Atlantic City Method For Computing PI

Here's the slowest, most inefficient method known for computing pi:

Choose an arbitrary initial value x (real) and iterate the function

              x  -->   (2-x)/(3-4x)

M times.  Count the number of iterates that fall within a small 
interval around zero.  For example, let N denote the number of 
iterates that fall between -u/2 and +u/2 for some small u.  Then 
the limiting value of the ratio uM/N is pi (for sufficiently 
large M as u goes to zero).  I call this the Atlantic City method 
of computing pi.