% 
% Written by:
% -- 
% John L. Weatherwax                2006-12-31
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; 
close all; 

randn('seed',0); 
rand('seed',0); 

N = 10000; 
                  % index:   1  ,   2  ,   3  ,   4  ,   5 
n_i = zeros(1,5); % holds n_{15},n_{16},n_{17},n_{18},n_{19} 
for ii=1:N,

  x = 0; 
  while( 1 )
    roll = randi(6);
    if( roll==6 )
      x = 0;
    else
      x = x + roll;
    end
    if x>=15
      break;
    end
  end

  spot = x - 15 + 1;
  n_i(spot) = n_i(spot) + 1;
  
end

disp('probabilities of each n_i are');
n_i / N 
disp('expectation of winning are');
dot( 15:19, n_i/N )