This is a purely mathematical question, and there should be a factual answer in the form of a formula.

First, the background. I often hear that “the odds of finding [that phrase] in the bible, using ELS, are too great to be by chance.” Obviously that is an argument from personal incredulity, but I got to thinking, just what *are* the odds of finding something in the bible using ELS?

Let’s set the stage with these requirements:

[ol][li]Specify the language like Hebrew or English and the version, just so we are all on the same page(s)[*]Specify if all spaces and/or punctuations are to be removed or not[*]Allow a starting point for the first character of the search string to be anywhere in the text[*]Allow ELS (Equidistant Letter Spacing, or skip) to be any whole number, and positive or negative[*]The text/search string can be of any length, so that must factor into the equation[*]Ignore case everywhere[*]The search string will be specified in advance, so we aren’t fishing for matches of unspecified characters.[/ol][/li]We will also ignore the actual characters we are searching for, which might bias the outcome. Example: the likelihood of finding “moses” in English text is probably greater than “XQW9”, but let’s ignore that for now. I suspect the formula might have to consider a limited number of possible characters in the search string (like A…Z, 0…9)

We must also assume, for this exercise, that the text block (the “bible”) is of random characters, but of fixed length, once the above provisions are considered. So I want to know what the odds of finding a text string X in large text block Y.

There must be a mathematical formula we can use to calculate the odds of that. What is it?

And for extra credit, what are the odds of finding TWO specified text strings within Z distance of each other? Example: If I find “TWIN” starting at character M using skip N, what are the odds of finding “TOWERS” within character range P-Q?