# 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?

## closed as off-topic by elias, w l, Glorfindel, feelinferrety, ChowzenNov 9 '18 at 20:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – elias, w l, Glorfindel, feelinferrety, Chowzen
If this question can be reworded to fit the rules in the help center, please edit the question.

• Dice is plural -- one die, two dice. – Glen_b Sep 3 '17 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). – Klaws Sep 3 '17 at 9:23
• You should document the source of this puzzle.   Don’t do it in a comment; edit your question. – Peregrine Rook Sep 5 '17 at 4:23

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