% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

format rat;

% compute the probabilities of rolling two die that sum to "i":
% (note "i" starts at *two*) 
num = [ 1:6 5:-1:1 ]; 
den = 36; 
p_i = num/den;

% compute the probabilities that we "keep" going (don't roll another initial sum 
% of "i" and don't roll a sum of seven:
% 
p_kg = 1 - p_i - 1/6; 

% compute the probabilities that we win when the initial roll is "i"
% 
p_w = p_i .* ( 1 ./ (1-p_kg) ); 
p_w(1:2) = 0; 
p_w(6) = 1; p_w(10) = 1; p_w(11) = 0; 

% the total probability that we win is then given by:
%
fprintf('the total probability that we win at craps is then given by...\n'); 
dot( p_i, p_w )