Dr. Pepper-
I’m afraid I’m totally stumped.
I tried to Google various things to help, including the constant you referenced, but no luck.
The factors I can think of are width of the table, width of the lines, width and length of the pencil, spacing between the lines, and the probability of the angle between the pencil and the lines.
Why don’t you repost it here? Maybe some of the sharp new folks can solve it.