# Doorgame

%Author:minster
%————————————————————
% A prize is hidden behind one of three doors: 1, 2, or 3.
% The user guesses which door. Computer then tells him
% another door that the prize is NOT behind and offers to
% let him change his guess. User decides whether or not
% to change and computer then tells him whether or not he
% wins.
%
% Play this game many times with each strategy and count
% number of wins / number of times played to see which
% strategy is better.
%————————————————————

% Put prize behind one of the doors (i=1,2,3), with equal
% probability 1/3 for each.

%Enjoy

x=rand;
if x < 1/3, i=1; end; if x >= 1/3 & x < 2/3, i=2; end; if x >= 2/3, i=3; end;

% Ask user to pick a door (j).

j = input(‘ Pick a door (1,2,3): ‘);

% Decide which door to tell him it is NOT behind.
% If he guessed wrong, tell him the other wrong door;
% if he guessed right, tell him one of the other two, with
% equal probability.

if j~=i, % Guess is wrong.
if j~=1 & i~=1, noti = 1; end;
if j~=2 & i~=2, noti = 2; end;
if j~=3 & i~=3, noti = 3; end;
else % Guess is right.
if j==1, noti1 = 2; noti2 = 3; end;
if j==2, noti1 = 1; noti2 = 3; end;
if j==3, noti1 = 1; noti2 = 2; end;
y=rand;
if y < .5, noti=noti1; end; if y >= .5, noti=noti2; end;
end;

fprintf(‘ Prize is not behind door number %i’, noti)

% Give user the opportunity to change his guess.

yesno = input(‘ Do you want to change doors? (yes=1, no=0) ‘);

if yesno==1, % Change to the door that he
if j~=1 & noti~=1, newj=1; end; % did not guess and that you
if j~=2 & noti~=2, newj=2; end; % did not tell him does not
if j~=3 & noti~=3, newj=3; end; % contain the prize.
else
newj = j; % Stick with original guess.
end;

% Print result.

if i==newj,
fprintf(‘ You win. Prize is behind door %i \n’, i)
else
fprintf(‘ Sorry, you lose. Prize is behind door %i \n’, i)
end;