The four doors problem
A new game show uses rules similar to those of the three doors but there are four doors, and the host explains: ‘First you will point to one of the doors, and then I will open one of the other doors, guaranteeing to choose a non-winner. Then you decide whether to stick with your original pick or switch to one of the remaining doors. Then I will open another non-winner (but never the current pick). You will then make your final decision by sticking with the door picked on the previous decision or by switching to the only other remaining door.' What is the optimal strategy? Should you switch on the first opportunity? Should you switch on the second opportunity?