Winners in a game

There is a new game in which 3 person play each other and only one wins. If 81 person participated in the tournament give a quick reply that how many matches will be played to decide the winner.
Answer:

Its logarithmic, 
   27   27  27  
   |    |   |   
   9    9   9 = 27   
   |    |   | +  
   3    3   3 = 9  
   |    |   | +
   1    1   1 = 3
              +
                1
-------------------
i=3
∑ i         = 81
i=0
-------------------

   

    \   /    \  /
      9       9
       \     /