Animals compete in contests over limited resources, and contestants with greater fighting ability, or resource holding potential (RHP), typically win contests. Contest strategies have evolved to balance contest costs with the benefit of winning resources. Sometimes, contestants decide to leave by estimating their opponent’s relative RHP . This strategy (mutual assessment) is cost-effective because it allows weaker opponents to leave contests against formidable opponents before accruing higher costs. However, acquiring reliable information can be costly. Here, we showed that in snapping shrimp contests, contestants assessed relative RHP quickly and costeffectively by assessing their opponent’s recent contest success. By staging 26 contests between randomly matched individuals and 24 contests between RHPmatched individuals, we determined that snapping shrimp assessed their opponent’s RHP during initial contest phases but no longer assessed relative RHP during escalated phases. Then, after staging 24 contests between individuals with contest experience the day prior, we found that snapping shrimp integrated RHP and recent contest success to make contest decisions. This strategy facilitated fast and accurate judgments when the recent winner was also larger but often resulted in the larger individual retreating when facing a small recent winner. Notably, these systematic biases were corrected when RHP differences were stark. Taken together, our findings demonstrate that by assessing recent contest success early in a contest, snapping shrimp can avoid risky contests. Furthermore, by integrating recent contest success with direct observations of RHP, contestants avoid losing contests prematurely. Similar assessment strategies may be widespread, because they circumvent risky contests while minimizing premature defeats from weaker recent winners.