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<< MC APPLICATIONS >>

Tossing A Die

In tossing a die a 6 can occur one way out of six ways,
hence P=1/6.

Algorithm:

 Determine N
 Set Six = 0 

 LOOP from i=0 to N
     Generate a random number R 
     from a uniform distribution
     Set Dice = 1 + INT(6*R)
     Check if Dice=6 THEN 
       Increment Six by 1
     END IF
 END LOOP 

 OUTPUT N, Six, Six/N

Output:

      N            Six      Six/N
-------------    --------  ---------
           10           3  0.3000000
          100          19  0.1900000
        1,000         186  0.1860000
       10,000        1659  0.1659000
      100,000       16748  0.1674800
    1,000,000      166705  0.1667050
   10,000,000     1667210  0.1667210
  100,000,000    16666290  0.1666629
1,000,000,000   166672853  0.1666728


The computer implementations of the algorithm : die.f90 | die.c