Check out Janggi (Korean Chess), our featured variant for December, 2024.

Enter Your Reply

The Comment You're Replying To
Peter Hatch wrote on Fri, May 10, 2002 09:05 PM UTC:
> When you're really stuck with probabilities, you can use the
> laborious case-by-case analysis.

Indeed.  Instead of checking each case for two-path bonus, it's easier to
just check each case to see whether it is blocked, and just add up the
probabilites.  With 5 squares that can be blocked (e3, d2, d4, f2, and f4)
there will be 2^5 = 32 total possibilities.  1 possibilty has no squares
blocked, 5 have one square blocked, 10 have two squares blocked, 10 have
three squares blocked, 5 have four squares blocked, and 1 has all five
squares blocked.  The probability of each possibility is 0.7^(number of
unblocked square) * 0.3^(number of blocked squares).

The no squares blocked possibility lets us reach the destination square, as
do 4 of the one square blocked possibilities (all but e3), and 2 of the two
squares blocked possibilities (d2 and d4, f2 and f4).  None of the rest do.
 So the total probability is 0.7^5 + 4 * 0.7^4 * 0.3 + 2 * 0.7^3 * 0.3^2 =
0.51793, which agrees with my formula.  So I'm confident I'm right again.
:)

Edit Form

Comment on the page Revisiting the Crooked Bishop

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.
Avoid Inflammatory Comments
If you are feeling anger, keep it to yourself until you calm down. Avoid insulting, blaming, or attacking someone you are angry with. Focus criticisms on ideas rather than people, and understand that criticisms of your ideas are not personal attacks and do not justify an inflammatory response.
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.