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The Iron Knight

What's It Worth?

Long ago, there was a box of crudely-made iron Knights in the Columbia University Chess Club. Of course, people tried to use them in games, with the rule that an Iron Knight could only be captured by the move "fe".

Nobody would allow this to happen, so the Iron Knight was basically an uncapturable piece, with a Knight's normal powers of movement and capture.

What's It Worth?

Aren't we lucky, we already have an experimental lab set up, in which we can assay this piece and get a very approximate value for it; I am referring, of course, to the games of Muenster Cheese, which were invented in order to investigate the value of doublemove pieces.

The Rules of Iron Muenster Cheese

  • The rules of chess except,
  • Black starts with a full army of pieces, White starts with a King, 8 normal Pawns, and one or more iron pieces.
  • Iron pieces cannot be captured.
  • Sometimes Black moves first.

Various Sizes of Pieces of Cheese

According to the simplest way of counting material, a Rook is worth 5, a Knight or bishop is worth 3, a Queen is worth 9, and so White's whole army is worth 31 points of material.

An Iron Rook seems to be worth much more than that: White plays 1. h4, 2. Rh3, 3. Re3, 4. R:e5+, 5. R:e7+, 6. Re8+, and can at least draw by perpetual check (and slaughter many pieces along the way). White cannot lose, and probably should win every game.

A single Iron Knight seems to be worth much less than that: 1. Nc3 e5 2. Nd5 Qh4 3. N:c7+ Kd8 4. N:a8 Q:h2, and can there be any doubt that Black will win?

This seems a lot like doublemove values, where the value of a 2move piece had an exponential relationship to the value of its 1move counterpart. If the relationship is "squared", which seems logical for 2move, this would mean, for example, that if a 1move Rook is worth 1.6 1move Knights, then a 2move Rook should be worth 2.56 times as much as a 2move Knight (2.56 is 1.6 squared).

For 2move pieces there were also an effect of distance, and a blitzkrieg bonus, and other considerations to worry about.

For Iron pieces, "squared" does not seem to be logical, but distance should be very important.

Following

For Iron pieces, one important consideration is not so much the value or the distance of the base piece, but the ability of the base piece to follow a King.

As proof of this, think of a game where WHite has one Iron WD: 1. (WD)b1-b3, e5 2. (WD)b3-b5, Qh4 3. (WD)b5:b7, Q:h2 4. e3 Qh1+ 5. Ke2 Q:g2 6. (WD)b7:b8, h7-h5 7. (WD)b8:c8+; because Black threatens to make a new Queen and give mate, White must give perpetual check, and because the Iron piece has full coverage of the board, Black cannot escape from perpetual check.

It seems that having a single Iron piece that can follow the King guarantees at least a draw.

What We Have Learned So Far

With certain types of piece, if you give White a few moves of peace, he can "always" draw by perpetual check, so Black cannot win unless he gives mate soon enough. This simply obscures the basic value of the pieces. An Iron Wazir (uncapturable piece that moves like a Rook but only one square) probably loses if it starts on a1, and draws if it starts on d1.

If it takes two pieces to cover all the squares, it takes twice as many moves to develop them, and there is the possibility of running away. For example, suppose we have a Black Ke4 and White Iron Ferz on e2 and d2. After 1. Fd3+ Kd5! 2. Fe4+ Ke6 3. Fd5+ Kd7 4. Fe6+ Kd8!, Black has outrun the Fd2, and will have 4 moves of free choice before being in check again.

Iron Ferz Muenster Cheese

Before analyzing the game in detail, I'd guess the following:
  • White would lose by playing defensively.
  • Advancing only one Ferz to the attack is not much of a threat, because Black's King simply moves to the other color square.
  • Advancing two Ferz to the attack does not threaten checkmate or perpetual check, but could lead to capturing quite a few pieces with check.
  • Advancing every Ferz to the attack leaves White's King undefended. White must start with enough Iron Ferzes to have some defense as well as some attack.
According to the above, the game might be played with 4 or 5 Ferzes. 4 of them should start at b1, c1, f1, and g1; if there are 5 Ferzes, one should start at d1. If the four-Ferz game is an even game, the Iron Ferz is worth about 8 points, but if the 5-Ferz game is even, the Iron Ferz is worth only 6 points.

However, if you look at things closely, it turns out that the defensive formation of Ff1 and Fc1 is so strong that White wins easily: first he runs one Ferz up to d7, disorganizing Black's position and forcing many pieces to run away onto dark squares, then he starts a dark-squared F on another raid, and Black loses tons of material without ever getting an attack.

Therefore, we have to try Three.

Three Iron Ferz Muenster Cheese

White has three Iron Ferzes, at a1, h1, and d1. The Fs at a1 and h1 are poorly placed, and this is necessary to make the game potentially playable (if you doubt this, try it!).

I have looked at 1. e3 e5 2. g3 (can't allow ...Qh4) h5!? 3. Fe2 h4 4. g4 h3 5. Ff3 Nh6 6. Fh1-g2 f5! with the idea that Black doesn't mind losing a few Pawns if he can trade some and get some open lines. I think Black is doing well in this position, and no better was 1. e3 e5 2. g3 h5 3. h3 d5 4. Fg2 f5!

When the Ferzes start at b1/g1 or f1/c1, they win (I think). This would make them worth more than ten points each, or seven times their base value. Because they don't do well when they start in bad positions, I think this is fairly close to their actual value -- at least, this is a better guess than we ever had before.

Bigger pieces would get a bigger multiplier, but the multiplier probably doesn't grow as quickly as it does for doublemove pieces; an Iron Knight is worth more than two Iron Ferzes, but less than four (less than three, in fact, I think). Distance also counts, so two Iron Bishops are worth lots more than two Iron Knights.

Since the Muenster games didn't seem very interesting or playable, how about

Gorgonzola Cheese

Replace White's Queen with an Iron Ferz.

According to the above analysis, this should be a fairly even game: because White has only one F, you have to apply a "colorbound penalty" to its value, and so it ought to be worth about 9 points, same as a Queen.

According to the above analysis, this should be a fairly even game, for example 1. e3 e5 2. (iF)d1-e2 b6 3. (iF)e2-d3 a5 4. (iF)d3-c4 Nf6 5. (iF)c4-b5 Be7! (can't save the Bc8) 6. (iF)b5-c6 O-O 7. (iF)c6-b7 Ra7 8. (iF)b7:c8 d7-d5 9. d3 d4 10. e4 Bb4+! and after White's difficult choice, I cannot tell who is winning.

If Black has the Colorbound Clobberers, it will be difficult to save the light-squared colorbound pieces; if Black has the Nutty Knights or the Remarkable Rookies, even though there are no colorbound pieces White's blitzkrieg will still win some pawns and disorganize Black's position (or perhaps White can win a piece because it will be hard for Black to get everything onto dark squares).

In short, this seems to be a playable game, and proves that the Muenster setup is a valid testbed for powerful pieces.

Rusty

How about a Rusty Iron Knight: can be captured by Pawns but not by pieces? Or a Heavy Iron Knight: can be captured by pieces but not by Pawns ("heavy" because Pawns are small, and presumably not strong enough).

Either of these forms of immunity would be considerably less valuable than the complete invulnerability of the Iron Knight.

Would a Rusty Ferz be worth only as much as a Rook or even a Bishop? Perhaps somebody else would like to figure this out. Imagine having a whole army of pieces that all move the same, but have different types of armor; and the whole army equal in strength to the regular army, so you could sit down and play a game of Chess versus Iron-Chess! What a trick it would be to design that army, and what a Chess Variant (capitalized and in bold letters) that would be!

It would take a lot of thinking and playtesting to design that army; I haven't done it and don't plan to.

Friendly

Andrew Juell's interesting game (somewhere on the web, but I forget where) includes a piece that makes adjacent pieces invulnerable.

This is not as strong as an Iron piece, because the piece that protects others cannot be protected (you only get one of them), so it is a target.

I still cannot begin to guess the value of such a piece.

Iron Pawn Chess

If each player has one Iron Pawn, and if each player gets to choose in secret which Pawn it is, and if the Ironic nature of the chosen Pawn is not revealed until you try to capture it, we have a very strange and interesting game.

Perhaps promotion of the Iron Pawn should be forbidden: when it reaches the 8th rank, it cannot move, and has become a Lump. I think that this additional rule is needed to prevent the Iron Pawn from being too powerful, but you can try the game with or without this rule.

Powerlessness

Suppose you have an Iron Queen that cannot capture; what's it worth?

This piece must have some value. For example, if White has one of these pieces at d1, the opening 1. e4 c5 2. Qg4 d5? 3. Qd7 blocks and disorganizes the Black pieces quite a bit.

I think a piece of this type would be worth only a couple of Pawns.

In the game of csipgs chess, it might be good to have each player start the game with one or three Iron Lumps in reserve; an Iron Lump can't move or capture, and can't be captured, and you can't buy any more than the few you start with. The reason for making them part of the game would be that, in csipgs chess, you have no Pawns, and so you have no Pawn-chains to create a fixed terrain; a few Lumps might substitute for Pawn-chains.

Even better might be to start each player with two Go stones. They can be captured, but it is difficult to do so; they may not be placed to make a Go capture, but the "normal" pieces can capture them by surrounding them; I wonder, though, if they make groups with friendly "normal" pieces, just what the rules would be....

Magic Check

If both sides have Iron Knights that cannot capture but can give check, it is a playable game. Normally, a piece that cannot capture cannot give check, but for this game it is good to adopt a special rule.

1. (iN)b1-c3 (iN)g8-f6 2. (iN)c3-e4 d7-d6 3. (iN)g1-f3 e7-e5 4. (iN)f3-d4 Bc8-e6 5. (iN)d4-c6 Bf8-e7 6. (iN)e4-c5 (iN)b8-d7

White has tried to advance the iron Knights to a position where they would block Black's development, Black has countered by developing nicely. Black stands better.

Notice that 4. (iN)e4-c5 was better, because White would get to play the iN to either d7 or e6, and either move prevents castling (since the iN can give check, by attacking f8 it prevents O-O).

1. (iN)b1-c3 (iN)g8-f6 2. (iN)c3-e4 d7-d6 3. (iN)e4-c5 (iN)b8-d7! 4. (iN)c5-e6? (iN)d7-e5! and Black is happy.

this should be a good game because the Iron Knights have many uses, and the Kings can never feel safe.

What Else?

Now you have read everything you ever wanted to know about uncapturable pieces...

Note

The move "fe" is a move where a pawn on the f column captures a piece on the e column. Old versions of the algebraic notation used this abbreviation for such a move. The rule is merely a joke, pointing to the fact that fe is the symbol for iron. (Note added by Hans Bodlaender, after an email of Ralph Betza.)

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