This app was mentioned in 2 comments, with an average of 5.50 upvotes
The big question here is where can i get one.
Edit: Some quick Googling
Neat Wiki info on them, simulations at the bottom - also lists games based on them.
Edit 2:
Binomial probability demonstrator (source, bigger generator from muzeum) The Hexstat is a modern version of the Galton Box invented by Sir Francis Galton(1894) to demonstrate the De Moivre-Laplace Central Limit Theorem showing how random processes gather around the mean. In this case the binomial distribution seen here would approximate the normal distribution if the number of final bins were greatly increased. In addition the number of balls in each bin can be predicted by Pascal's triangle.
256 balls fall down 7 levels of branching paths and always end up in the same distribution. Each ball has a 50/50 chance of following each branch such that the balls are distributed at the bottom by the mathematical binomial distribution. This pattern can be observed directly in nuclear magnetic resonance spectra Galton board at Wolfram Alfa, Wiki info, simulations at the bottom - also lists games based on them. An Android and Java simulator, the Plinko game and the Binomial Distribution.