Using rolls of many die, we examine the frequency of various patterns of outcomes that are consistent with a given mean. As the number of rolls gets large the most common pattern is given by the distribution that maximised the entropy, and the multiplicity of the distributions is sharply peaked around this value.

To be completed

2 Making probabilities more uniform

To be completed

3 Entropy limits

A closer look at the limits of entropy and what they imply about the underlying probability distribution.