This paper tests whether logically equivalent risk formats can lead to different health state utilities elicited by means of the traditional standard gamble (SG) method and a modified version of the method that we call ``double lottery.'' We compare utilities for health states elicited when probabilities are framed in terms of frequencies with respect to 100 people in the population (i.e., X out of 100 who follow a medical treatment will die) with SG utilities elicited for frequencies with respect to 1,000 people in the population (i.e., Y out of 1,000 who follow a medical treatment will die). We found that people accepted a lower risk of death when success and failure probabilities were framed as frequencies type ``Y deaths out of 1,000'' rather than as frequencies type ``X deaths out of 100'' and hence the utilities for health outcomes were higher when the denominator was 1000 than when it was 100. This framing effect, known as Ratio Bias, may have important consequences in resource allocation decisions.