Develops an analogy between foraging for cryptic prey and basic signal detection problems. An optimization model based on this analogy predicts partial preferences for cryptic prey, with the probability of attack varying between 0 and 1 as a function of the relative frequency of prey. Experiments with Parus major show that they respond to unpredictable changes in prey relative frequency by adjusting their probabilities of attack in the predicted directions, but the responses lag behind. The birds' behaviour is most appropriate to long-term average conditions (over a span of hours, extending into the preceding day. -from Authors