certain condition that from the learned of the Middle Ages has received the curt name of "_ceteris paribus_." Advantages and disadvantages being equal, being evenly balanced - that is the meaning of this condition. The above proposition is certainly not valid in all situations. As a proposition in Euclid, the above thesis would be a rank failure, but __ceteris paribus__ it is as true as gold.
Now the method of Euclid would do no good in Chess. Reason in Chess - we shall see that the more clearly later on - is not of the mathematical order. Chess is no certainty. And when it becomes one, Chess will have ceased to be useful. To enable the Chess players to follow an argument, the idea of the learned of the Middle Ages embodied in the curt Latin __ceteris paribus__ is indispensable.
By means of the __ceteris paribus__ we are within our rights to suppose that all the other pieces, being of equal force and value, have fought a drawn battle, at the end of which they, like the two lions that devoured each other up to the two tails, have emigrated from the Chess-board into the box, thus leaving the stronger side with Rook in a safe position and the King, against the bare King.
If the stronger side has the Move, we can demonstrate that Rook and King against King can always force a Checkmate. This demonstration is mathematical. It is founded upon a certain process, by which the weaker side is eventually shorn of its mobility, its King being confined in a prison with ever narrowing walls, and finally forced into a Checkmate. The demonstration begins by showing that with the pieces available certain Mating positions exist and continues by making evident that the weaker side, in the course of the above process, may be driven into one of these Mating positions.
As long as the King is in the middle of the board, it cannot be Mated by King and Rook. For let us suppose that the two aggressive pieces have arrived at their position of strongest effect. Then the two Kings will stand opposite each other and the Rook will give Check on line or row, and thus the besieged King will be Checked and have five squares of its domain cut off by the enemy. This is easily seen.
Strongest Effect of King versus King.
Here the Kings stand as near to each other as possible since they must not expose themselves to capture, not even to capture by the opposing King.
They stand in King "Opposition," they prevent each other from moving on any one of the three squares White's Q3, Q4, Q5.