Here is a 'lunch break' problem from a rather old publication.
Devise one set of rules for a dice game, where any number of players and one representative of the bank (mandatory), with one die each, can be playing, and where the players and the representative can roll their respective dice any number of times. The rules have to be such that the game is attractive to all the players (i.e. the players feel like there is a good chance of them winning), but that the bank would generate a good profit in the long run. In your game, how much would it cost for a player to play the game, and how much would the bank pay out in the case of a win for one player? What are the odds of a player winning, and what is the ‘house edge’?
This seems rather open-ended to me. Can anyone think of some interesting and profitable rules?