You can see it in another way.
If you pick the girl you want with R-medals, there is no chance to get her with the random ticket. That's okay.
If you use the ticket first, there is a really tiny small chance to get the girl you want and keep the R-medals for another later girl.
Even if the chances are close to zero, it's better to use random ticket and then R-medals or choose ticket.
On a less shiny and colorful tone, we have a winner guys:
http://img110.xooimage.com/files/2/f...al-54f223c.jpg
And you know the worste in that story? I saw it comes. Just when I saw Mint got her Character Quest.
I bless the day I came in our DMM paradise.