# Probability matching

The optimal Bayesian decision strategy (to maximize the number of correct predictions, see Duda, Hart & Stork (2001)) in such a case is to always predict "positive" (i.e., predict the majority category in the absence of other information), which has 60% chance of winning rather than matching which has 52% of winning (where p is the probability of positive realization, the result of matching would be ${\displaystyle p^{2}+(1-p)^{2}}$, here ${\displaystyle .6\times .6+.4\times .4}$). The probability-matching strategy is of psychological interest because it is frequently employed by human subjects in decision and classification studies (where it may be related to Thompson sampling).