Rewards have important influences on the motor planning of primates and the firing of neurons coding visual information and action. When eye movements to a target are differentially rewarded across locations, primates execute saccades towards the possible target location with the highest expected value, a product of sensory evidence and potentially earned reward (saccade to maximum expected value model, sMEV). Yet, in the natural world eye movements are not directly rewarded. Their role is to gather information to support subsequent rewarded search decisions and actions. Less is known about the effects of decision rewards on saccades. We show that when varying the decision rewards across cued locations following visual search, humans can plan their eye movements to increase decision rewards. Critically, we report a scenario for which five of seven tested humans do not preferentially deploy saccades to the possible target location with the highest reward, a strategy which is optimal when rewarding eye movements. Instead, these humans make saccades towards lower value but clustered locations when this strategy optimizes decision rewards consistent with the preferences of an ideal Bayesian reward searcher that takes into account the visibility of the target across eccentricities. The ideal reward searcher can be approximated with a sMEV model with pooling of rewards from spatially clustered locations. We also find observers with systematic departures from the optimal strategy and inter-observer variability of eye movement plans. These deviations often reflect multiplicity of fixation strategies that lead to near optimal decision rewards but, for some observers, it relates to suboptimal choices in eye movement planning.