Your best friend is at a game show and he has just answered the final question to win the grand prize. For the prize he is shown two envelopes, each of which has some money inside (more than zero). The host informs him that one envelope contains twice the amount of money contained in the other envelope. He is asked to choose one of the envelopes. The envelope your friend chooses is opened and it contains a cheque for Rs. 1 crore (Rs. 10 million).
The host then tells your friend that he can choose to pay Rs. 5 lacs (Rs. 0.5 million) to get the option to exchange the envelope he picked with the unopened envelope. Your friend thinks that the other envelope will either have Rs. 2 crore (Rs. 20 million) or Rs. 50 lacs (Rs. 5 million) and he starts doing calculations on probability and expected values, but he is thoroughly confused. He uses the "Phone-a-friend" facility to call you up as you are the mathematics wizard. What should you advise your friend to do? Please provide complete explanation with your answer.