[First Edition : 25 July 2002]
[Second Edition : 15 March 2005]
[Second Edition Enhancement: 08 October 2008]
An interactive LiChess study of the important critical positions is here.
The purpose of atomic mate studies is to discover the smallest amount / combinations of material with which you can mate in atomic. There are several unique positions in which we can mate or cannot mate due to the position itself. One of the most important things in atomic endgames are whether or not the kings are touching (next to each other) or not. That could be all the difference between an atomic mate and a theoretical draw. For our purposes, we will not consider endgames that involve pawns. We want to learn the essentials before we throw pawn position into the mix along with other unbalances.
Hopefully this is the definitive pawnless atomic endgame guide:
1.1 (No Material for Black – Kings Not Connected)
| Material | Best Result | Best Result Possible Forced | Final Position |
| (a) 2 Bishops | Can atomic-mate | Only in special positions |  |
| (b) 3 Bishops | Can atomic-mate | Only in special positions |  |
| (c) 2 Knights | Can stalemate | Only in special positions |  |
| (d) 3 Knights | Can atomic-mate | Only in special positions |  |
| (e) 2 Bishops + Knight | Can atomic-mate | Yes |  |
| (f) 2 Knights + Bishop | Can atomic-mate | Yes |  |
| (g) 1 Rook | Can stalemate | Yes |  |
| (h) 2 Rooks | Can atomic-mate | Yes |  |
| (i) Rook + Knight | Can atomic-mate | Yes |  |
| (j) Rook + Bishop | Can atomic-mate | Yes |  |
| (k) 1 Queen | Can atomic-mate | Yes |  |
| (l) 2 Queens | Can atomic-mate | Yes |  |
| (m) Bishop + Knight | Can atomic-mate | Only in special positions |  |
1.2 (No Material for Black – Kings Connected)
| Material | Best Result | Best Result Possible Forced | Critical Position |
| (a) 2 Bishops | Can atomic-mate | No | |
| (b) 3 Bishops | Can atomic-mate | No | |
| (c) 2 Knights | Can stalemate | No | |
| (d) 3 Knights | Can atomic-mate | No | |
| (e) 2 Bishops + Knight | Can atomic-mate | Yes |  |
| (f) 2 Knights + Bishop | Can atomic-mate | Yes |  |
| (g) 1 Rook | Can stalemate | No (Cannot ever force draw!) | |
| (h) 2 Rooks | Can atomic-mate | Yes |  |
| (i) Rook + Knight | Can atomic-mate | Yes |  |
| (j) Rook + Bishop | Can atomic-mate | Yes |  |
| (k) 1 Queen | Can atomic-mate | No (Cannot ever force draw!) | |
| (l) 2 Queens | Can atomic-mate | Yes |  |
| (m) Bishop + Knight | Can atomic-mate | No |
Supplementary Information for Studies
1.2
Remember that the first thing you need to do to atomic-mate is to create separation between the two kings. This is the first thing you must do, force the two kings to separate. Only after that happens can you worry about actually performing the mate.
1.2.e
In the critical position, White is forced to vacate his King’s adjacent position to Black’s. Here’s an example of how Black mates White after creating the separation via the critical position. Thanks to siggemannen (Sergey Krakov) for playing the White side in this analysis with me:
1. Kg3 Kd3
2. Kg4 Kc2
3. Kf5 Bd3+
4. Ke6 Bb4
5. Kd5 Kd1
6. Ke6 Be4
7. Kf6 Bf5
8. Kg7 Be7
9. Kh6 Nh4
10. Kh5 Bg4+
11. Kh6 Bf6
12. Kh7 Be6
13. Kh6 Bf7
14. Kh7 Nf3
15. Kh6 Kd2
16. Kh7 Ng5+
17. Kh6 Bg7#
1.2.f
In the critical position, White has a choice of where to move after Black moves a Knight where White’s King was. Here are the two major variations from my own analysis after 1. Ke4 N6d5:
Variation 1: 2. Kd4 Kd6+ 3. Ke5 Ne6 4. Ke4 Kc7 5. Ke5 Bd6+
Variation 2: 2. Kf5 Ne6 3. Kf4 Kd6+ 4. Ke5 Bd4 5. Ke4 Be5
1.2.i
From the critical position, we can get the following (thanks once again to Sergey):
1. … Kc2
2. Rc1+ Kb2
3. Nc3 Kb1
4. Rc2 Kb2
5. Kb1 Ka2
6. Kc1+ Kb1
7. Kd2+ Kc1
8. Nd1
1.2.j
The bishop appears destined for the same doom as the knight. However! You must get your king to the opposite colored corner as your bishop is if you want to mate. The king will be able to move to 3 different spots… but two of them immediately lead to mate after the Rook takes the King’s spot. The other seems to lead to stalemate but it isn’t so. Simply use a windmill technique with the Bishop, rotating it around until the King is on b1 (in the critical position) with Black’s Rook on b2 and Black’s Bishop somewhere on the b1 diagonal. Ka2, Bb1! Ka3, Ba2! and then the mate is simple to force through.
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