Everything You Need to Know About Bishop and Knight Checkmate
The bishop and knight checkmate is said to be one of the toughest checkmates to master. Even then, it is worthwhile studying because it appears regularly enough. In the recent three years of competitive play, I have seen it more than 10 times! Given that there are already many articles and videos covering this checkmate, I believe I should offer additional perspectives beyond simply showing the technique.
My purpose is to help you better understand how bishops and knights coordinate, as well as some of their characteristics and properties. On top of that, I would like to show you different winning methods which will hopefully inspire creativity in your own games.
Before we explore the position, there are three things that you need to note:
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Checkmate can only be forced in a corner of the same colour complex as your bishop. For example, if you have a dark-squared bishop, you can only force checkmate at a dark-squared corner.
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Waiting moves are sometimes necessary, and should only be done by the king or the bishop, never by the knight.
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The bishop and knight will coordinate best when the knight is on a square of the same colour complex as the bishop. For example, if you have a light-squared bishop, the knight is best placed on a light square.
For any bishop and knight checkmate, we must first drive the enemy king away from the centre. You can expect the king to put up the toughest resistance by running towards a corner opposite to the bishop’s colour. There are two ways to take it from here. The first is known as the Triangle. While this checkmate might not be the most efficient, it nevertheless requires much fewer than 50 moves. Moreover, it demands little memory.
With only three checkpoints, the campaign plan is straightforward. The first checkpoint is to trap the king in a "big triangle" with the help of all three pieces.
We will then work towards shrinking that into a medium-sized triangle, where the bishop and knight are doing all of the work, leaving the king free to further restrict the enemy.
And we will finish with a "small triangle" which involves the king and bishop only. After this is accomplished, it should not take more than three moves to mate the enemy king.
Let us now take a look at the second method. It is significantly faster than the Triangle, but requires accurate moves at certain critical junctures. Should you choose to adopt this technique, please review it thoroughly. I will highlight those moments with an exclam(!) later as we play through the game. Since you already know how to force the enemy king from the centre to the unfavourable corner, I will start the demonstration with the king at a8.
That’s all for today. As always, I hope you got something out of this article. Take care 
