ThreeWayDualProbability.m

%Author:Alex Dytso
%Date: 02/18/2013
%Description: This code simulates a dual between 3 players. Where first has a probability of hiting 30% 
%second man has probability of hiting 50%
%third man has probability of hiting 100%
%This porgram similates possible outcomes for two different strategies.
%First strategy all players shoot
%Second strategy player 1 missus his first shot on purpose.
%This code will show that suprisingly the second strategy is much better
%for player 1


clc, clear all, clf
t=input('how many times do you want to run the simulation \n')
rounds=0;
count=[0,0,0];

%First Strategy

while rounds<t % number of itereation of the simulation

 % if alive alivei=1 if dead alivei=0
alive1=1; 
alive2=1;
alive3=1;% all alive

while (alive1==1 && alive2==1) ||( alive1==1 && alive3==1) || (alive2==1 && alive3==1) %simulation runs while at least 2 is alive
  
 %Player 1 makes a shot. By problems statement his probability of success
 %is 30% so the following is how he shoots
   
   
 if alive1==1 %player 1 must be alive to shoot
      s1=floor(3*rand)+1;% makes a shot. If s1=1 or 2 it's miss if s1=3 target is shoot
      
   if s1==3 && alive3==1 % Player 1 shoots at Player 3 first 
      alive3=0; %shoots player 
   elseif s1==3 && alive2==1 % if plyer 3 is dead, shoots player 2
      alive2=0;
   end
 end
   
    
  if alive2==1 %% if second player  is alive
      s2=floor(2*rand)+1; %makes a shot. If s1=1 it's miss if s1=2 target is shoot
      
     if s2==2 && alive3==1 %Player 2 shoots at Player 3 first 
         alive3=0;
     elseif s2==2 && alive1==1
         alive1=0;
     end
  end
  
  if alive3==1 %% third player is alive
      %Player 3 never misses
      if alive2==1 %if player 2 is alive shoots player 2
          alive2=0;
      else
          alive1=0; %else shoots player 2
      end
  end
end
 rounds=rounds+1; %count of simulation rounds
 %counting frequencey of wins
 count(1)=count(1)+alive1; 
  count(2)=count(2)+alive2;
   count(3)=count(3)+alive3;
end
subplot(1,2,1)
pie(count)
title('First Strategy')
 count
 
 
 %Second strategy. Fisrt Player misses on purpose on the first shot.
 %As you will see such a strategy improves his odds
 
 rounds=0;
count=[0,0,0];

%First Strategy

while rounds<t % number of itereation of the simulation

 % if alive alivei=1 if dead alivei=0
alive1=1; 
alive2=1;
alive3=1;% all alive

d=0;
while (alive1==1 && alive2==1) ||( alive1==1 && alive3==1) || (alive2==1 && alive3==1) %simulation runs while at least 2 is alive
  
 %Player 1 makes a shot. By problems statement his probability of success
 %is 30% so the following is how he shoots
   
   if d==1 %this skips the first round
       
 if alive1==1 %player 1 must be alive to shoot
      s1=floor(3*rand)+1;% makes a shot. If s1=1 or 2 it's miss if s1=3 target is shoot
      
   if s1==3 && alive3==1 % Player 1 shoots at Player 3 first 
      alive3=0; %shoots player 
   elseif s1==3 && alive2==1 % if plyer 3 is dead, shoots player 2
      alive2=0;
   end
 end
 
   end
    
   d=1;
    
  if alive2==1 %% if second player  is alive
      s2=floor(2*rand)+1; %makes a shot. If s1=1 it's miss if s1=2 target is shoot
      
     if s2==2 && alive3==1 %Player 2 shoots at Player 3 first 
         alive3=0;
     elseif s2==2 && alive1==1
         alive1=0;
     end
  end
  
  if alive3==1 %% third player is alive
      %Player 3 never misses
      if alive2==1 %if player 2 is alive shoots player 2
          alive2=0;
      else
          alive1=0; %else shoots player 2
      end
  end
end
d=0;
 rounds=rounds+1; %count of simulation rounds
 %counting frequencey of wins
 count(1)=count(1)+alive1; 
  count(2)=count(2)+alive2;
   count(3)=count(3)+alive3;
end
subplot(1,2,2)
pie(count)
title('Second Strategy')
legend('Player1-30% Accur.','Player2-50% Accur.','Player3-100% Accur.')

 count