Algorithms are currently used to assist in a wide array of health care decisions. Despite the general utility of these health care algorithms, there is growing recognition that they may lead to unintended racially discriminatory practices, raising concerns about the potential for algorithmic bias. An intuitive precaution against such bias is to remove race and ethnicity information as an input to health care algorithms, mimicking the idea of "race-blind" decisions. However, we argue that this approach is misguided. Knowledge, not ignorance, of race and ethnicity is necessary to combat algorithmic bias. When race and ethnicity are observed, many methodological approaches can be used to enforce equitable algorithmic performance. When race and ethnicity information is unavailable, which is often the case, imputing them can expand opportunities to not only identify and assess algorithmic bias but also combat it in both clinical and nonclinical settings. A valid imputation method, such as Bayesian Improved Surname Geocoding, can be applied to standard data collected by public and private payers and provider entities. We describe two applications in which imputation of race and ethnicity can help mitigate potential algorithmic biases: equitable disease screening algorithms using machine learning and equitable pay-for-performance incentives.