Chess and I: click here for the homepage.
21 October 2026
§1 A few general words about basic endings in chess
In the days of our chess childhood (a childhood that, depending on the individual, may have been lived as readily at 7 as at 25), there was a time when, if we had the skill or the good fortune to reach an ending of king and heavy piece against the lone king -- it makes very little difference whether the heavy piece is a queen or a rook --, we did not know how to proceed correctly and, in a good many cases, ended up drawing instead of winning. (For many amateur players, this chess childhood lasts for decades, or for life! They are easy to find.)
Now, well, let us speak objectively: winning these endings is truly child's play, a trifle for youngsters. Other endings of standard chess, by contrast, such as the famous case of king and bishop and knight against the lone king, require focused study and repeated practice. (I have learnt it! And by now it would be nice if, one day, it actually came up in a game...)
I can also win the ending of king and queen against king and knight. On the other hand, I have given up the idea of learning king and queen against king and rook, because it is too complicated: there is more than one YouTube channel devoted expressly to this ending, each with a series of long videos...! But it is true that, if I find myself in this situation against an opponent of my own level or weaker than me, I have reasonable hopes of winning (whether I have the queen or, conversely, the rook).
§2 Basic endings with some fairy pieces, with particular reference to the B+N
From here on, we shall consider basic endings with fairy pieces against the lone king, in which checkmate can be forced.
Since 2024, I have passionately played a number of variants, such as Paradigm 30, Seirawan, Gothic Chess, and so on. At present, I can say that my absolute favourite chess game is Spartan Chess.
In these variants there are pieces such as the R+N (called the chancellor, or by other pointless names) and the B+N (the so-called archbishop, or... etc. etc.). In the particular case of Spartan Chess, we have the aforesaid B+N and, in addition, the non-royal R+K. In Paradigm 30, by contrast, there is a single special piece (each player has two, in place of the bishops), and this piece is similar to the B+N: when the board is nearly empty, its behaviour becomes so like that of the B+N that the checkmating procedure in the basic ending can be said to be the same.
Pieces compounded with the rook, such as the R+N and the R+K, pose no particular dilemmas. Someone who can play chess but is new to these special pieces can use the same procedure as when holding an ordinary rook, provided that s/he pays particular attention to the increased possibilities of stalemate.
The B+N, on the other hand, requires an entirely different procedure. (K and B+N against the lone K.) At first I was unable to do it, and I drew games that I ought to have won. Then I learnt it, a little over a year ago, and now I find it easy. I learnt on my own, by practising against Fairy Stockfish. Are there pages on the web that teach this checkmating procedure? Yes, there is something, but not much (as far as I know). I suggest, for example, these links:
https://www.chess.com/forum/view/chess-variants/tutorial-on-how-to-checkmate-with-the-princess
https://greenchess.net/endgame.php?type=fairy
A PyChess user, who is himself learning the procedure, has published a dedicated PyChess study, together with the other "Spartan Endgames":
https://www.pychess.org/study/lcneKQ5E/2Iv1RWxq
(On PyChess, the Studies section was introduced at the end of September 2026!)
Postscript. See also, from his personal website, https://dominikmoos.com/notes/checkmating-a-bare-king-with-archbishop-and-king.
§3 Other fairy pieces: the Spartan Chess "captain" (W+D) and the GreenChess augmented knights (N+F, N+D, N+A)
(Abbreviations: W, F, D, A = wazir, ferz, dabbaba, alfil.)
One of the minor pieces of the Spartan army in Spartan Chess is the W+D ("captain"). A very beautiful piece. It is worth roughly as much as a knight or a bishop but, in endings, it is worth somewhat more. As is well known from the analyses of H.G. Muller, it is possible to force checkmate with the W+D in the basic ending against the lone king.
(It is not particularly strange that a minor piece, in the world of fairy chess, should be able to give checkmate. There are other cases, the most famous being the non-royal K. In H.G. Muller's own terminology, pieces that can give checkmate are called major. So some minor pieces... are major! Well, it depends on terminological conventions.)
What is it like to checkmate with the W+D? Easy, or difficult? I was convinced that it was very easy. But recently, prompted by the PyChess user who created the study on the "Spartan Endgames" (this endgame is of course included), I realized that I could not improvise the procedure instinctively. However, I learnt it easily. I made a note, a memorandum, and I shall never forget it again.
Among the chess variants I play are also the GreenChess variants with the augmented knights (links here and here). These are four different pieces: N+W, N+F, N+D, N+A. Until a few weeks ago, I had a rather superficial view of these pieces. I told myself: they are heavy pieces, and each is worth as much as a rook, or very slightly less than a rook. I believed that one could give checkmate with each of the four, and that it was not complicated! I was not sure, but I believed so.
In fact, the N+W cannot give checkmate in any way in the basic ending (which is, therefore, a draw). With the other three, checkmate is possible and can be forced, but the degrees of difficulty and the number of moves required differ. With the N+F, the procedure is fairly simple, though not trivial (I mean procedures comfortably practicable by a human player, with no pretensions to perfect play). With the N+D, I managed to learn it, but I had to overcome some significant difficulties. With the N+A, on the other hand, I am almost groping in the dark! Perhaps I should simply abandon the enterprise. (... I ought rather to go back to the ending of king and queen against king and rook, which is truly useful in life.)
It may be that, some day, I shall myself publish some PyChess studies on the checkmating procedures with the augmented knights -- at least N+F and N+D.
§4 Here are some extraordinary tools (Checkmating Applet), for which we must thank H.G. Muller
https://www.chessvariants.com/membergraphics/MSinteractive-diagrams/EGT.html?betza=BN
https://www.chessvariants.com/membergraphics/MSinteractive-diagrams/EGT.html?betza=WD
https://www.chessvariants.com/membergraphics/MSinteractive-diagrams/EGT.html?betza=NF
etc.
https://www.chessvariants.com/rules/checkmating-applet
https://www.chessvariants.com/page/MScheckmating-applet-3-vs-1
With the "potent knight" (another kind of modified knight!) together with the king and another piece of your choice:
(You can change "other=B", "other=N", etc. in the URL; you can also enter other pieces in the "Custom" field within the page, for example "NmW" or other codes in Betza notation.)