function [ sample_path ] = blackjack_winnings_sample_path(f, V_0,vs,ps, Nts) 
% 
% 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.
% 
%-----

sample_path    = zeros(1,Nts+1); 
sample_path(1) = V_0;
for ii=2:Nts+1, 
  random_index    = find( mnrnd( 1, ps, 1 ) );
  random_draw     = vs( random_index );
  pct_win         = (1+f*random_draw);
  sample_path(ii) = sample_path(ii-1) * pct_win;
end