I heard / read / acquired this puzzle from somewhere:
Roll a die, win $2\times$ the value of the face if it is an even number, or win $1\times$ the value of the face if it is an odd number.
How much do you need to charge to play the game?
Then if you are given the opportunity to make a decision and play again, you will only be paid by the result of the last rolling.
Again, how much do you need to charge to play the game?
I understand the first part (pretty easy) and I got 5.5.
I don't really get the second part. According to the puzzle’s source, the correct answer is 7. Can anyone please go through the steps to getting 7 in detail please?