It doesn't get much simpler than this; the only mini-game in the first game, and one of the first mini-games in videogaming. There isn't a real name, but one of the senile men call it "Money-Making Game", since it usually works in their favor. There's nothing to it, but there is a little trick that can net someone lots of rupies in the first quest. How simple is it? Almost as simple and boring as those "guess the number" programs made by amateur programmers.
How to play
Upon entering the room, a senile man commands you to play "Money-Making Game!" In order to do so, you place 10 rupies in one of three slots. After you do so, you gain or lose a certain amount of rupies (you can't go below 0 rupies, fortunately). I'm not exactly sure about the probabilities, but the gain/loss usually breaks down to the following (-10 rupies to find out what you really get)
-40 - Happens sporadically, but often enough to frustrate any frequent player
-10 - Lose 10 more rupies, most common
+20 - Gain 20 rupies, for a net gain of 10 rupies
+50 - Gain 50 rupies, for a net gain of 40 rupies
Tricks
There is no strategy to this game, but there is a way to cheat it in the first quest. In the first quest, a MMG cave is only one screen left from your starting point on the overworld. Use the bombs about 5 or 6 squares from the right of the screen, and the passage will appear. Once inside, play normally. If you lose rupies, restart the game using the second controller (while on the map screen, push up and A), and choose to retry. If you gain rupies, choose to save your progress. Eventually, you'll be able to fill up. I personally don't use this method, and I just kill bad guys while getting to where I want to go.
