# The Effect of Sample Size and Cognitive Strategy on Probability Estimation Bias

Probability estimation is an essential cognitive function in perception, motor control, and decision making. Many studies have shown that when making decisions in a stochastic operant conditioning task, people and animals behave as if they underestimatethe probability of rare events. It is commonly assumed that this behavior is a natural consequence of estimating a probability from a small sample, also known as sampling bias. The objective of this paper is to challenge this common lore. We show that in fact, probabilities estimated from a small sample can lead to behaviors that will be interpreted as underestimatingor as overestimating the probability of rare events, depending on the cognitive strategy used. Moreover, this sampling bias hypothesis makes an implausible prediction that minute differences in the values of the sample size or the underlying probability will determine whether rare events will be underweighted or overweighed. We discuss the implications of this sensitivity for the design and interpretation of experiments. Finally, we propose an alternative sequential learning model with a resetting of initial conditions for probability estimation and show that this model predicts the experimentally-observed robust underweighting of rare events.