# Generating uniformly random data from skewed input: biased coins, loaded dice, skew correction, and the Von Neumann extractor

In a famous article published 1951 ((Various techniques used in connection with random digits. NIST journal, Applied Math Series, 12:36-38, 1951. This article does not seem to be available online, though it is widely cited. It is reprinted in pages 768-770 of Von Neumann’s collected works, Vol. 5, Pergamon Press 1961)), John Von Neumann presented a way of skew-correcting a stream of random digits so as to ensure that 0s and 1s appeared with equal probability. This article introduces a simple and mentally workable generalization of his technique to random dice, so a loaded die can be used to uniformly draw numbers from the set $$\{1, 2, 3, 4, 5, 6\}$$, with reasonable success.

# The cafeteria paradox: stop using the water dispenser while someone else does!

Most cafeteria water dispensers will let two (sometimes more) people fill a jug at the same time. This article uses simple maths to prove that it’s a waste of time. In other words, two people should never use the same water dispenser at the same time: I call this the cafeteria paradox.