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 Wed, May 22, 2019 10:52 PM UTC:

Today I was looking at the wiki re: the mathemematical concept of Game Complexity, which led to the following sub-link on Game-tree Complexity, that gave me food for thought about CVs that might one day compete in terms of popularity with such well known games as Chess (which arguably is slowly being played out at elite level, in terms of opening theory):

https://en.wikipedia.org/wiki/Game_complexity#Game-tree_complexity

If the mathematically inclined on this CVP website are interested, perhaps there might be a way to evaluate the Game-tree Complexity of various CVs on CVP, and even slowly compile a list of those CVs with very large Game-tree Complexity number estimated for them; thus such CVs, if they ever become popular, might have a longer lifespan than e.g. Chess, and part of popularizing such CVs could be pointing out their great Game-tree Complexity number (as estimated).

Just as an example, here's a link to a 10x10 CV of my own invention:

https://www.chessvariants.com/rules/sac-chess

I'm not mathematically inclined, but I'd guess that the branching factor for Sac Chess (based on the Chess and Sac Chess armies operating at maximum centralized power for each piece in each game's setup) would be 2 to 3 times higher than for Chess on average, and I'd also guess that the average game of Sac Chess (especially for well-played games) would be about 2 to 3 times more than for Chess in terms of number of ply (a piece is traded in Chess about every 10 ply, I've read long ago, so a game of Chess [or possibly Sac Chess?!] would thus be over on average with a total of 32-2x(70/10)=18 units left on the board), and thus Sac Chess' Game-tree Complexity may be ((35 [=avg. # moves in chess] x2.5) to the power of 70 [=avg. # ply in a game of chess] x2.5, if I understand the Game tree Complexity estimate formula right) which may well easily exceed that of e.g. the game of Go - see the chart given further below in the sub-link on Game-tree Complexity that I first gave. Note that in played Sac Chess games I've looked so far, it seems a pair of pieces are traded about every 8 ply (rather than every 10 ply, as in Chess) on average, but this is based only on a small observation.


Edit Form
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.