Comments/Ratings for a Single Item

Ralph Betza wrote: 'The Chancellor is roughly equivalent to the Queen even though the ideal value of N is presumably less than Bishop: the Bishop is colorbound and its practical value is ever so slightly more than a Knight, combining it with R removes the colorboundness, and therefore is a classical case of 'combining pieces to mask their weaknesses and thus allow their practical values to be fully expressed'; and therefore one might expect the Q to be worth notably more than the Chancellor.'

'One hypothesis about why the Chancellor does so well is that the R has a weakness that is masked when N is added to form Chancellor. This weakness would be its relative slowness and difficulty of development, and perhaps its lack of forwardness (it has only one forwards direction).'

P=100, N=300, B=300, R=500, C=850, Q=900 are my preferred values on 8x8 boards. Sometimes I like to say that the value of a Bishop is 5/8 times that of a Rook on any square board, which would bump the Bishop up to 312.5 points here (an insignificant change, which does not affect my strategy when playing FIDE chess). Back in the 1990s I used to debate the relative values of Queen and Chancellor with Betza. Years later I came up with a way to compare these two pieces indirectly, by introducing some new pieces. The 'Elephant' moves like a Ferz or an Alfil, and is worth 50 points less than a Bishop (I believe Joe Joyce agrees with me on that). The 'Grand Rook' moves like a Rook or an Elephant, and is worth 50 points less than a Queen (I am casting my solitary vote for that value). The Grand Rook and the Chancellor are similar enough in design that I would expect them to have the same value on any square board.

Happy Easter, all!

This is a totally fascinating topic I can't stay away from, even though I am terrible at it. I seem to be much better at asking questions and confusing the issue than I am at answering questions and casting light. Well, everyone has a role in life. 

David Paulowich recently commented that I believe the modern elephant, FA, is worth about half a pawn less than a bishop, and I fully agree, on any board they are liable to play on together. But if we change the rules a bit, maybe that answer changes. 

Mike Nelson made a comment [in 2003?] about pieces having a value that is relative to which other pieces are on the board, and gnohmon picked up on it a little. I'd like to take that idea, maybe add a little to it, and run with it, full-tilt, right over a cliff, or two or three. 

Let's start by asking what is the value of the queen in a multi-move game? There are various types of multi-movers, each of which may have a different influence on the piece values. A Marseilles variant has to play differently than a progressive variant. Are the piece values in all 3 games the same? Would the rooks get out faster in progressive, or not at all, because the game is over on a 5 piece attack? 

The game I recently posted can be considered a large Marseilles variant, with batteries. The batteries need to be charged for the piece to move. A king charges the battery of 1 piece that starts the move within 2 squares of that king. What is a queen worth under these conditions? It has unlimited movement, once. If it is then stranded, what happens to its value? Clearly, it becomes seriously reduced, as do all the other long range pieces. They act as slightly variable short range pieces, or as a one-shot missile. 

Here, let me suggest we have another potential measurement for the 'chessness' of a variant. On that scale, which can in theory be computer-evaluated numerically by someone like HG Muller, both Warlord and Chieftain show some distance. But I submit that it is likely Marseilles will show a little distance, and Progressive a fair bit more. While I haven't played either variant, one thing seems apparent, and that is when you expose a major piece, you are very likely to lose it before you can move it again. I'd think especially in progressive, all the pieces become 'one-shot', and in that sense, the values of the pieces contract toward each other along their range of values, or alternatively, and maybe more likely, all [non-royal] piece values fall toward 1, and the fall is Aristotelian - the more valuable pieces fall faster.

Joyce's ''chessness'' of a cv was a comment once by Gifford:
http://www.chessvariants.org/index/displaycomment.php?commentid=19665.

To continue messing with piece values, let's look at different boards. The piece values given are based on a more or less standard 2D chessboard, rectangular in shape. Change that in any significant way, and you've changed the piece values. Take a 1D board. There are 2 ways you can 'cut' a 1D board from a standard 2D board, orthogonally or diagonally. Consider the value of a rook and a bishop on each board for the slider rook and the slider bishop - not the jumping bishops of One Ring Chess [LLSmith] for example. One one board, the bishop can't move, and the rook has unlimited [except for blocking pieces] movement. So on average in these 2 systems, the rook and bishop are exactly equal. This is carried over into some games played with standard pieces on a diamond-shaped board, where the rooks and bishops trade the number of squares they can move to without trading any other aspect of their respective moves. Clearly this increases the value of the bishop and decreases the value of the rook. 

Now consider the knight's move in 2, 3, and 4 dimensions. That move, the only 2D move in standard chess, explodes in higher dimensions - attacking 8 squares in 2D, 24 in 3D, and 48 in 4D, if I did my numbers right. Beyond that, it takes a Dan Troyka, a Larry Smith, or a Vernon Parton to go. But it's easy to see the value of the knight rises considerably in comparison to, say, the rook. 

So, to sum this up, we seem to have established that the value of a piece depends on both the kinds of other pieces on the board with it, not just the number, and it also depends on the shape of the board it's on. 

Does any piece have an intrinsic value? :)