%car-goat-goat
%Matthew Miller
%10/8/2021

%select number of iterations
loopLimit=1e7;

%create variables 
%After seeing the Omnicient Host open a door, the contestant should stay
OHCorrectToStay = 0;

%After seeing the Omnicient Host open a door, the contestant should switch
OHCorrectToSwitch = 0;

%The contestant guessed right before seeing the hosts door
guessRight = 0;

%The contestant guessed right at first
guessWrong = 0;

for n=1:loopLimit
    
%random number to assign goats and car behind doors
a = rand(1);
  
%random number to assign contestant guesses
b = rand(1);
    
%random number to assign host guesses
c = rand(1);

%cargoatgoat assignment       
if a < 1/3
    doors = ([1 0 0]);
elseif a > 1/3 && a < 2/3
    doors = ([0 1 0]);
elseif a > 2/3
    doors = ([0 0 1]);
end

%Constestant with Omnicient Host (OHContestant) guesses door
if b < 1/3
    OHContestant = 1;
elseif b > 1/3 && b < 2/3
    OHContestant = 2;
elseif b > 2/3
    OHContestant = 3;
end

%before the host opens a door, is the contestant right?
if (doors(OHContestant) == 1)
    guessRight = guessRight +1;
else
    guessWrong = guessWrong +1;
end

%the door the car is behind
car = find(doors);

%omnicient host (OHost) selecting a door with a goat
%first 6 cases, the contestant is wrong
if OHContestant == 1 && car == 2
    OHost = 3;
elseif OHContestant == 1 && car == 3
    OHost = 2;
elseif OHContestant == 2 && car == 1
    OHost = 3;
elseif OHContestant == 2 && car == 3
    OHost = 1;
elseif OHContestant == 3 && car == 1
    OHost = 2;
elseif OHContestant == 3 && car == 2
    OHost = 1;
    
    
%next cases, the contestant is right
%now the host has a choice of which goat to reveal
%recall, because the contestant guessed correctly, both other doors have
%goats, so the host can reveal either one

%these if-then statements are nested purely for ease of reading
elseif (doors(OHContestant) == 1)
    if (OHContestant==1) && c < 0.5
        OHost = 2;
    else
        OHost = 3;
    end
elseif (doors(OHContestant) == 2)
    if (OHContestant==1) && c < 0.5
        OHost = 1;
    else
        OHost = 3;
    end
 elseif (doors(OHContestant) == 3)
    if (OHContestant==1) && c < 0.5
        OHost = 1;
    else
        OHost = 2;
    end
end

if (doors(OHContestant) ==0)
    OHCorrectToSwitch = OHCorrectToSwitch +1;
else
    OHCorrectToStay = OHCorrectToStay +1;
end
    
end

%These exist for debugging and personal clarity
display('Correct guess at first');
guessRight

display('Wrong guess at first');
guessWrong


display('Should keep the original guess');
OHCorrectToStay/loopLimit

display('Should switch guesses');
OHCorrectToSwitch/loopLimit