Check out Grant Acedrex, our featured variant for April, 2024.

Enter Your Reply

The Comment You're Replying To
George Duke wrote on Fri, Aug 6, 2010 03:51 PM UTC:
How many Bishops? Black's generalization of Karakus is a kind of power series, exponential, because he can as well use 3x3 next after or skipping 2x2, which expands each space just from 1 to 4 pieces/spaces. [Reference is to Quadd Shogi Chess and to Giant Chess.] In 3x3 there are nine Queens where there was one, and so on. With all squares three-by-threes, an 8x8 board becomes 24^2, 576 squares. They are like Frolov's moving palace nine-space, out of one or as if one; but in pure Black each of the nine has the same residual piece-type without variation. That is the methodology of Karakus and the Black twosome, incidentally specified by that Xiangqi-size restricted area having 3 its specific instance. Missoum's approach here differs still in growing boards. 'N=3' is the first nontrivial case, where we find ourselves today; or as Missoum writes, ''The reader may have found extensive literature about the 8x8 chess game.'' Some systems characterize by period-doubling towards Chaos abruptly, but Chaos(or Chess) can prove manageable mathematically. Let's say the play is rather on a Missoum board n=8. You want to know how many Bishops you have. There is the formula used in the first (2005) of these three comments, taken from Missoum's text, arriving at 126 Bishops with n=8. (The example is Missoum's late in the article.) Why? Knowing the number of Bishops and full piece disposition allow interim values to be calculated, settled on, and adjusted player and computer. As for Knights, closely following or duplicating Bishop in numbers, notice Missoum's method of extending their reach with longer leap-lengths available by board sizes emerged. Sustainable growth; where governments fail we succeed.

Edit Form

Comment on the page Geometric sequence of Chess Games

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.