HOW TO Mate with K+B+N vs K - Finally!
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After recently seeing several different forums (and probably just a fraction of all forums on this topic) about how to mate with K+B+N vs K I finally decided to just copy out the entire procedure from GM Ruben Fine's classic Basic Chess Endings (BCE) - starting from the longest position to win from: mate-in-33; presumably the most difficult position for this type of basic checkmate.
There have been innumerable discussions at chess.com and elsewhere I'm sure about whether or not you should memorize this procedure. CONS: It rarely if ever occurs OTB.
PROS: Knowing it will greatly increase your knowledge of how to coordinate Knights and Bishops, and you'll amaze all your friends, family and fellow chessplayers by announcing "Mate in 33" and then doing it in under two minutes. Plus you'll know how to mate with K+B+N vs K so you don't end up looking like a chump if you ever reach this admittedly rare situation OTB.
For a description of BCE see my blog on endgame books. The old cover is on the right, the new algebraic edition cover on the left.
Check out all the other diagrams before proceding to read the main one demonstrating the forced mating procedure
These 2 diagrams illustrate the only possible mates that are not forced
These 2 diagrams illustrate the only forced mates possible - on the left, the Bishop can obviously be anywhere on b7 - g2; on the right the Knight may also be on c6 or d7.