Quite a lots of pictures to explain, so I'll hide in spoiler then.
The ticket you got is used to play Sugoroku (board game) located here
In phase 1, there're three difficulty, clear each to get event girl, exclusive skill and item slot x2, and limit break gem x10.
This is the board game pic
roll a die to proceed, each time consumes the tickets you have. You'll get coins, rose, and treasure box just by passing them. (don't have to land on square to get) Only automaton, power up/down, heart (recover hp), trap, and the likes will take effect if you land on the square.
Board game can be played again to farm rose and items.
Rose you got from playing Sugoroku can be traded for items here.