In social psychology, a common finding is that people prefer confirmation-biased information. Although this confirmatory information seeking is commonly treated as an error in judgment, we note that biased sources of information can sometimes be more useful than more accurate sources. Such confirmatory sources will only advise someone to deviate from the policy they think is most useful when these sources are sure taking alternative action is correct. For this reason, these sources can allow people to avoid particularly costly errors. Avoiding such costly errors can sometimes be worth the price of inaccurate beliefs, even though these beliefs lead to more errors in total. In two studies, we find initial support for this idea. Within a Partially Observable Markov Decision process, we show that participants prefer optimistically-biased information when they would otherwise miss out on a particularly large reward, and pessimistically-biased information when they would otherwise face particularly strong punishment.