# define procedure to generate random integer from choices {1, 2, 3}
four := rand(1..4);
# define procedure to generate random integer from choices {1, 2, 3}
three := rand(1..3):

# define procedure to generate random integer from choices {1, 2}
two := rand(1..2):

# set the number of games in the simulation
num_games := 1000;


montyhall := proc(num_games)
# initialize counters
win_via_keep := 0:
win_via_switch := 0:

##########  BEGIN LOOP  ##########

for game_count from 1 to num_games do

  # shuffle one prize and two goats behind doors 1, 2 and 3 
  prize := three();

  # contestant makes first choice of three doors
  c1 := three();

  # host reveals a goat behind one of the doors NOT chosen
  if c1 = prize
    then
      # select one of other two goats at random
      choices := {1, 2, 3} minus {prize};
      host := choices[two()];
    else
      # must select the other goat
      choices := {1, 2, 3} minus {prize, c1};
      host := choices;
    fi;

  # contestant elects to switch
  choices := {1, 2, 3} minus {c1, host};
  c2 := choices;

  # tabulate wins according to strategy
  if c1 = prize
    then
      win_via_keep := win_via_keep + 1;
    else
      win_via_switch := win_via_switch + 1;
    fi;

##########  END LOOP  ##########

od:

# compute empirical probabilities
prob_win_via_keep := evalf(win_via_keep/num_games);
prob_win_via_switch := evalf(win_via_switch/num_games);
print('prob_win_via_keep',prob_win_via_keep,' prob_win_via_switch',prob_win_via_switch);
# total probabilities will not be one
#total_prob := prob_win_via_keep + prob_win_via_switch;
end;