<t>The following strategy should work. It is only the leader that is allowed to switch OFF the left switch and he will do it when he enters the room and it is ON. All the other enters the room and switch the left switch to ON, if they have not done it twice before and of course if it is not already ...

<t>I agree with FV. It is clear that receiving the million by opening on the first run is 1/4. The probability to get the right one by open on the second run is 3/4*1/3=1/4. The probability to get the right one on the third run is 1/4*1/2=1/8. Finally, the probability to get it right on the fourth a...