I agree with Sol. Earlier, I calculated (post #400) that a clueless Monty that opens a random door that is not the player's pick gives equal chances of winning the game regardless of keep or switch. I thought this was fairly obvious, but since it appears that some people won't be convinced without a program and I've a few minutes to spare, here's an ugly MATLAB script:
Code:
trials = 2e5; cars = 0; valid_trials = 0; for n=1:trials
car = 1+floor(3*rand); player = 1+floor(3*rand); %
monty = player; % Monty guesses until his pick
while ( monty == player ) % is different from the player's
monty = 1+floor(3*rand); % (equivalent to picking a random
end % door that is not the player's)
if ( monty ~= car ) % Car not revealed
valid_trials = valid_trials+1;
% Player switches to the other door
for k=1:3 if (k~=player & k~=monty) guess2 = k; end; end
if ( guess2 == car ) cars = cars+1; end
end
end; valid_trials, cars/valid_trials
The result was 133172 trials in which Monty did not accidentally reveal the car, 49.82% of the player won by switching.
