%odd.m/created by PJNahin for "Duelling Idiots"(7/1/98)
%This m-file simulates 1,000 games of odd-person-out, for N people as
%defined by the user, with each person flipping a fair coin. The elements 
%of the row vector duration are the number of games of length i, i.e.,
%duration(i)=# of games that require i flips to complete, where i=1,2,3...
%
%
duration=zeros(1,50);         %initialize to zero the number of games
                              %that have durations from 1 to 50 flips
N=input('Enter number of people playing the game:');
rand('state',100*sum(clock))  %set new seed for the random number
                              %generator
for game=1:1000               %simulate 1,000 games
   gameover=0;                %gameover=1 is the flag that the
                              %current game is done
   flip=1;                    %initialize duration of current game
  while gameover==0           %keep playing current game
   s=0;                       %initialize number of heads before
                              %each flipping of N coins
   for n=1:N                  %flip a fair coin for each of the N
      coin=rand;              %people, and increment s by 1 for
      if coin<1/2             %each head
         s=s+1;
      end
   end
      if s==1 | s==N-1        %is there an odd-person-out?
         gameover=1;          %yes, set game-over flag
      else
         flip=flip+1;         %no, so flip again
      end                     %check while statement for end of game
   end
      duration(flip)=duration(flip)+1; %game is over, up-date duration vector
   end                        %play new game
   average=0;
   for i=1:length(duration)
      average=average+i*duration(i);
   end
average=average/1000;
disp(['The average number of flips/game for ',num2str(N),' players is ',num2str(average)])
bar(duration)                 %plot a bar graph of duration vector 
title('Fig.9.1-Relative Frequency of the Duration of Odd-Person-Out')
xlabel('duration of games, in units of flips')
ylabel('number of games')