According to the Shafi'i school, dice are Haram. That includes Monopoly, and includes games where there is no gambling. It is not the result of being too legalistic. The Islamic law frequently distinguishes between the "reason" for a prohibition and the prohibition itself. In these cases, if the reason for the prohibition is not there, then the prohibited thing is not prohibited. If dice were such a case, then they would be always Haram.