Rolling a dice - Expectation Question [closed]

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?

• Dice is plural -- one die, two dice. Commented Sep 3, 2017 at 2:12
• I interpreted "play again" not as "re-roll", but as "pay again to re-roll". The question could be a bit more precise...unless the task is to figure out the meaning of the question (which is, in that case, possible since the correct answer to part 2 is given). Commented Sep 3, 2017 at 9:23
• You should document the source of this puzzle.   Don’t do it in a comment; edit your question. Commented Sep 5, 2017 at 4:23

$(10*1/3) + (5.5*2/3)=7$