Coin versus die

Question

A coin is less informative than a $6$-sided die, but by how many times?

Solution

The entropy of a fair coin is $H_{\text{moneta}} = 1$ bit; that of a fair die is $H_{\text{dado}} = \log_2 6 \approx 2{,}585$ bits. The ratio is $\frac{H_{\text{dado}}}{H_{\text{moneta}}} = \frac{\log_2 6}{1} = \log_2 6 \approx \boxed{2{,}585}.$ A die roll therefore carries about $2{,}6$ times more information than a coin toss.

Links

Topics: Probability distributions
Concepts: Entropy
Skills: Computing
Exercise type: Expression evaluation