(1) The Horseback Cannon

When we come to checkmates that involve a Cannon and a Horse, the text books invariably mention only the ‘Cannon-behind-Horse’ (马后炮) checkmate, or simply the ‘Horseback Cannon’ checkmate. The left diagram below illustrates a position in which Black is checkmated by this well known tactic.

There are also other checkmating patterns involving a Cannon and a Horse. Why does the Horseback Cannon gets all the limelight? Perhaps it is because of its frequent use as a threat in real games. More over, in this format the Cannon does not need another piece as its carriage; nor is there the need for other pieces to act as intercepting forces.

Points to note: The Horse must be two spots away from the enemy King, either on a vertical line (file) as in this diagram, or on a horizontal line (rank). The Horse controls the two spots besides the King, so that the latter is unable to flee when the Cannon checks from behind the Horse.
Black could parry the checkmate if he had a piece to veil his King or to slot into the space between the Horse and the Cannon.

The Red Horse is already in position, C1+7 completes the mission. On the other side of the board, the Black Cannon is facing the Red King directly, you need a Horse at the R62 spot to form the Horseback Cannon checkmate. H3-4 does it, if it is Black’s turn to move.

(2) CH Double Checkmate

The double check is a lethal weapon. In most cases, there is no way to lift both checks with a single move, except by moving the King to a safe spot if one is available.

Red wins at once with H7-6. Black cannot parry the Cannon check with E5-3 or capture the Horse with A5+4 at the same time. Nor can he get the King out of check by moving it to the second rank.

Black is checkmated, despite both of Red’s both attackers are being en prise.