The position on the circle is given in units of one circumference and is measured along the circumference. Therefore if the distance between two points is more than one half, its complement is taken. The distance along the arc must be under 1/6 circumference for the chord distance to be less than one radius.

DefDbl A-Z

Dim crlf$, ptpos(3)

Function mform$(x, t$)

  a$ = Format$(x, t$)

  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$

  mform$ = a$

End Function

Private Sub Form_Load()

 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"

 Text1.Text = ""

 crlf$ = Chr(13) + Chr(10)

 Form1.Visible = True

 DoEvents

 

 For trial = 1 To 12000

   For pt = 1 To 3

     ptpos(pt) = Rnd(1)

   Next pt

   good = 1

   For pt1 = 1 To 2

     For pt2 = pt1 + 1 To 3

       dist = Abs(ptpos(pt1) - ptpos(pt2))

       If dist > 0.5 Then dist = 1 - dist

       If dist > 1 / 6 Then good = 0: Exit For

     Next

   Next

   If good Then goodct = goodct + 1

   If trial Mod 120 = 0 Then

     Text1.Text = Text1.Text & mform(goodct, "#######") & mform(trial, "########") & mform(goodct / trial, "##0.000000") & mform(trial / goodct, "###.0000") & crlf

     DoEvents

     Randomize Timer

   End If

 Next

 

 

 Text1.Text = Text1.Text & crlf & "done"

End Sub

It finds, in one run:

 939   12000  0.078250 12.7796

 

That is, the condition held in 939 out of 12,000 trials or 0.07825 of the time, or 1/12.7796.

Another run of the program:

1018   12000  0.084833 11.7878

and another:

998   12000  0.083167 12.0240