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It doesn't have a checkmate entry - it says see Endgame. Under Endgame is a section on checkmate, and it discusses checkmate with a bishop and knight (§4.4), with a queen (§4.1), with a rook (§4.2), with two bishops (§4.3), and with two knights versus a pawn (§5). The middle three are covered in detail in this article.
The bishop and knight mate is one of the four basic checkmates and occurs when the king works together with a bishop and knight to force the opponent king to the corner of the board. The bishop and knight endgame can be difficult to master: some positions may require up to 34 moves of perfect play before checkmate can be delivered.
The two bishops checkmate is the checkmate of a lone king by the opponent's two bishops and king. [ b ] The superior side is able to drive the lone king into a corner and force mate using the two bishops and king collaboratively.
A method for checkmate applicable when the lone king is in the corner of the opposite color from the bishop (the "wrong" corner, where checkmate cannot be forced), was given by François-André Danican Philidor in the 1777 update [5] to his famous 1749 treatise, L'Analyse des Échecs. [6]
The two knights endgame is a chess endgame with a king and two knights versus a king. In contrast to a king and two bishops (on opposite-colored squares), or a bishop and a knight, a king and two knights cannot force checkmate against a lone king (however, the superior side can force stalemate [1] [2]).
2 rooks – look like castle towers and have a relative value of 5 points each. 2 bishops – stylized after mitres (bishops' hats), and have a relative value of 3 points each. 2 knights – usually look like horse heads and have a relative value of 3 points each. 8 pawns – smallest pieces in the game, each topped by a ball. Pawns have a ...
Promotion to a queen or rook would pin the bishop, leaving Black with no legal moves, resulting in a stalemate; promotion to knight may appear to threaten checkmate via 2.Nb6#, but Black moves their bishop next turn, so there is no mate, and White cannot make any further progress. Promotion to bishop is the only way to win, threatening mate ...
And you had Muller and Lamprecht saying "Checkmate can be forced in at most thirty-three moves from any starting position (unless the defender can immediately win one of the pieces) (Müller & Lamprecht 2001:19)" for years in the sentence you reverted in the Bishop and knight checkmate article, which is a beginners mistake.