Check out Glinski's Hexagonal Chess, our featured variant for May, 2024.

Enter Your Reply

The Comment You're Replying To
Kevin Pacey wrote on Sat, Jan 27 11:11 AM UTC in reply to H. G. Muller from 07:07 AM:

To be fair, I find the value given for a knight (alone) in Omega Chess in that link I gave (i.e. just 2 pawns worth) to be very unlikely - I'd put it around 3 pawns, personally.

If I recall correctly, I once estimated a Champion as worth 4.75 pawns on 8x8, with my 'standard' value for a rook on almost any square/rectangular board size being 5.5 pawns. On larger board sizes I figure a single wazir (W) is worth less than on 8x8, and I think the same in the case of an alfil (A) or dabbabah (D), so that affects my value for a Champion (WAD) adversely.

How to understand that more concretely? Well, a wazir power enhances the power of a spider (AD), but using the wazir power on a bigger board only benefits a Champion the most when it takes certain paths, in terms of number of moves spent getting to a certain square (if it luckily is a relevant one). It is a similar story sometimes even for alfil and dabbabah powers, say compared to some paths a knight can take. Note that an alfil has one more 'binding' than a dabbabah, but the former is generally speedier and so gets a bonus, one making them about equal in value in my eyes.

edit: for what it's worth, here is a diagram to help illustrate that a Champion is sometimes slower than a knight. It takes it 3 moves to reach the N on b4 (which can reach it in 2 moves) and it takes 5 moves for it to reach the N on b8 (which can reach it in 4 moves) - on bigger boards there would be more such cases than on smaller ones, I'd think:

For wide boards, a Champion can go deep faster than on a deep board, it's true, but sometimes the Champion would want to go from one side of the board to the other. I do generally give a bishop a higher value on a rectangular board than on a square board, though on square boards greater than 10x10 I think a B's value should be put higher - though I balk at making a B worth 4 pawns or more as a general rule (restraining 3 pawns in an endgame can be tough enough). Thus for me, single B=3.5 on 8x8 or 10x10, but B=3.75 on 10x8 (based on cases of number of squares reached from each board square) or 12x12, for example. I have no set formula for estimating Bs values otherwise, but put it at 3.99 if a board is really huge. I have a more precise-value-oriented way of calculating a N's value on square or rectangular boards up to 16x16, but at that point my method + formula break down completely, not just because I think that on a board that big a N's value should be tiny.

Aside from all that, arriving at a precise average value for any piece type (even chess ones) I regard as something not to be completely sure of, even if it becomes the consensus. In WWII the main Axis powers were sure their codes were unbreakable, and may have had plenty of inductive reasoning to back that feeling up. Yet, they were eventually proven shockingly wrong, in more than one instance.


Edit Form

Comment on the page Parity Chess

Conduct Guidelines
This is a Chess variants website, not a general forum.
Please limit your comments to Chess variants or the operation of this site.
Keep this website a safe space for Chess variant hobbyists of all stripes.
Because we want people to feel comfortable here no matter what their political or religious beliefs might be, we ask you to avoid discussing politics, religion, or other controversial subjects here. No matter how passionately you feel about any of these subjects, just take it someplace else.
Quick Markdown Guide

By default, new comments may be entered as Markdown, simple markup syntax designed to be readable and not look like markup. Comments stored as Markdown will be converted to HTML by Parsedown before displaying them. This follows the Github Flavored Markdown Spec with support for Markdown Extra. For a good overview of Markdown in general, check out the Markdown Guide. Here is a quick comparison of some commonly used Markdown with the rendered result:

Top level header: <H1>

Block quote

Second paragraph in block quote

First Paragraph of response. Italics, bold, and bold italics.

Second Paragraph after blank line. Here is some HTML code mixed in with the Markdown, and here is the same <U>HTML code</U> enclosed by backticks.

Secondary Header: <H2>

  • Unordered list item
  • Second unordered list item
  • New unordered list
    • Nested list item

Third Level header <H3>

  1. An ordered list item.
  2. A second ordered list item with the same number.
  3. A third ordered list item.
Here is some preformatted text.
  This line begins with some indentation.
    This begins with even more indentation.
And this line has no indentation.

Alt text for a graphic image

A definition list
A list of terms, each with one or more definitions following it.
An HTML construct using the tags <DL>, <DT> and <DD>.
A term
Its definition after a colon.
A second definition.
A third definition.
Another term following a blank line
The definition of that term.