I agree with my old Gothic Chess friend the chesscarpenter. It seems a bit harsh to transfer the label "underpromotion" to the Chancellor and Archbishop. In chess, there are only two major pieces, the Queen and the Rook. Promoting to anything but the Queen represents a significant "under" promotion, but in Gothic, with a Chancellor being so close in strength to a Queen, I think it can be associated with a promotion. Heck, from the pawn's point of view, everything is a promotion, is it not? :) Even if delegated to the ranks of "middle management" and being made an Archbishop is still a promotion!

Wow, I am impressed! You are correct and you have a keen eye. I did transpose the nomenclature regarding the b2/a1 note. Thanks for being so thorough.

Well if you figure out some way to determine the BEST move in ANY given position, then you MUST, and I mean MUST, tell me how the heck you do it!!! :)

Various issues of Gothic Chess Review showcase them. Also, there are some animated games online at http://www.geocities.com/bow_of_odysseus/index.html if you click on the SAMPLE GAMES link. I am in the process of cleaning up the website substancially.

There are a few. The first was the Gothic King's Indian, a natural extension of 8x8 chess. I decided to name the variations after cities, so there is a Philadelphia System with some variations. But I do not want to copy the existing chess names to Gothic like the "Gothic Reti" for example. These should be named after the pioneer in Gothic Chess who molds it into a formidable system.

I only want one opening named after me.

1. Nh3 is Trice's Opening :)

I know that one will be around for a while.

To derive a nice formula for the strength of a Rook on a board of Y height and Z width, here is what you do.

First, examine the geometry of the board. You can see that from the 4 corners, the King can be safely checked a total of (Y - 2) + (Z - 2) times. Recall is a Rook is next to the king while delivering check (like Y -1 or Z - 1) then the king can just capture it.

So, we have 4((Y-2)+(Z-2)) so far.

Basically, in the corner, the king can recapture 2 of the rook checks.

Now move over one square for the king (b8) or move down one square (a7). The king would be able to recapture against 3 rook checks. In the case of the a7 king, it could capture a Rook checking on a8,a6, or b7.

You notice on any rectangular board, there are 4 pairs of squares where this is true. On the 8x8 chessboard these are b8/a7, g8/h7, b2/a1, and g2/h1. So, we have 4 instances of (Y-2) + (Z-1) and 4 instances of (Y-1) + (Z-2).

To 4((Y-2)+(Z-2)) from the 1st calculation we add 4((Y-2) + (Z-1)) + 4((Y-1) + (Z-2)).

Recall a probability is a quotient, that being these total squares of safe check divided by the entire population of arrangements. After placing one piece on the board, there are ZY - 1 slots remaining for the next piece. But the first piece can occupy any one of those ZY squares, so you get fractions in terms of ZY-1 and ZY(ZY-1) when you compute the probabilities.

When you collect all such terms for the rook, you get:

P(safe check) = Z + Y - 6/(ZY - 1) + 2(Z + Y)/[ZY(ZY-1)] for the probability that a Rook can safely check a king on any such size board.

Plug in Y = Z = 8, and you get:

8+8-6/63 + 2(8+8)/64(63) =
10/63 + 32/64x63 =
640/64x63 + 32/64x63 =
672/4032 = 1/6

So my results match Taylor, I just computed it a different way since Gothic Chess has a rectangular board.

The concept of a "safe check", i.e. a check delivered by a piece that cannot result in a trivial capture by an enemy king, was first used by Taylor in 1876. Taylor reasoned that the probability associated with delivering a safe check on an empty board featuring just the piece in question and the enemy king should be proportional to its strength.

Let's take a Rook for an example. Ok, place a Rook on a1,a2,a3...a6. It can safely check a king on a8. It cannot safely check a king on a8 when it is on a7, since Kxa7 violates "safe check".

You essentially "sum" these safe checks over the entire board, placing the king on each square, and computing the number of squares on which a rook resides. The ratio of safe checks to total arrangements on an 8x8 board is 1:6 for the Rook.

Bishops get a little messy in the computation (explanation is not too intuitive) but basically varying diagonal lengths as a function of bishop location and king placement make it very recalcitrant to derive. Knight computations are easy, so are the other pieces.

So, I set out to do the same for a board of dimensions Y by Z, not just a square board like Taylor did.

More on the algebra of the Rook computation in the next post...

Hi Juan,

You beat me to the first post! :) Sure, this is a good place to discuss piece values now. Should I show how to rederive them, or just list their values?