Figure 1

Comparison between (a) a fully rational decision maker and (b) a decision maker with random beliefs. There are two biased coins. The probability of throwing the first coin is $\frac{1}{4}$, the probability of throwing the second coin is $\frac{3}{4}$. The first coin has a probability of $\frac{1}{4}$ for the outcome Head and the second coin has a probability of $\frac{3}{4}$ for Head. The decision-maker has to predict the most likely outcome. A correct guess is rewarded with $1, an incorrect guess yields $0.