I was actually going to do Knightmate as my first variant of the week. But it was enough work I figured I'd shift it to variant of the month. Then I never got around to finishing it. Here's the draft I was working on:
Knightmate
Knightmate is a rather simple chess variant invented by Bruce Zimov in 1972. You just swap the knights and the kings. That is, each player has one knight, which starts where the king usually does. Each player also has two kings, which start where knights usually do. To win, you must checkmate the knight. The kings are normal pieces, so they can be attacked without check, and captured without losing the game. The knight can castle with the rooks usings the same rules as king castling in standard Chess.
Opening Goals
Nimzovich defines developing your pieces as moving them toward the center line. In normal chess, if you place any of the pieces on the 1st rank of an empty board, they can get to the fourth rank in one or two moves, with only the knight requiring two moves. On the other hand, the king takes four. So developing the king as a piece becomes a problem.
This affects the other opening goal of controlling the center. Normally this is done with a couple central pawns. There is nothing in Knightmate stopping the pawns from getting to the center, but now they don't have knights to back them up. This will make controlling the center harder.
When it comes to protecting the knight there is the issue of the king on the side you wish to castle on. In Chess the knight on the castling side can just hop over the pawns and get out of the way. The king in Knightmate must slip through the space opened by a moved bishop, or slip into a space vacated by a moved pawn. Diagram A shows four castled positions in Knightmate. Given the slowness of slipping through the bishop spot, the castling on the lower right is the slowest option. I don't think the castling on the upper left is a good idea, as it puts your king and knight on a diagonal exploitable by a bishop. Of course, given the old adage that a knight on the rim is dim, castling may not really protect the king. Castling king side cuts your knight down from four potential moves to three.
Let's look at the classic 1. e4 e5 opening. Now what? you can't attack the pawn with Nf3, but how about 2. d4? Black can't defend with d6 (2. d4 d6 3. dxe5 dxe5 4. Qxd8#!). If he captures the queen retakes (2. d4 exd4 3. Qxd4), and now there is no knight to make the standard attack on the queen.
Midgame Tactics
The king, when treated as a normal piece, is generally considered to be worth four pawns. Zillions of Games evaluates it to be between a bishop and a rook in value. Interpolation of the ZoG values (a screwy proposition at best) puts at three and a half pawns. A king is slower than a knight, but has better coverage close in. A king can reach every square within two in two moves. A knight will need three or four moves to get to some those squares. But a knight can get across the board in four moves compared to a king's seven.
Discovered attacks are not really affected by the changes. Kings can't be the attack part of a discovered attack, but knights couldn't either. Kings' lack of mobility may make it harder for them to get into position discover part of the attack.
Pins and skewers are still available tools. As with discovered attacks, kings can do neither since they only move one square, but knight couldn't do them either. The terminology gets a bit vague with the bishops, because anything they could pin down now (except pawns) is worth more than the bishop is. At that point it's more like a skewer.
Forks are harder to come by. The knight fork is so useful because the knight can attack any other piece without possibly being attacked by that piece. The same is not always true of the king. Pawn forks are still useful, perhaps even more useful given the slight power increase on the board. And queens are safer, as they can't be attacked without being able to strike back (except for the now royal knight, which probably shouldn't be attacking the queen).
If a king is truly stronger than a bishop in this game, it allows for a greater possibility of off balance games. While people will argue forever about the relative values of a knight and a bishop, they'll still give up a knight for a bishop. I wouldn't give up a king for a bishop in this game. But you might see king for bishop and a pawn frequently, giving a theoretically even game with difference forces available to each side.
Endgames
As in normal chess, a queen and knight are sufficient to mate another knight. From diagram B (WNh8 Qf8 BNe4):
1. Qf4+ Nc5
2. Qf5+ Nb3
3. Qd5+ Nc1
4. Qc4#
This perfectly illustrates how a queen can force a knight around the board, either from one or three away orthogonally, or two away diagonally. However, no other knight and piece combination can mate another knight. On the other hand, a knight and any two other pieces can mate another knight. (according to a table base analysis by H. G. Muller).
I ran a knight and two bishops against a lone knight as shown in diagram C (WNc3 Bd5 Bf4 BNb6). This is the mate that Zillions of Games came up with:
1. Be3+ Nc8
2. Be4 Nd6
3. Bd4 Ne8
4. Bd5 Nd6
5. Bf6 Ne8
6. Ne4 Nc7
7. Bc4 Na8
8. Bd4 Nc7
9. Nf6 Na8
10. Nd7 Nc7
11. Be5+ Ne8
12. Bf7#
Sample Game
Here's a game with Zillions of Games playing itself at highest skill, just under moderate variation, and 15 seconds per move:
1. e4 e5
2. d4 Qh4 {ZoG's solution to the center game}
3. dxe5 Qxe4+
4. Qe2 d5 {Looks like a Hyper Petrof to me}
5. Qxe4 dxe4
6. c3 c6
7. Be3 Kc7
8. Kc2 Be6 {symetrical position}
9. O-O-O Be7 {Odd, ZoG is not big on castling}
10. Be2 h5
11. h4 f6
12. exf6 gxf6
13. g3 Kg7
14. Kg2 a5
15. a4 b6
16. Rd4 f5
17. Bf4 Bd6
18. Bg5 Bc5
19. Rd1 Bf8
20. c4 Bd6
21. f3 Be5
22. Rhe1 Kf7
23. Bf1 exf3
24. Kxf3 Kd6
25. Re3 c5
26. Bf4 Kf6
27. Bg5 Kf7
28. Bf4 Kf6
29. Bg5 Kf7 {draw by three fold repitition}
Actually, I ran two games with ZoG. The first one drew the same way, so I increased the variation. The second game (above) was the same at the start, different as the midgame began, but came back to a similar draw.
My Opinion
It's a tricky little game. It's so close to chess that you are lulled into missing the differences. And the differences are critical, because they involve the knight/king. One time I was castled and though my pawns were defended, but the knight wasn't defending them. Scrunched down into the corner, I'd blocked off all my escape squares, and a rook took the pawn in front of my king to mate me.
In the end, I don't think I like it. It doesn't seem to bring enough to the game to override the confusing similarity. I think with more play the confusion would go away, and perhaps I could find play with the king interesting. But with so many variants available I'll probably just move on to the next one.
Zillions of Games
Normally I will try to provide a Zillions of Games file for the variants I review. However, this is one the standard variants provided with Zillions of Games. There are also numerous chess engines out there that have been programmed to play this.
Knightmate (also called Mate The Knight) is a game invented by Bruce Zimov in 1972.
This is a variant in which the knight and kings switch roles. There are four kings on the b and g files and a single pair king on the e file. The kings are no longer "royal" and thus may be taken without the game ending.
The objective is therefore to checkmate your opponents knight.
Pawns may promote to kings, but not knights.
A website you can play this variant on is http://www.pathguy.com/chess/KnightMt.htm