Algorithm:

 Determine N
 Set Head = 0 

 LOOP from i=0 to N
     Generate a random number R 
     from a uniform distribution
     Check IF R<0.5 THEN 
        Increment Head by 1
     END IF
 END LOOP 

 OUTPUT N, Head, Head/N

Output:

     N             Head      Head/N
-------------    --------  ---------
           10           4  0.4000000
          100          41  0.4100000
        1,000         466  0.4660000
       10,000        5059  0.5059000
      100,000       49942  0.4994200
    1,000,000      500351  0.5003510
   10,000,000     4998906  0.4998906
  100,000,000    50006417  0.5000641
1,000,000,000   500008369  0.5000084